Frequency response of sampled-data systems

Glossary for Feedback Control of Dynamic Systems自动控制理论词汇表Chapter 1thermostat n.恒温器predictive control 预测控制power generation plant 发电厂micron n.微米cell phone 移动电话jumbo jet 巨型喷气式客机block diagram 方框图actuator 执行机构process n.过程feedback n.反馈plant n.被控对象mph=mile per houropen-loop 开环closed-loop 闭环throttle n.油门gain n.增益orifice n.孔、小孔controlled variable 被控变量error n.误差incubator n.孵化器flue n.烟道chronicle n.编年史、年代记录conical a.圆锥体的mill wright 技工、造水车工匠inertia n.惯性、惯量oscillate about…在….周围振荡reference input 参考输入prescribed direction 预定的方向actual direction 实际方向flyball n.飞球governor n.控制器、调节器、总督、省长equilibrium n平衡点differencial equation 微分方程characteristicequation 特征方程third-order 三阶polynomial n.多项式state variable 状态变量distortion n.畸变complex variable 复变量methdology n.方法论proportional a. 比例的、成比例的integral a.积分的derivative a.微分的stochastic a.随机的servomechanism n.伺服机构calculus n.微积分ubiquitous a.到处存在的、普遍存在的radar-tracking 雷达跟踪SISO systems 单输入单输出系统Laplace transform 拉普拉斯变换pole n.极点zero n.零点transfer function传递函数trajectory optimization 轨迹优化root locus 根轨迹specifications n.指标、规格、规范discrete-data 离散数据sampled-data 采样数据performance n.性能Chapter 2desired reference variable 期望参考变量prototype n.原型system identification 系统辨识time response 时域响应step input 阶跃输入defer n.推迟、延期vector n.向量、矢量slug n.斯（勒格），质量单位（32.2磅）impart n.赋予、传授、告知heavy line 粗实线dashed line 虚线coordinate n.坐标numerator n.分子denominator n.分母suspension n.悬架、悬挂deflection n.偏移、偏转、偏差displacement n.位移shock absorber 减震器、缓冲器dashpot n.缓冲器bump n. vt.颠簸bounce n. vt.反弹、跳跃moment of inertia 转动惯量、惯性矩attitude n.姿态、姿势antenna n.天线perpendicular n.垂直线 a.垂直的asymmetry a.不对称的torque n.转矩resonant n.谐振、共振damper n.阻尼器prudent a.谨慎的，有远见的，精打细算的anti-alias 抗混频operational amplifer 运算放大器passive circuit 无源电路Kirchhoff’s current law 基尔霍夫电流定律algebraic sum 代数和summer n.加法器integrator n.积分器tesla n.特斯拉(磁通量单位)louderspeaker n.扬声器bobbin线轴，线筒stator n.定子rotor n.转子back emf 反电势maze n.曲径，迷宫specific heat 比热spatially ad.空间地hydraulic a.液压的、水力学的gimbal n.平衡环，万向接头nozzle n.喷嘴grooming n.修饰，美容piston n.活塞porous a.可渗透的，多孔的laminar a.多层的、层流的n.层流turbulent a.湍流的Chapter 3linear time-invariant systems 线性时不变（定常）系统signal flow graph 信号流图simulation n.仿真frequency-response 频率响应superposition n.叠加convolution n.卷积inpulse-response 脉冲响应unit step function 单位阶跃函数root-locus 根轨迹stability properties 稳定性特性principles linear algebra 线性代数原理state variable methods 状态变量法matrix n..矩阵nonlinear n.非线性mathematical mode 数学模型trivial a.琐碎的、不重要的linearize vt.线性化operating point 工作点state-space 状态空间partial differential equations 偏微分方程equilibrium n.平衡点complex frequency variables 复频率变量zero initial conditions 零初始条件steady-state 稳态ramp input 斜坡输入dc gain 直流增益inverse Laplace transform 逆拉氏变换partial fraction expansion 部分分式展开rantional a.有理的residue n.余式unilateral a.单边的convergence n.收敛final-value theorem 终值定理homogeneous differential equation 齐次微分方程ordinary differential equation 常微分方程overall transfer function 总的传递函数“loading” effect 负载效应cascade blocks 方框串联（级联）to reduce 化简eliminating 消去equivalent a.等效的simplification n.化简、简化integrodifferential a.积分-微分的time constant 时间常数imaginary axis 虚轴damping ratio n.阻尼比natural undamped frequency 自然无阻尼频率overdamped a.过阻尼critically damped n.临界阻尼rectangular coordinate 直角坐标oscillatory a.振荡的transient response 瞬态响应overshoot n.超调量delay time 延迟时间peak time 峰值时间rise time 上升时间settling time 调节时间steady state 稳态characteristic equation 特征方程RHP(Right Half-Plane) 右半平面elevator n.飞机升降舵，飞机升降仪，电梯nonminimum-phase 非最小相位diverge v.发散、分歧asymptotically stable 渐进稳定stability n.稳定性absolute stability 绝对稳定性relative stability 相对稳定性stability criterion 稳定性判据equilibrium state 平衡状态product n.乘积coefficient n..系数nagtive feedback 负反馈positive feedback 正反馈unity feedback system 单位负反馈系统reduction n.化简simultaneous a.联立的common factor 公因子expedient a.权宜的，有用的attenuate v.变弱，衰减，变细，变薄，稀释cofactor n.公因子Routh stability criterion 劳斯稳定性判据determinant n. 行列式tune v.调节retune v.再调节pseudorandom-noise 伪随机噪声signal-to-noise ratio 信-噪比Mason Gain Formula 梅森（增益）公式term n.术语signal flow graph 信号流图nodepathenvelope n.包络线dominant root 主导极点Chapter 4steady-state 稳态with respect to 关于….deviation n.偏离steady-state error 稳态误差load torque 负载转矩viscous friction 粘性摩擦repeater n.中继器drift v.漂移fidelity n.准确性，忠实，忠诚parabolic antenna 抛物线天线position error constant. 位置误差常数velocity error constant 速度误差常数robust property 鲁棒性shaft n.轴tachometer n.转速计inductance n.电感sampled v.采样quantized v.量化extrapolate v.预测，推测trapezoid n.梯形，不等边四边形vertices n.顶点order n.阶次，数量级proportional control 比例控制derivative control 微分控制sinusoidal a.正弦parameter n.参数Chapter 5root-locus method 根轨迹法monic a.首一的feedforward a.前向的denominator n.分母numerator n.分子quadratic n.二次项branch n.分支factored a.分解的asymptote vt.渐进n.渐进线division n.除法vantage point 有利地位，观点imaginary part 虚部breakaway point 分离点common denominator 公分母conjugate pairs 共扼对multiplicity n.多重，多数trial and error 凑试（法）spirule n.螺旋尺intersection n.交汇symmetrical a.对称的magnitude condition 幅值条件angle condition 相角条件phase condition 相角条件origin n.起始点terminus n.终点angle of departure 分离角、出发角angle of arrival汇合角、到达角cubic a.三阶的、立方的quartic a.四次的remainder n.留数、余数remainder theorem 留数定理taking the limit 取…极限synthetic division 综合除法dominant root 主导根compensator n.补偿器azimuth n.地位角、地平经度inertial guidance 惯性导航constant term 常数项symmetrical with respect to 关于…对称trial point 试验点terminate vt.终止于first differentiate 一阶微分real parts实部imaginary part 虚部lag compensator 滞后补偿器lead compensator 超前补偿器spill over 溢出，无法容纳autopilot n.自动导航trim v.n.使整齐，微调trim tab 平衡调整片margin n.裕量iteration n.重复、循环、迭代intact a.完好无缺的，原封不动的Chapter 6frequency response 频率响应rendered v.使成为，提供，报答，着色; 执行ratio of the magnitudes 幅值比bandwidth n.带宽resonant peak 谐振峰值low-pass filter低通滤波器sanity n.神智健全，头脑清楚，健全tangent n.正切、切线reciprocal a.互补的，相互的，互惠的phase difference 相角差transport lag 传输延迟irrational factor 非有理因子phase shift 相位移动moduli n.模(复数)poke vt.戳、刺、捅drudgery n.苦工、单调乏味的工作logarithmic coordinate 对数坐标semilog n.半对数decibel n.分贝decade n.十倍量程octave n.八倍频程、八度、八阶asymptotic behavior 渐进行为dotted n.虚线break frequency 转折频率corner frequency 转折频率slope n.斜率20dB/decade 20分贝/十倍频程superimpose vt.迭加polar plot 极坐标图pass function 旁路函数servomotor-amplifier 伺服电机-放大器angular velocity 角速度minimum phase 最小相位tilt angle 倾斜角lateral force 侧面力、横向力perceived velocity 可察觉的速度croseover frequency 穿越频率appendage n.附件、备件Nyquist criterion 奈奎斯特判据Semi-graphical 半图形Nyquist plot 奈奎斯特图Bode diagram 伯德图positive real part 正实部necessary and sufficient condition 充分必要条件left half of the s-plane s平面左半平面formidable a. 可怕的、令人生畏的determinant 行列式pole-zero cancellation 零极点相消rational functions 有理函数quotient n. 商、份额multi-loop control system 多环控制系统encircled vt. 环绕enclosed vt. 包围closed path 闭合路径counterclockwise a.逆时针的clockwise a.顺时针的encirclement n. 环绕enclosure n. 包围contour n.围线，轮廓线argument principle 幅角原理complex variable 复变量single-valued rational function 单值有理函数analytic a.解析的Nyquist path 奈奎斯特路径singularity n.奇异（点、值）semicircle n.半圆artifice n.技巧、技能gain margin 增益裕量phase margin 相角裕量vicinity n.邻近compromise n.折中，妥协trapezoidal a.梯形的iterate v.重复、循环、迭代bracket v.放在括号内，归入一类，包含octave n.八个一组的事物，八度enumerate v.数，点detrimental a.有害的，不利的threshold n.阈值Chapter 8sampling n.采样sample period 采样周期aliasing n.混频，别名inherent a.内在的z transform Z变换radar tracking system 雷达跟踪系统discrete period 离散周期discrete equivalent 离散等效digitization n.数字化recursive a.递归的，循环的difference equation 差分方程sample rate 采样速率sampler 采样器zero-order holder 零阶保持器inverse Z transform 反Z变换、逆Z变换long division 长除法unit circle 单位圆overlap n.重叠rephrase v.重新措辞，改述extrapolate v.预测，推测alleviate v.减轻，使 ... 缓和judicious a.明智的，贤明的，审慎的fictitious a.假想的，虚伪的impulse transfer function 脉冲传递函数piecewise-continuous 分段连续的pseudo-continuous-time 准连续时间Pade approximation Pade 近似Fourier analysis 傅立叶分析modulation n.调制Fourier transform 傅立叶变换spurious a.寄生的、伪的、假的ideal sampler 理想采样器impulse train 脉冲列、脉冲串transcendental a.超自然的、超常的rational function 有理函数closed form 封闭形式degree n.阶denominator n 分母numerator n 分子initial value 初始值identical a.相等的starred a.打星号的impulse response transfer function 脉冲响应传递函数uniformly spaced 均匀分布map into 影射、映射circles of radius 圆弧multiple-sheeted surfaceRiemann surface 黎曼曲面radial ray 射线by virtue of 借助、凭借、依靠….（的力量）logarithmic spiral 对数螺旋intersection n.相交power series 幂级数sampling instant 采样时刻natural logarithm 自然对数rationalizing 有理化cascading property 串联（级联）特性attenuation factor 衰减因子warp vt.使弯曲、使变形tune vt.调节、调整cross-hatched vt.用交叉线画出（图画上）阴影performance specification 性能指标trial-and-error approach 试凑法bilinear n.双线性Chapter 9equilibrium point 平衡点neighborhood n.邻域saturate n.饱和robotic n.机器人学heuristic a.启发式的，搜索式的sinusoidal a.正弦的sinusoid n.正弦harmonic a.谐波的describing-function 描述函数static nonlinearity 静态非线性dynamic nonlinearity. 动态非线性periodic response 周期响应phase-plane 相平面catastrophe n.灾难、浩劫shaky a.不稳定的，不可靠的scalar function 标量函数Liapunov function 李亚普诺夫函数linearization n.线性化inverse nonlinearity 可逆非线性perturbation n.摄动operating point 工作点eigenvalue n.特征值bearing n.轴承levitate v.浮动，使漂浮，使悬浮turbo n.汽轮机deviation n.偏差rigid link 刚性连接regime n.情形，体制dead-zone 死区viscous friction 粘性摩擦coulomb friction 库仑摩擦relay n.继电（特性）limit cycle 极限环deflect v.使偏，使歪windup n.终结，结束akin a.同类的，相似的odd function 奇函数backlash n.齿轮间隙magnetic hysteresis 磁滞coincident a.重合的，一致的on/off system 通断（控制）系统superposition n. 迭加sub-harmonic a.谐波的magnetic flux 磁通iron-cored coil 铁芯线圈stiction n. 静摩擦力autonomous a.自治的hypersphere n. 超球stability in the sense of Liapunov 李亚普诺夫意义下的稳定性asymptotically stable 渐进稳定monotonically stable 单调稳定origin n. 原点globally stable 全局稳定locally stable 局部稳定electronic oscillator 电子谐振器Van der Pol’s differential equation 范德波尔微分方程nonsinusoidal waveform 非正弦波形rated voltage 额定电压phase variable 相变量phase portrait 相图perpendicular a. 垂直的、正交的、成直角的Taylor series 泰勒级数increment n.增量Euler method 欧拉法singular point 奇异点。

频率响应FRA测试中的噪声分析频率响应FRA是一种检测电力变压器绕组变形的测试方式，与其它现场检测方式相类似，频率响应FRA方式也容易受到现场噪声的影响。

噪声会模糊干扰一些重要的测试信息，这将会影响到对频率响应FRA结果的评估。

因此，了解噪声的来源、影响和抑制方式是非常必要的。

标签：变压器；FRA测试；噪声1.频率响应FRA方式频率响应FRA 方式用于在变压器发生故障之前，检测出变压器绕组的几何变形。

需要注意的是，本文讨论的FRA方式是扫频式的FRA，即SFRA方式（Sweep Frequency Response Analysis ），而非过去所用的脉冲式IFRA方式（Impulse Frequency Response Analysis）。

这是因为，相较于低压脉冲方式（IFRA），扫频方式（SFRA）在现场具有更好的重复性，因此，目前使用越来越广泛。

从图一可以看出，在变压器线圈的一端输入一个变频的正弦电压信号“U”，并从此点测量参考信号“U1”，与此同时，测量线圈的另一端的输出或响应信号“U2”。

这样，便可计算出传递函数H（f），表达式为（1）。

这意味着H（f）仅取决于频率响应FRA仪器的测量阻抗Rm和变压器阻抗Ztra。

图二是常见的频率响应FRA测试波形，对于大多数的测试而言，都是对频率响应的幅值图进行分析与评估。

不过，频率响应的相位图也具有一定的参考价值，图二的左下部分为相位图。

幅值的计算依据公式（2），相位的计算依据公式（3）。

2.FRA方式中的噪声介绍噪声定义为有害的干扰信号，它可能被添加在一个想获得的有用信号上。

噪声往往会模糊有用信号的信息内容，因此，噪声的检测与降低是很有必要的。

与任何其它的电气诊断方式一样，在现场，频率响应FRA的测试结果也会受到噪声的影响。

了解噪声的来源、影响与抑制方式是非常重要的，特别是比较不同厂家制造的频率响应FRA仪器时。

本文分析了频率响应FRA仪器的技术规格和噪声抑制能力的关系，并通过在电力变压器上进行的频率响应FRA测试实例来说明。

#include <c8051f000.h>#include <intrins.h>//----------------------------------------------------------------------------- #define uchar unsigned char#define uint unsigned int#define BAUDRATE#define SYSCLKvoid SYSCLK_Init (void);void delaynus(unsigned int q) ;void PORT_Init (void);void SPI0_Init (void);void LCD_Init(void);void SendSPIByte(unsigned char ch);void delaynms (unsigned int j);void writecom(unsigned char com);void writedata(unsigned char d);void writechar(unsigned char ua);void Write_COM(uchar ins);void lcden(datad);void LCD_set_xy( unsigned char x, unsigned char y );void LCD_write_string(unsigned char n);void lcd_key1(void);void lcd_key2(void);void lcd_key3(void);void lcd_key4(void);void UART0_Init (void);void presskey(void);//----------------------------------------------------------------------------- // Global CONSTANTS//----------------------------------------------------------------------------- sbit S3=P1^0;sbit S4=P1^1;sbit S5=P1^2;sbit S6=P1^3;sbit lcdcs=P3^0;unsigned char comd,kk,sdf,ppca;unsigned char virt_port,v,b,m;unsigned char lcd_data_count;unsigned char *lcdpoint;unsigned char qqq;unsigned char data8;unsigned int i;//----------------------------------------------------------------------------- //-----------------------------------------------------------------------------void main(void){WDTCN = 0xde; // disable watchdog timerWDTCN = 0xad;SYSCLK_Init ();PORT_Init ();UART0_Init() ; // initialize crossbar and GPIOSPI0_Init ();LCD_Init() ;delaynms (20);delaynus (100);LCD_set_xy(0X00,0);delaynus (200);presskey();delaynus (200);LCD_write_string(16);delaynus (200);while(1){if(S3==0){Write_COM(0X01);delaynms (200);LCD_set_xy(0X00,0);delaynus (200);lcd_key1();delaynus (200);LCD_write_string(6);delaynus (200);}else if(S4==0){Write_COM(0X01);delaynms (200);LCD_set_xy(0X00,0);delaynus (200);lcd_key2();delaynus (200);LCD_write_string(6);delaynus (200);}else if(S5==0){Write_COM(0X01);delaynms (200);LCD_set_xy(0X00,0);delaynus (200);lcd_key3();delaynus (200);LCD_write_string(6);delaynus (200);}else if(S6==0){Write_COM(0X01);delaynms (200);LCD_set_xy(0X00,0);delaynus (200);lcd_key4();delaynus (200);LCD_write_string(6);delaynus (200);}else{}}}//-----------------------------------------------------------------------------// Initialization Subroutines//-----------------------------------------------------------------------------//-----------------------------------------------------------------------------// PORT_Init//-----------------------------------------------------------------------------void PORT_Init (void){XBR0 = 0x27; // XBAR0: Initial Reset ValueXBR1 = 0x00; // XBAR1: Initial Reset ValueXBR2 = 0x5c; // XBAR2: Initial Reset ValuePRT0CF = 0x14; // Output configuration for P0PRT1CF = 0x10; // Output configuration for P3PRT3CF = 0x01; // Output configuration for P3}//-----------------------------------------------------------------------------// SYSCLK_Init//-----------------------------------------------------------------------------void SYSCLK_Init (void){OSCXCN = 0x67; // start external oscillator withfor (i=0; i < 256; i++) ; // XTLVLD blanking interval (>1ms)while (!(OSCXCN & 0x80)) ; // Wait for crystal osc. to settleOSCICN = 0x88; // select external oscillator as SYSCLK }//-----------------------------------------------------------------------------// SPI0_Init//-----------------------------------------------------------------------------void SPI0_Init (void){SPI0CFG = 0x07; // data sampled on 1st SCK rising edge SPI0CFG|=0xC0; //CKPOL =1;SPI0CN = 0x03; // Master mode; SPI enabled; flagsSPI0CKR = SYSCLK/2/2000000-1; // SPI clock <= 8MHz (limited by// EEPROM spec.)}//-----------------------------------------------------------------------------// UART0_Init//-----------------------------------------------------------------------------void UART0_Init (void){SCON = 0x50; // SCON: mode 1, 8-bit UART, enable RX TMOD = 0x20; // TMOD: timer 1, mode 2, 8-bit reload TH1 = -(SYSCLK/BAUDRATE/16); // set Timer1 reload value for baudrate TR1 = 1; // start Timer1CKCON |= 0x10; // Timer1 uses SYSCLK as time basePCON |= 0x80; // SMOD = 1TI = 1; // Indicate TX ready}//-----------------------------------------------------------------------------// LCD_Init//-----------------------------------------------------------------------------void LCD_Init(void) //向LCD送命令{// unsigned int xdata x;delaynms(100);datad=0x00;SendSPIByte(datad);delaynms(10);Write_COM(0x30);delaynms(10);Write_COM(0x30);delaynms(10);Write_COM(0x30);delaynms(10) ;Write_COM(0x28);delaynms(100);virt_port=0;SendSPIByte(virt_port);lcden(virt_port);Write_COM(0x01);delaynms(100);Write_COM(0x06);delaynms(10) ;Write_COM(0x0C);delaynms(500) ;}//----------------------------------------------------------------------------- // SendSPIByte//----------------------------------------------------------------------------- void SendSPIByte(unsigned char ch){ lcdcs=1;delaynus(100);SPIF = 0;SPI0DAT = ch;while (SPIF == 0);delaynus(100);lcdcs=0;delaynus(100);_nop_(); // 等待写结束}//----------------------------------------------------------------------------- // lcden//----------------------------------------------------------------------------- void lcden(datad){datad|=0x08;SendSPIByte(datad);datad&=0xf7;SendSPIByte(datad);}//----------------------------------------------------------------------------- // delaynms//----------------------------------------------------------------------------- void delaynms (unsigned int uu){unsigned int oo,ll;for (oo=0;oo<uu;oo++){for(ll=0;ll<1140;ll++);}}//----------------------------------------------------------------------------- // writechar//----------------------------------------------------------------------------- void writechar(unsigned char ua){uint j;uchar t,x;for(j=0;j<500;j++);datad|=0x02;SendSPIByte(datad);datad|=ua&0xf0;SendSPIByte(datad);datad|=0x08;SendSPIByte(datad);for(x=0;x<3;x++);datad&=0xf7;SendSPIByte(datad);for(x=0;x<3;x++);datad&=0x07;delaynus(100);SendSPIByte(virt_port);t|=ua&0x0f;datad|=t<<4;SendSPIByte(datad);for(x=0;x<3;x++);datad|=0x08;SendSPIByte(datad);for(x=0;x<3;x++);datad&=0xf7;SendSPIByte(datad);for(x=0;x<3;x++);datad=0x00;t=0x00;SendSPIByte(datad);}//----------------------------------------------------------------------------- // Write_COM//----------------------------------------------------------------------------- void Write_COM(uchar ins){uchar t;uint j;for(j=0;j<5000;j++); //用延时代替查询virt_port|=ins&0xf0;SendSPIByte(virt_port);//LCDE=1;virt_port|=0x08;SendSPIByte(virt_port);for(i=3;i>0;i--);virt_port&=~0x08;SendSPIByte(virt_port);virt_port&=0x07;SendSPIByte(virt_port);t=ins<<4;virt_port|=t&0xf0;SendSPIByte(virt_port);virt_port|=0x08;SendSPIByte(virt_port);for(i=3;i>0;i--);virt_port&=~0x08;SendSPIByte(virt_port);virt_port=0;SendSPIByte(virt_port);}//-----------------------------------------------------------------------------// LCD_set_xy//-----------------------------------------------------------------------------void LCD_set_xy( unsigned char x, unsigned char y ){unsigned char address;if (y == 0) address = 0x80 + x;elseaddress = 0xc0 + x;Write_COM(address);}//-----------------------------------------------------------------------------// LCD_write_string//-----------------------------------------------------------------------------void LCD_write_string(unsigned char n){unsigned char data1;for(n;n>0;n--){data1=*lcdpoint;writechar(data1);delaynms(100);lcdpoint++;delaynus(10);}}//-----------------------------------------------------------------------------// presskey//-----------------------------------------------------------------------------void presskey(void){unsigned char xdata DDCdata[16]={0x50,0x4c,0x45,0x41,0x53,0x45,0x20,0x50,0x52,0x45,0x53,0x53,0x20,0x4b,0x4 5,0x59};lcdpoint=&DDCdata;}//-----------------------------------------------------------------------------// lcd_key1//-----------------------------------------------------------------------------void lcd_key1(void){unsigned char xdata key1ok[6]={0x53,0x33,0x20,0x4f,0x4b,0x21};lcdpoint=&key1ok;}//-----------------------------------------------------------------------------// lcd_key2//-----------------------------------------------------------------------------void lcd_key2(void){unsigned char xdata key2ok[6]={0x53,0x34,0x20,0x4f,0x4b,0x21};lcdpoint=&key2ok;}//-----------------------------------------------------------------------------// lcd_key3//-----------------------------------------------------------------------------void lcd_key3(void){unsigned char xdata key3ok[6]={0x53,0x35,0x20,0x4f,0x4b,0x21};lcdpoint=&key3ok;}//-----------------------------------------------------------------------------// lcd_key4//-----------------------------------------------------------------------------void lcd_key4(void){unsigned char xdata key4ok[6]={0x53,0x36,0x20,0x4f,0x4b,0x21};lcdpoint=&key4ok;}//-----------------------------------------------------------------------------// delaynus//-----------------------------------------------------------------------------void delaynus(unsigned int q) //N us延时函数{for (i=0;i<q;i++){_nop_();}}本程序已经完全调试通过，欢迎参考。

1。

"In most cases, these signals originate as sensory data from the real world：seismic vibrations visual images， sound waves， etc。

DSP isthe mathematics，the algorithms, and the techniques used to manipulate these signals after they have been converted into a digital form.”在大多数情况下，这些信号来源于人对真实世界的感觉，比如地震的震动，视觉图像,声音波形等。

数字信号处理是一种数学工具,是一种用来处理那些将上述信号转换成数字形式后的信号的算法和技术.2.Fourier’s representation of functionsas a superposition of sines and cosines has become Ubiquitous for both the analytic and numerical solution of differential equations and for the analysis and treatment of communication signals 函数的傅里叶表示,即将函数表示成正弦和余弦信号的叠加，这种方法已经广泛用于微分方程的解析法和数值法求解过程以及通信信号的分析和处理。

3。

If f （t ） is a nonperiodic signal, the summation of the periodic functions ,such as sine and cosine, does not accurately represent the signal. You couldartificially extend thesignal to make it periodicbut it would requireadditional continuity at the endpoints . 如果f(t)是非周期信号，那么用周期函数例如正弦和余弦的和，并不能精确的表示该信号f(t).你可以人为的拓展这个信号使其具有周期性，但是这要求在端点处附加连续性4。

Digital signal processingFrom Wikipedia, the free encyclopediaJump to: navigation, searchThis article needs additional citations for verification. Pleasehelp improve this article by adding citations to reliablesources. Unsourced material may be challenged and removed. (May2008)Digital signal processing (DSP) is the mathematical manipulation of an information signal to modify or improve it in some way. It is characterized by the representation of discrete time, discrete frequency, or other discrete domain signals by a sequence of numbers or symbols and the processing of these signals. Digital signal processing and analog signal processing are subfields of signal processing. DSP includes subfields like: audio and speech signal processing, sonar and radar signal processing, sensor array processing, spectral estimation, statistical signal processing, digital image processing, signal processing for communications, control of systems, biomedical signal processing, seismic data processing, etc.The goal of DSP is usually to measure, filter and/or compress continuous real-world analog signals. The first step is usually to convert the signal from an analog to a digital form, by sampling and then digitizing it using an analog-to-digital converter(ADC), which turns the analog signal into a stream of numbers. However, often, the required output signal is another analog output signal, which requires a digital-to-analog converter(DAC). Even if this process is more complex than analog processing and has a discrete value range, the application of computational power to digital signal processing allows for many advantages over analog processing in many applications, such as error detection and correction in transmission as well as data compression.[1]DSP algorithms have long been run on standard computers, on specialized processors called digital signal processor on purpose-built hardware such as application-specific integrated circuit (ASICs). Today there are additional technologies used for digital signal processing including more powerful general purpose microprocessors, field-programmable gate arrays (FPGAs), digital signal controllers (mostly for industrial apps such as motor control), and stream processors, among others.[2][edit] Signal samplingMain article: Sampling (signal processing)With the increasing use of computers the usage of and need for digital signal processing has increased. To use an analog signal on a computer, it must be digitized with an analog-to-digital converter. Sampling is usually carried out in two stages, discretization and quantization. In the discretization stage, the space of signals is partitioned into equivalence classes and quantization is carried out by replacing the signal with representative signal of the corresponding equivalence class. In the quantization stage the representative signal values are approximated by values from a finite set.The Nyquist–Shannon sampling theorem states that a signal can be exactly reconstructed from its samples if the sampling frequency is greater than twice the highest frequency of the signal; but requires an infinite number of samples. In practice, the sampling frequency is often significantly more than twice that required by the signal's limited bandwidth.[edit] DSP domainsIn DSP, engineers usually study digital signals in one of the following domains: time domain (one-dimensional signals), spatial domain (multidimensional signals), frequency domain, and wavelet domains. They choose the domain to process a signal in by making an informed guess (or by trying different possibilities) as to which domain best represents the essential characteristics of the signal. A sequence of samples from a measuring device produces a time or spatial domain representation, whereas a discrete Fourier transform produces the frequency domain information, that is the frequency spectrum. Autocorrelation is defined as the cross-correlation of the signal with itself over varying intervals of time or space.[edit] Time and space domainsMain article: Time domainThe most common processing approach in the time or space domain is enhancement of the input signal through a method called filtering. Digital filtering generally consists of some linear transformation of a numberof surrounding samples around the current sample of the input or output signal. There are various ways to characterize filters; for example:∙ A "linear" filter is a linear transformation of input samples; other filters are "non-linear". Linear filters satisfy the superposition condition, i.e. if an input is a weighted linear combination ofdifferent signals, the output is an equally weighted linearcombination of the corresponding output signals.∙ A "causal" filter uses only previous samples of the input or output signals; while a "non-causal" filter uses future input samples. A non-causal filter can usually be changed into a causal filter by adding a delay to it.∙ A "time-invariant" filter has constant properties over time; other filters such as adaptive filters change in time.∙ A "stable" filter produces an output that converges to a constant value with time, or remains bounded within a finite interval. An "unstable" filter can produce an output that grows without bounds, with bounded or even zero input.∙ A "finite impulse response" (FIR) filter uses only the input signals, while an "infinite impulse response" filter (IIR) uses both theinput signal and previous samples of the output signal. FIR filters are always stable, while IIR filters may be unstable.Filters can be represented by block diagrams, which can then be used to derive a sample processing algorithm to implement the filter with hardware instructions. A filter may also be described as a difference equation, a collection of zeroes and poles or, if it is an FIR filter, an impulse response or step response.The output of a linear digital filter to any given input may be calculated by convolving the input signal with the impulse response.[edit] Frequency domainMain article: Frequency domainSignals are converted from time or space domain to the frequency domain usually through the Fourier transform. The Fourier transform converts the signal information to a magnitude and phase component of each frequency.Often the Fourier transform is converted to the power spectrum, which is the magnitude of each frequency component squared.The most common purpose for analysis of signals in the frequency domain is analysis of signal properties. The engineer can study the spectrum to determine which frequencies are present in the input signal and which are missing.In addition to frequency information, phase information is often needed. This can be obtained from the Fourier transform. With some applications, how the phase varies with frequency can be a significant consideration.Filtering, particularly in non-realtime work can also be achieved by converting to the frequency domain, applying the filter and then converting back to the time domain. This is a fast, O(n log n) operation, and can give essentially any filter shape including excellent approximations to brickwall filters.There are some commonly used frequency domain transformations. For example, the cepstrum converts a signal to the frequency domain through Fourier transform, takes the logarithm, then applies another Fourier transform. This emphasizes the frequency components with smaller magnitude while retaining the order of magnitudes of frequency components.Frequency domain analysis is also called spectrum-or spectral analysis. [edit] Z-plane analysisMain article: Z-transformWhereas analog filters are usually analysed in terms of transfer functions in the s plane using Laplace transforms, digital filters are analysed in the z plane in terms of Z-transforms. A digital filter may be described in the z plane by its characteristic collection of zeroes and poles. The z plane provides a means for mapping digital frequency (samples/second)to real and imaginary z components, where for continuous periodicsignals and ( is the digital frequency). This is useful for providing a visualization of the frequency response of a digital system or signal.[edit] WaveletMain article: Discrete wavelet transformAn example of the 2D discrete wavelet transform that is used in JPEG2000. The original image is high-pass filtered, yielding the three large images, each describing local changes in brightness (details) in the original image. It is then low-pass filtered and downscaled, yielding an approximation image; this image is high-pass filtered to produce the three smaller detail images, and low-pass filtered to produce the final approximation image in the upper-left.In numerical analysis and functional analysis, a discrete wavelet transform (DWT) is any wavelet transform for which the wavelets are discretely sampled. As with other wavelet transforms, a key advantage it has over Fourier transforms is temporal resolution: it captures both frequency and location information (location in time).[edit] ApplicationsThe main applications of DSP are audio signal processing, audio compression, digital image processing, video compression, speech processing, speech recognition, digital communications, RADAR, SONAR, seismology and biomedicine. Specific examples are speech compression and transmission in digital mobile phones, room correction of sound in hi-fi and sound reinforcement applications, weather forecasting, economic forecasting, seismic data processing, analysis and control of industrial processes, medical imaging such as CAT scans and MRI, MP3 compression, computer graphics, image manipulation, hi-fi loudspeaker crossovers and equalization, and audio effects for use with electric guitar amplifiers.[edit] ImplementationDepending on the requirements of the application, digital signal processing tasks can be implemented on general purpose computers (e.g. supercomputers, mainframe computers, or personal computers) or with embedded processors that may or may not include specialized microprocessors called digital signal processors.Often when the processing requirement is not real-time, processing is economically done with an existing general-purpose computer and the signal data (either input or output) exists in data files. This is essentially no different than any other data processing, except DSP mathematical techniques (such as the FFT) are used, and the sampled data is usually assumed to be uniformly sampled in time or space. For example: processing digital photographs with software such as Photoshop.However, when the application requirement is real-time, DSP is often implemented using specialised microprocessors such as the DSP56000, the TMS320, or the SHARC. These often process data using fixed-point arithmetic, though some more powerful versions use floating point arithmetic. For faster applications FPGAs[3] might be used. Beginning in 2007, multicore implementations of DSPs have started to emerge from companies including Freescale and Stream Processors, Inc. For faster applications with vast usage, ASICs might be designed specifically. For slow applications, a traditional slower processor such as a microcontroller may be adequate. Also a growing number of DSP applications are now being implemented on Embedded Systems using powerful PCs with a Multi-core processor。

DSP 专业英语词汇AAbsolutely integrable 绝对可积Absolutely integrable impulse response 绝对可积冲激响应Absolutely summable 绝对可和Absolutely summable impulse response 绝对可和冲激响应Accumulator 累加器Acoustic 声学Adder 加法器Additivity property 可加性Aliasing 混叠现象All—pass systems 全通系统AM （Amplitude modulation ）幅度调制Amplifier 放大器Amplitude modulation （AM) 幅度调制Amplitude-scaling factor 幅度放大因子Analog—to-digital (A-to—D）converter 模数转换器Analysis equation 分析公式（方程）Angel (phase) of complex number 复数的角度（相位）Angle criterion 角判据Angle modulation 角度调制Anticausality 反因果Aperiodic 非周期Aperiodic convolution 非周期卷积Aperiodic signal 非周期信号Asynchronous 异步的Audio systems 音频（声音）系统Autocorrelation functions 自相关函数Automobile suspension system 汽车减震系统Averaging system 平滑系统BBand—limited 带（宽）限的Band—limited input signals 带限输入信号Band—limited interpolation 带限内插Bandpass filters 带通滤波器Bandpass signal 带通信号Bandpass—sampling techniques 带通采样技术Bandwidth 带宽Bartlett (triangular) window 巴特利特（三角形）窗Bilateral Laplace transform 双边拉普拉斯变换Bilinear 双线性的Bilinear transformation 双线性变换Bit （二进制）位，比特Block diagrams 方框图Bode plots 波特图Bounded 有界限的Break frequency 折转频率Butterworth filters 巴特沃斯滤波器C“Chirp" transform algorithm “鸟声”变换算法Capacitor 电容器Carrier 载波Carrier frequency 载波频率Carrier signal 载波信号Cartesian （rectangular) form 直角坐标形式Cascade （series）interconnection 串联，级联Cascade-form 串联形式Causal LTI system 因果的线性时不变系统Channel 信道,频道Channel equalization 信道均衡Chopper amplifier 斩波器放大器Closed-loop 闭环Closed-loop poles 闭环极点Closed-loop system 闭环系统Closed-loop system function 闭环系统函数Coefficient multiplier 系数乘法器Coefficients 系数Communications systems 通信系统Commutative property 交换性（交换律）Compensation for nonideal elements 非理想元件的补偿Complex conjugate 复数共轭Complex exponential carrier 复指数载波Complex exponential signals 复指数信号Complex exponential（s) 复指数Complex numbers 复数Conditionally stable systems 条件稳定系统Conjugate symmetry 共轭对称Conjugation property 共轭性质Continuous—time delay 连续时间延迟Continuous-time filter 连续时间滤波器Continuous-time Fourier series 连续时间傅立叶级数Continuous-time Fourier transform 连续时间傅立叶变换Continuous-time signals 连续时间信号Continuous-time systems 连续时间系统Continuous-to-discrete—time conversion 连续时间到离散时间转换Convergence 收敛Convolution 卷积Convolution integral 卷积积分Convolution property 卷积性质Convolution sum 卷积和Correlation function 相关函数Critically damped systems 临界阻尼系统Crosss—correlation functions 互相关函数Cutoff frequencies 截至频率DDamped sinusoids 阻尼正弦振荡Damping ratio 阻尼系数Dc offset 直流偏移Dc sequence 直流序列Deadbeat feedback systems 临界阻尼反馈系统Decibels (d 分贝Decimation 抽取Decimation and interpolation 抽取和内插Degenerative （negative) feedback 负反馈Delay 延迟Delay time 延迟时间Demodulation 解调Difference equations 差分方程Differencing property 差分性质Differential equations 微分方程Differentiating filters 微分滤波器Differentiation property 微分性质Differentiator 微分器Digital-to-analog (D—to—A) converter 数模转换器Direct Form I realization 直接I型实现Direct form II realization 直接II型实现Direct—form 直接型Dirichlet conditions 狄里赫利条件Dirichlet，P。

1automation 自动化1closed-loop 闭环1open-loop 开环1feedback反馈1closed-loop feedback control system 闭环反馈控制系统1open-loop control system 开环控制系统1negative feedback 负反馈1positive feedback 正反馈1control system控制系统1complexity of design 设计复杂性1design 设计1design gap设计差距1engineering design 工程设计1feedback signal 反馈信号1flyball governor飞球调节器1multivariable control system 多变量控制系统1optimization 优化1plant 对象1process过程1productivity 生产率1risk 风险1robot机器人1specifications 指标说明1synthesis 综合1system 系统1trade-off折中2actuator 执行机构/执行器2assumptions 假设条件2block diagrams框图2characteristic equation 特征方程2transfer function 传递函数2closed-loop transfer function 闭环传递函数2open-loop transfer function 开环传递函数2damping阻尼2damping ratio 阻尼系数/阻尼比2critical damping 临界阻尼2damping oscillation 阻尼振荡2DC motor直流电机2differential equation 微分方程2error误差2error signal 误差信号2final value终值2final value theorem 终值定理2homogeneity齐次性2Laplace transform 拉普拉斯变换2linear approximation 线性近似2linear system线性系统2linearized线性化的chterm translation2linearization线性化2Mason loop rule梅森回路规则2Mason formula梅森公式2natural frequency固有频率/自然频率2necessary condition必要条件2overdamped过阻尼的2poles极点2zeros零点2principle of superposition叠加原理2reference input参考输入2residues留数2signal-flow graph信号流图2simulation 仿真2steady state稳态2s-plane s平面2Taylor series泰勒级数2time constant时间常数2underdamped欠阻尼的2unity feedback单位反馈3canonical form标准型3diagonal canonical form对角标准型/对角线标准型3discrete-time approximation离散时间近似3Euler's method欧拉方法3fundamental matrix基本矩阵3input feedforward canonical form输入前馈标准型3Jordan canonical form约当标准型3matrix exponential function矩阵指数函数3output equation输出方程3phase variable canonical form相变量标准型3phase variable相变量3physical variables物理变量3state differential equation状态微分方程3state space状态空间3state variables状态变量3state vector状态向量/状态矢量3state of a system系统状态3state-space representation状态空间表示/状态空间表达式3state variable feedback状态变量反馈3time domain时域3time-varying system时变系统3time-invariant system时不变系统/非时变系统3transition matrix转移矩阵4closed-loop system闭环系统4complexity复杂度4components组件4direct system直接系统4disturbance signal扰动信号4error signal误差信号4instability不稳定性4loss of gain增益损失4open-loop system开环系统4steady-state error稳态误差4system sensitivity系统灵敏度4transient response暂态响应/瞬态响应4steady-state response稳态响应5acceleration error constant，Ka加速度误差常数,Ka5position error constant,Kp位置误差常数,Kp5velocity error constant,Kv速度误差常数,Kv5design specifications设计要求5domainant roots主导极点5optimum control system最优控制系统5peak time峰值时间5percent overshoot百分比超调/超调量5maximum percent overshoot最大超调量5performance index性能指标5rise time 上升时间5settling time 调整时间5test input signal测试输入信号5tyoe number型数5unit impulse单位脉冲6absolute stability绝对稳定性6auxiliary polynomial辅助多项式6marginally stable临界稳定6relative stability相对稳定性6Rooth-Hurwitz criterion Rooth-Hurwitz判据/劳斯-赫尔维茨判据6stability稳定性6stable system稳定系统7angle of departure出射角7angle of the asymptotes渐近角7asymptote渐近线7asymptote centroid渐近中心7breakaway point分支点7dominant roots主导极点7locus轨迹7logarithmic sensitivity对数灵敏度7number of separate loci根轨迹的段数7parameter design参数设计7PID controller PID控制器7proportional plus derivative (PD) controller比例加微分（PD）控制器7proportional plus integral (PI) controller比例加积分（PI）控制器7root contours根等值线7root locus根轨迹7root locus method根轨迹法7root locus segments on the real axis实轴上的根轨迹段7root sensitivity根灵敏度8all-pass network全通网络8bandwidth带宽8Bode plot Bode图/波德图8break frequency截止频率8corner frequency转折频率8decade十倍频程8Decibel/dB分贝8Fourier transform Fourier变换/傅里叶变换8Fourier transform pair Fourier变换对/傅里叶变换对8frequency response频率响应8Laplace transform pair拉普拉斯变换对8Logarithmic magnitude对数幅值8Logarithmic plot对数坐标图8maximum value of the frequency response频率响应的最大值8minimum phase transfer dunction最小相位传递函数8nonminimum phase system非最小相位系统8polar plot极坐标图8resonant frequency谐振频率8transfer function in the frequency domain频域传递函数9Cauchy's theorem Cauchy定理9closed-loop frequency response闭环频率响应9conformal mapping保角映射9contour map围道映射9gain margin增益裕度/增益裕量9logarithmic (decibel) measure对数（分贝）度量9Nichols chart Nichols图9Nyquist stability criterion Nyquist稳定判据/奈奎斯特稳定判据9phase margin相角裕度/相位裕度9principle of the argument幅角原理9time delay时滞10cascade compensation network串联校正网络10compensation校正10compensator校正装置10deadbeat response最小拍响应10design of a control system控制系统设计10integration network积分网络10lag network滞后网络10lead network超前网络10lead-lag network超前滞后网络10phase lag compensation相角滞后校正10phase lead compensation相角超前校正10phase-lag network相角滞后网络10phase-lead network相角超前网络10prefilter前置滤波11command following给定跟踪11controllability matrix能控性矩阵11controllable system能控系统11detectable能检测11estimation error估计误差11full-state feedback control law全状态反馈控制律11internal mode design内模设计11Kalman state-space decomposition Kalman状态空间分解/卡尔曼状态空间分解11linear quadratic regulator线性二次型调节器11observable system能观系统11observability matrix能观性矩阵11observer观测器11optimal control system最优控制系统11pole assignment极点配置11separation principle分离原理11stabilizable能镇定11stabilizing controller镇定控制器11state variable feedback状态变量反馈12additive perturbation加性摄动12complementary sensitivity function补灵敏度函数12internal model principle内模原理12mulplicative perturbation乘性摄动12process controller过程控制器12robust control system鲁棒控制系统12robust stability criterion鲁棒稳定判据12root sensitivity根灵敏度12system sensitivity系统灵敏度12three-mode controller三模态控制器12three-term controller三项控制器13amplitude quantization error幅值量化误差13backward difference rule后向差分规则13digital computer compensator数字计算机校正装置13digital controll system数字控制系统13forward rectangular integration前向矩形积分13microcomputer微型计算机13minicomputer小型计算机13digital PID controller数字PID控制器13precision精度13sampled data采样数据13sampled-data system采样数据系统13sampling period采样周期13stability of sampled-data system采样数据系统的稳定性13z-plane z平面13z-transform z变换13zero-order hold零阶保持13zero-order holder零阶保持器。

AAbsolutely integrable 绝对可积绝对可积冲激响应Absolutely integrable impulse response绝对可和Absolutely summable绝对可和冲激响应Absolutely summable impulse response累加器Accumulator声学Acoustic加法器Adder可加性Additivity property混叠现象Aliasing全通系统All-pass systems幅度调制AM (Amplitude modulation )放大器Amplifier幅度调制Amplitude modulation (AM)幅度放大因子Amplitude-scaling factor模数转换器Analog-to-digital (A-to-D) converter分析公式（方程）Analysis equation复数的角度（相位）Angel (phase) of complex number角判据Angle criterion角度调制Angle modulationAnticausality 反因果AperiodicAperiodic convolution Aperiodic signal AsynchronousAudio systems Autocorrelation functions Automobile suspension system Averaging systemBBand-limitedBand-limited input signals Band-limited interpolation Bandpass filtersBandpass signalBandpass-sampling techniques BandwidthBartlett (triangular) window Bilateral Laplace transform BilinearBilinear transformationBit 非周期非周期卷积非周期信号异步的音频（声音）系统自相关函数汽车减震系统平滑系统带（宽）限的带限输入信号带限内插带通滤波器带通信号带通采样技术带宽巴特利特（三角形）窗双边拉普拉斯变换双线性的双线性变换（二进制）位，比特Block diagramsBode plotsBoundedBreak frequencyButterworth filtersC“ Chirp ” transform algorithm CapacitorCarrierCarrier frequencyCarrier signalCartesian (rectangular) form Cascade (series) interconnection Cascade-formCausal LTI systemChannelChannel equalizationChopper amplifierClosed-loopClosed-loop polesClosed-loop system 方框图波特图有界限的折转频率巴特沃斯滤波器“鸟声”变换算法电容器载波载波频率载波信号直角坐标形式串联，级联串联形式因果的线性时不变系统信道，频道信道均衡斩波器放大器闭环闭环极点闭环系统Closed-loop system function 闭环系统函数系数乘法器Coefficient multiplier系数Coefficients通信系统Communications systems交换性（交换律）Commutative property非理想元件的补偿Compensation for nonideal elements复数共轭Complex conjugate复指数载波Complex exponential carrier复指数信号Complex exponential signals复指数Complex exponential(s)复数Complex numbers条件稳定系统Conditionally stable systems共轭对称Conjugate symmetry共轭性质Conjugation property连续时间延迟Continuous-time delay连续时间滤波器Continuous-time filter连续时间傅立叶级数Continuous-time Fourier series连续时间傅立叶变换Continuous-time Fourier transform连续时间信号Continuous-time signalsContinuous-time systems 连续时间系统Continuous-to-discrete-time conversion 连续时间到离散时间转换Convergence 收敛卷积Convolution卷积积分Convolution integral卷积性质Convolution property卷积和Convolution sum相关函数Correlation function临界阻尼系统Critically damped systems互相关函数Crosss-correlation functions截至频率Cutoff frequenciesD阻尼正弦振荡Damped sinusoids阻尼系数Damping ratio直流偏移Dc offset直流序列Dc sequence临界阻尼反馈系统Deadbeat feedback systems分贝Decibels (dB)抽取Decimation抽取和内插Decimation and interpolation负反馈Degenerative (negative) feedback延迟DelayDelay time 延迟时间DemodulationDifference equations Differencing property Differential equations Differentiating filters Differentiation property DifferentiatorDigital-to-analog (D-to-A) converter Direct Form I realization Direct form II realization Direct-form Dirichlet conditions Dirichlet, P.L. Discontinuities Discrete-time filtersDiscrete-time Fourier series Discrete-time Fourier series pair Discrete-time Fourier transform ( DFT) Discrete-time LTI filters Discrete-time modulationDiscrete-time nonrecursive filters 解调差分方程差分性质微分方程微分滤波器微分性质微分器数模转换器直接I 型实现直接II 型实现直接型狄里赫利条件狄里赫利间断点，不连续离散时间滤波器离散时间傅立叶级数离散时间傅立叶级数对离散时间傅立叶变换离散时间线性时不变滤波器离散时间调制离散时间非递归滤波器Discrete-time signals 离散时间信号Discrete-time systems 离散时间系统Discrete-time to con ti nu ous-time conv ersion离散时间至U连续时间转换Dispersion 弥撒（现象）Distortion 扭曲，失真Distribution theory(property)分配律Dominant time constant 主时间常数Double-sideband modulation (DSB) 双边带调制Downsampling 减采样Duality 对偶性EEcho 回波Eigenfunctions 特征函数Eigenvalue 特征值Elliptic filters 椭圆滤波器Encirclement property 围线性质End points 终点—、八、、Energy of signals 信号的能量Energy-density spectrum 能量密度谱Envelope detector 包络检波器Envelope function 包络函数EqualizationEqualizer circuitsEquation for closed-loop poles Euler, L.Euler ' s relationEven signalsExponential signalsExponentialsFFast Fourier transform (FFT) FeedbackFeedback interconnection Feedback pathFilter(s)Final-value theoremFinite impulse response (FIR) Finite impulse response (FIR) filters Finite sum formulaFinite-duration signalsFirst differenceFirst harmonic components 均衡化均衡器电路闭环极点方程欧拉欧拉关系（公式）偶信号指数信号指数快速傅立叶变换反馈反馈联结反馈路径滤波器终值定理有限长脉冲响应有限长脉冲响应滤波器有限项和公式有限长信号一阶差分基波分量（一次谐波分量）First-order continuous-time systems 一阶连续时间系统一阶离散时间系统First-order discrete-time systems一阶递归离散时间滤波器First-order recursive discrete-time filters一阶系统First-order systems受迫响应Forced response正向通路Forward path傅立叶级数Fourier series傅立叶变换Fourier transform傅立叶变换对Fourier transform pairsFourier, Jean Baptiste Joseph 傅立叶（法国数学家，物理学家）频率响应Frequency response线性时不变系统的频率响应Frequency response of LTI systemsFreque ncy scali ng of contin uous-time连续时间傅立叶变化的频率尺度Fourier transform （变换性质）Frequency shift keying (FSK) 频移键控Frequency shifting property 频移性质Frequency-division multiplexing (FDM) 频分多路复用Frequency-domain characterization 频域特征Frequency-selective filter 频率选择滤波器Frequency-shaping filters 频率成型滤波器Fundamental components 基波分量Fundamental periodGGainGain and phase margin General complex exponentials Generalized functions Gibbs phenomenon Group delayHHalf-sample delay Hanning window Harmonic analyzerHarmonic components Harmonically relatedHeat propagation and diffusion Higher order holds Highpass filterHighpass-to-lowpass transformations Hilbert transformHomogeneity (scaling) propertyFundamental frequency 基波频率 基波周期增益 增益和相位裕度 一般复指数信号 广义函数 吉伯斯现象 群延迟半采样间隔时延 汉宁窗 谐波分析议 谐波分量 谐波关系 热传播和扩散现象 高阶保持 高通滤波器 高通到低通变换 希尔波特滤波器 齐次性（比例性）IIdeal 理想的理想带阻特征Ideal bandstop characteristic理想频率选择滤波器Ideal frequency-selective filter理想化Idealization恒等系统Identity system虚部Imaginary part冲激响应Impulse response冲激串Impulse train增量线性系统Incrementally linear systems独立变量Independent variable无限长脉冲响应Infinite impulse response (IIR)无限长脉冲响应滤波器Infinite impulse response (IIR) filters无限项和公式Infinite sum formula无限项泰勒级数Infinite taylor series初值定理Initial-value theorem冲激串采样Inpulse-train sampling瞬时的Instantaneous瞬时频率Instantaneous frequency时域积分Integration in time-domainIntegration property 积分性质Integrator 积分器Linear 线性InterconnectionIntermediate-frequency (IF) stage Intersymbol interference (ISI) Inverse Fourier transform Inverse Laplace transform Inverse LTI system Inverse system design Inverse z-transformInverted pendulum Invertibility of LTI systems Invertible systemsLLag network Lagrange, J.L.Laplace transform Laplace, P.S. de lead network互联 中频级 码间干扰 傅立叶反变换 拉普拉斯反变换 逆线性时不变系统 逆系统设计 z 反变换 倒立摆 线性时不变系统的可逆性 逆系统滞后网络 拉格朗日（法国数学家，力学家） 拉普拉斯变换 拉普拉斯（法国天文学家， 数学家） 超前网络left-half plane 左半平面 left-sided signal左边信号Linear constant-coefficient difference 线性常系数差分方程equationsLinear constant-coefficient differential线性常系数微分方程equations线性反馈系统Linear feedback systems线性插值Linear interpolation线性性Linearity对数幅－相图Log magnitude-phase diagram对数模图Log-magnitude plots无损失码Lossless coding低通滤波器Lowpass filters低通到高通的转换Lowpass-to-highpass transformation线性时不变系统响应LTI system response线性时不变系统分析LTI systems analysisM幅度和相位Magnitude and phase匹配滤波器Matched filter测量仪器Measuring devices记忆Memory无记忆系统Memoryless systemsModulating signal 调制信号Modulation 调制Modulation index 调制指数Modulation property 调制性质Moving-average filters移动平均滤波器Multiplexing 多路技术Multiplication property 相乘性质Multiplicities 多样性NNarrowband 窄带Narrowband frequency modulation 窄带频率调制Natural frequency 自然响应频率Natural response 自然响应Negative (degenerative) feedback 负反馈Nonanticipatibe system 不超前系统Noncausal averaging system非因果平滑系统Nonideal 非理想的Nonideal filters 非理想滤波器Nonmalized functions 归一化函数Nonrecursive 非递归Nonrecursive filters 非递归滤波器Non recursive lin ear con sta nt-coefficie nt 非递归线性常系数差分方程difference equationsNyquist frequency 奈奎斯特频率奈奎斯特率Nyquist rate奈奎斯特稳定性判据Nyquist stability criterionO奇次谐波Odd harmonic奇信号Odd signal开环Open-loop开环频率响应Open-loop frequency response开环系统Open-loop system运算放大器Operational amplifier正交函数Orthogonal functions正交信号Orthogonal signals示波器Oscilloscope过阻尼系统Overdamped system过采样Oversampling超量OvershootP并联Parallel interconnection并联型框图Parallel-form block diagramsParity check 奇偶校验检查Parseval ' s renlatioPartial-fraction expansionParticular and homogeneous solution PassbandPassband edgePassband frequencyPassband ripplePendulumPercent modulationPeriodicPeriodic complex exponentials Periodic convolutionPeriodic signalsPeriodic square wavePeriodic square-wave modulating signal Periodic train of impulsesPhase (angle) of complex number Phase lagPhase leadPhase marginPhase shift 帕斯伐尔关系（定理）部分分式展开特解和齐次解通频带通带边缘通带频率通带起伏（或波纹）钟摆调制百分数周期的周期复指数周期卷积周期信号周期方波周期方波调制信号周期冲激串复数相位（角度）相位滞后相位超前相位裕度相移Phase-reversal Phase modulation Plant Polar form PolesPole-zero plot(s) PolynomialsPositive (regenerative) feedback Power of signalsPower-series expansion method Principal-phase function Proportional (P) control Proportional feedback system Proportional-plus-derivative(PID) controlPulse-amplitude modulation Pulse-code modulation Pulse-train carrierProportional-plus-derivative feedback Proportional-plus-integral-plus-differential 相位倒置 相位调制 工厂 极坐标形式 极点 零极点图 多项式 正（再生）反馈 信号功率 幂级数展开的方法 主值相位函数 比例控制 比例反馈系统 比例加积分 比例加积分反馈比例－积分－微分控制脉冲幅度调制 脉冲编码调制 冲激串载波QQuadrature distortion Quadrature multiplexing Quality of circuitRRaised consine frequency responseRational frequency responses Rational transform RC highpass filter RC lowpass filter RealReal exponential signals Real partRectangular (Cartesian) form Rectangular pulse Rectangular pulse signal Rectangular windowRecursive (infinite impulse response) filters递归(无时限脉冲响应)滤波器Recursive linear constant-coefficient 递归的线性常系数差分方程 difference equationsRegenerative (positive) feedback正交失真 正交多路复用 电路品质（因数）升余弦频率响应 有理型频率响应 有理变换RC 高阶滤波器RC 低阶滤波器 实数 实指数信号 实部 直角（卡笛儿）坐标形式 矩形脉冲 矩形脉冲信号 矩形窗口再生（正）反馈Region of comvergence 收敛域right-sided signal 右边信号上升时间Rise time根轨迹分析（方法）Root-locus analysis动求和Running sumSS域S domain采样数据反馈系统Sampled-data feedback systems采样数据系统Sampled-data systems采样Sampling采样频率Sampling frequency采样函数Sampling function采样示波器Sampling oscilloscope采样周期Sampling period采样定理Sampling theorem比例性（齐次性）性质Scaling (homogeneity) propertyScaling in z domain z 域尺度变换扰频器Scrambler二次谐波分量Second harmonic components二阶Second-orderSecond-order continuous-time system 二阶连续时间系统Second-order discrete-time system 二阶离散时间系统Second-order systems 二阶系统序列sequenceSeries (cascade)级联（串联）interconnection筛选性质Sifting propertySinc functions sinc 函数单边带Single-sidebandSingle-sideband sinusoidal amplitude单边带正弦幅度调制modulation奇异函数Singularity functions正弦（信号）SinusoidalSinusoidal amplitude正弦幅度调制modulation正弦载波Sinusoidal carrierSinusoidal frequency正弦频率调制modulation滑动Sliding频谱系数Spectral coefficient频谱Spectrum语音加密器Speech scramblerS-plane S 平面方波Square waveStability 稳定性Step responseStep-invariant transformation StopbandStopband edgeStopband frequency Stopband ripple Stroboscopic effect SummerSuperposition integral Superposition property Superposition sum Suspension system Symmetric periodic SymmetrySynchronousSynthesis equationSystem function(s)T Table of propertiesTaylor series不稳定系统的稳定性（度）阶跃响应阶跃响应不定的变换阻带阻带边缘阻带频率阻带起伏（或波纹）频闪响应加法器叠加积分叠加性质叠加和减震系统周期对称对称性同步的综合方程系统方程性质列表泰勒级数Stabilization of unstable systemsTime advance property of unilateralz-transform单边z 变换的时间超前性质Time constants时间常数Time delay property z-transform ofunilateral单边z 变换的时间延迟性质Time expansion property时间扩展性质Time invariance时间变量Time reversal property时间反转（反褶）性Time scaling property时间尺度变换性Time shifting property时移性质Time window时间窗口Time-division multiplexing(TDM)时分复用Time-domain时域Time-domain properties时域性质Tracking system (s)跟踪系统Transfer function转移函数transform pairs变换对Transformation变换（变形）Transition band 过渡带Time 时间，时域Transmodulation (transmultiplexing) 交叉调制Triangular (Barlett) windowTrigonometric seriesTwo-sided signalType l feedback systemUUint impulse responseUint ramp function Undamped natural frequency Undamped system Underdamped systems UndersamplingUnilateralUnilateral Laplace transform Unilateral z-transformUnit circleUnit delayUnit doubletsUnit impulseUnit step functionsUnit step response Unstable systems 三角型（巴特利特）窗口三角级数双边信号l 型反馈系统单位冲激响应单位斜坡函数无阻尼自然相应无阻尼系统欠阻尼系统欠采样单边的单边拉普拉斯变换单边z 变换单位圆单位延迟单位冲激偶单位冲激单位阶跃函数单位阶跃响应不稳定系统VUnwrapped phaseUpsamplingVariableWWalsh functions Wave Wavelengths Weighted average WidebandWideband frequency modulation WindowingzZ domainZero force equalizer Zero-Input response Zero-Order holdZeros of Laplace transform Zero-state response z-transform z-transform pairs展开的相位特性增采样变量沃尔什函数 波形 波长 加权平均 宽带 宽带频率调制 加窗z 域置零均衡器 零输入响应零阶保持 拉普拉斯变换的零点 零状态响应 z 变换 z 变换对。

A Sufficient Condition for Convergence of Sampled-DataConsensus for Double-Integrator Dynamics With Nonuniform and Time-Varying Communication Delays Jiahu Qin,Student Member,IEEE,andHuijun Gao,Senior Member,IEEEAbstract—This technical note investigates a discrete-time second-order consensus algorithm for networks of agents with nonuniform and time-varying communication delays under dynamically changing communica-tion topologies in a sampled-data setting.Some new proof techniques are proposed to perform the convergence analysis.It isfinally shown that under certain assumptions upon the velocity damping gain and the sampling pe-riod,consensus is achieved for arbitrary bounded time-varying commu-nication delays if the union of the associated digraphs of the interaction matrices in the presence of delays has a directed spanning tree frequently enough.Index Terms—Double-integrator agents,sampled-data consensus,span-ning tree,time-varying communication delays.I.I NTRODUCTIONIn recent years,consensus problems for agents with single-integrator dynamics have been studied from various perspectives(see,e.g.,[4], [7],[10],[11],[14],[16],[17],[26]).Taking into account that double-integrator dynamics can be used to model more complicated systems in reality,cooperative control for multiple agents with double-integrator dynamics has been studied extensively recently,see[12],[18]–[20], [23],[28]for continuous algorithms and[1]–[3],[5],[6],[8],[13]for discrete-time algorithms.In[8],a sampled-data algorithm is studied for double-integrator dy-namics through a Lyapunov-based approach.The analysis in[8]is lim-ited to an undirected network topology and cannot be extended to deal with the directed case.However,the informationflow might be directed in practical applications.In a similar sampled-data setting,[1]studies two sampled-data consensus algorithms,i.e.,the case with an absolute velocity damping term and the case with a relative velocity damping term,in the context of a directed network topology by extensively using matrix spectral analysis.Reference[2]extends the algorithms in[1]to deal with a dynamic directed network topology.References[5]and[6] mainly investigate sampled-data consensus for the case with a relative velocity damping term under a dynamic network topology.In[5],the network topologies are required to be both balanced and strongly con-nected at each sampling instant.On the other hand,considering that it might be difficult to measure the velocity information in practice,[6] Manuscript received November17,2009;revised September15,2010; August15,2011,and January24,2012;accepted January25,2012.Date of publication February17,2012;date of current version August24,2012.This work was supported in part by the National Natural Science Foundation of China under Grants60825303,60834003,and61021002,by the973Project (2009CB320600),and by the Foundation for the Author of National Excellent Doctoral Dissertation of China(2007B4).Recommended by Associate Editor H.Ito.J.Qin is with Harbin Institute of Technology,Harbin,China,and also with the Australian National University,Canberra,A.C.T.,Australia(e-mail:jiahu. qin@.au).H.Gao is with the Research Institute of Intelligent Control and Systems, Harbin Institute of Technology,Harbin150001,China(e-mail:hjgao@. cn).Color versions of one or more of thefigures in this paper are available online at .Digital Object Identifier10.1109/TAC.2012.2188425proposes a consensus strategy using the measurements of the relative positions between neighboring agents to estimate the relative velocities. In[13],consensus problems of second-order multi-agent systems with nonuniform time delays and dynamically changing topologies is investigated.However,the paper considers a discrete-time model es-timated by using the forward difference approximation method rather than a sampled-data model.In general,a sampled-data model is more realistic.Also,in[13],the weighting factors must be chosen from a finite set.With this background,we study the convergence of sam-pled-data consensus for double-integrator dynamics under dynamically changing topologies and allow the communication delays to be not only different but also time varying.Here,considering the weighting factors of directed edges between neighboring agents usually represent confi-dence or reliability of the transmitted information,it is more natural to consider choosing the weighting factors from an infinite set,which is more general than thefinite set case in[2]and[13].Moreover,dif-ferent from that in[13],A(k),the interaction matrix in the presence of delays at time t=kT,is introduced in this technical note and the dif-ference between A(k)and A(k),the adjacency matrix at time t=kT, is further explored as well.The reason for introducing A(k)is that it is more relevant than A(k)to the strategies investigated in this technical note.It is worth pointing out that the method employed to perform the convergence analysis is totally different from most of the existing liter-ature which heavily relies on analyzing the system matrix by spectral analysis.By using the similar transformation as that used in[13],we can treat the sampled-data consensus for double-integrator dynamics as the consensus for multiple agents modeled byfirst-integrator dynamics. Then,in order to make the transformed system dynamics mathemati-cally tractable,a new graphic method is proposed to specify the rela-tions between0(A(k)),the associated digraph of the interaction matrix in the presence of delays,and the the associated digraph of the trans-formed system matrix.Finally,motivated by the work in[22,Theorem 2.33]and[27],by employing the product properties of row-stochastic matrices from an infinite set,we present a sufficient condition in terms of the associated digraph of the interaction matrix in the presence of delays for the agents to reach consensus.Note here that the proving techniques employed in this technical note can be extended directly to derive similar results by considering the discrete-time model in[13]. The rest of the technical note is organized as follows.In Section II, we formulate the problem to be investigated and also provide some graph theory notations,while the convergence analysis is given in Section III.In Section IV,a numerical example is provided to show the effectiveness of the new result.Finally,some concluding remarks are drawn in Section V.II.B ACKGROUND AND P RELIMINARIESA.NotationsLet I n2n2n and0n;n2n2n denote,respectively,the identity matrix and the zero matrix,and1m2m be the column vector of all ones.Letand+denote,respectively,the set of nonnegative and positive integers.Given any matrix A=[a ij]2n2n,let diag(A) denote the diagonal matrix associated with A with the ith diagonal element equal to a ii.Hereafter,matrices are assumed to be compatible for algebraic operations if their dimensions are not explicitly stated.A matrix M2n2n is nonnegative,denoted as M 0,if all its entries are nonnegative.Let N2n2n.We write M N if M0N 0.A nonnegative matrix M is said to be row stochastic if all its row sums are1.Let k i=1M i=M k M k01111M1denote the left product of the matrices M k;M k01;111;M1.A row-stochastic matrix M is ergodic0018-9286/$31.00©2012IEEE(or indecomposable and aperiodic )if there exists a column vector f2nsuch that lim k !1M k =1n f T .B.Graph Theory NotationsLet G =(V ;E ;A )be a weighted digraph of order n with a finite nonempty set of nodes V =f 1;2;...;n g ,a set of edges E V 2V ,and a weighted adjacency matrix A =[a ij ]2n 2n with nonnegative adjacency elements a ij .An edge of G is denoted by (i;j ),meaning that there is a communication channel from agent i to agent j .The adjacency elements associated with the edges are positive,i.e.,(j;i )2E ,a ij >0.Moreover,we assume a ii =0for all i 2V .The set of neighbors of node i is denoted by N i =f j 2V :(j;i )2Eg .Denote by L =[l ij ]the Laplacian matrix associated with G ,where l ij =0a ij ,i =j ,and l ii=n k =1;k =i a ik .A directed path is a sequence of edges in a digraph of the form (i 1;i 2);(i 2;i 3);....A digraph has a directed spanning tree if there exists at least one node,called the root node,having a directed path to all the other nodes.A spanning subgraph G s of a directed graph G is a directed graph such that the node set V (G s )=V (G )and the edge set E (G s ) E (G ).Given a nonnegative matrix S =[s ij ]2n 2n ,the associated di-graph of S ,denoted by 0(S ),is the directed graph with the node set V =f 1;2;...;n g such that there is an edge in 0(S )from j to i if and only if s ij >0.Note that for arbitrary nonnegative matrices M;N2p 2p satisfying M N ,where >0,if 0(N )has a di-rected spanning tree,then 0(M )also has a directed spanning tree.C.Sampled-Data Consensus Algorithm for Double-Integrator DynamicsEach agent is regarded as a node in a digraph G of order n .Let T >0denote the sampling period and k2denote the discrete-time index.For notational simplicity,the sampling period T will be dropped in the sequel when it is clear from the context.We consider the following sampled-data discrete-time system which has been investigated in [1],[2],and [8]asr i (k +1)0r i (k )=T v i (k )+12T 2u i (k )v i (k +1)0v i (k )=T u i (k )(1)where x i (k )2p ,v i (k )2p and u i (k )2p are,respectively,the position,velocity and control input of agent i at time t =kT .For simplicity,we assume p =1.However,all results still hold for any p2+by introducing the notation of Kronecker product.In this technical note,we mainly consider the following discrete-time second-order consensus algorithm which takes into account the nonuniform and time-varying communication delays as u i (k )=0 v i (k )+j 2N (k )ij (k )(r j (k 0 ij (k ))0r i (k ))(2)where >0denotes the absolute velocity damping gain,N i (k )de-notes the neighbor set of agent i at time t =kT that varies with G (k )(i.e.,the dynamic communication topology at time t =kT ), ij (k )>0if agent i can receive the delayed position r j (k 0 ij (k ))from agent j at time t =kT while ij (k )=0otherwise,and 0 ij (k ) max ,where ij (k )2,is the communication delay from agent j to agent i .Here,we assume ii (t ) 0,that is,the time delays affect only the in-formation that is transmitted from one agent to another.Moreover,we assume that all the nonzero and hence positive weighting factors areboth uniformly lower and upper bounded,i.e., ij (k )2[ ;],where 0< < ,if j 2N i (k ).Remark 1:In general,(j;i )2E (G (k ))or a ij (k )>0,which cor-responds to an available communication channel from agent j to agent i at time t =kT ,does not imply ij (k )>0even if the reverse is true.This is mainly because the communication topologies are dynamicallychanging and the communication delays are time varying,which may destroy the continuity of information.Note that ij (k )>0requires a ij >0for the whole time between k 0 ij (k )and k .DefineA (k )= 11(k )111 1n (k )......... n 1(k )111 nn (k):To distinguish A (k )from the adjacency matrix A (k )at time t =kT ,we call A (k )the interaction matrix in the presence of delays to em-phasize that A (k )is closely related to not only the available commu-nication channel but also the information transmission in the presence of delays.Let L (k )be L (k )=D (k )0A (k ),where D (k )is a diag-onal matrix with the i th diagonal entrybeing n j =1;j =i ij (k ).In fact,0(A (k )),the associated digraph of A (k ),is a spanning subgraph of the communication topology G (k )at time t =kT .To illustrate,consider a team of n =3agents.The possible communication topologies are modeled by the digraph as shown in Fig.1.Assume the communica-tion delays 21(k )and 32(k ),k2,are all larger than 1T ,while the communication topology switches periodically between Ga and Gb at each sampling instant.Clearly,A (k )=03;3at each sampling instant.However,in the special case that there is no communication delay be-tween neighboring agents,0(A (k ))=G (k ).In the case that both the communication topology and the communication delays are time in-variant,0(A (k ))=G (k )after max time steps.We say that consensus is reached for algorithm (2)if for any initial position and velocity states,and any i;j 2Vlim k !1r i (k )=lim k !1r j (k )and lim k !1v i (k )=0:It is assumed that r i (k )=r i (0)and v i (k )=v i (0)for any k <0and i;j 2V .III.M AIN R ESULTSDenote G=f G 1;G 2;...;G m g as the finite set of all possible com-munication topologies for all the n agents.In the sequel,when we men-tion the union of a group of digraphs f G i ;...;G i g G,we mean a digraph with the node set V =f 1;2;...;n g and the edge set given by the union of the edge sets of G i ,j =1;...;k .Firstly,we perform the following model transformation,which helps us deal with the consensus problem for an equivalent trans-formed discrete-time system.Denote r (k )=[r 1(k );111;r n (k )]T ,v (k )=[v 1(k );111;v n (k )]T ,x (k )=(2= )v (k )+r (k ),andy (k )=[r (k )T x (k )T ]T.Then,applying algorithm (2)and by some manipulation,(1)can be written in a matrix form asy (k +1)=40(k )y (k )+`=14`(k )y (k 0`)(3)where we get the equation shown at the bottom of the next page,and 4`(k )=T2A `(k )0n;n2T +12T 2A `(k )0n;n;`=1;2;...; max :Here in 4p (k ),p =0;1;...; max ,the ij th element of A p (k )is either equal to ij (k )if ij (k )=p ,or equal to 0otherwise and L (k )is the Laplacian matrix of the digraph of A (k ).1ObviouslyA 0(k )+A 1(k )+111+A(k )=A (k ):The following lemma will allow us to perform the convergence anal-ysis by using the product properties of row-stochastic matrices.1NoteL (k )is different from the Laplacian matrix of the communicationtopology G(k).Fig.1.Two possible communication topologies for the three agents.Lemma 1:Let d (k )be the largest diagonal element of the Lapla-cian matrix L (k ),i.e.,d (k )=max if n j =1;j =i ij (k )g .If the ve-locity damping gain and the sampling period T satisfy the following condition:4 T 0 T >2and T 01 2T d (k )(4)then 4(k )=40(k )+41(k )+111+4(k );k2+,is a row-stochastic matrix with positive diagonal elements.Proof:It follows from A 0(k )+A 1(k )+111+A(k )=A (k )=diag L (k )0L (k )that4(k )=40(k )+41(k )+111+4(k )=411(k )412(k )421(k )422(k )(5)where 411(k )=(10( =2)T +( 2=4)T 2)I n 0(T 2=2)L (k ),412(k )=(( =2)T 0( 2=4)T 2)I n ,421(k )=(( =2)T +( 2=4)T 2)I n 0((2= )T +(1=2)T 2)L (k )422(k )=(10( =2)T 0( 2=4)T 2)I n .One can easily check from (4)that all the matrices 411(k ),412(k ),421(k ),and 422(k )are nonnegative with positive di-agonal elements.That is,4(k )is a nonnegative with positive diagonal elements.Finally,it follows straightforwardly from L (k )1n =1n that 4(k )is a row-stochastic matrix.Remark 2:By some manipulation,we can get that (4)is equivalent to the following condition:1+1+8T 2d (k )2T <p 501:(6)This is achieved by solving ( T )2+2 T 04<0and T 20 02T d (k ) 0,which can be considered the quadratic inequalities in T and ,respectively.In the sequel,4(k )will be used to denote the row-stochastic matrix as described in Lemma 1.In order to make the transformed system dynamics mathematically tractable in terms of 0(A (k )),the associated digraph of the interaction matrix in the presence of delays,we need to explore the relations be-tween 0(A (k ))and the associated digraph of the transformed system matrix 0(4(k )).To this end,a new graphic method is proposed as follows.Lemma 2:Given any digraph G (V ;E ).Let G 1(V 1;E 1)be a graph with n nodes and an empty edge set,that is,V 1=f n +1;n +2;...;2n g and E 1=.Let ~G(~V ;~E )be a digraph satisfying the fol-lowing conditions:(A)~V=V [V 1=f 1;...;n;n +1;...;2n g ;(B)there is an edge from node n +i to node i ,i.e.,(n +i;i )2~",for any i 2V ;(C)if (j;i )2E ,then (j;n +i )2~Efor any i;j 2V ;i =j .Then,G has a directed spanning tree if and only if ~Ghas a directed spanning tree.Proof:Necessity:Denote G s as a directed spanning tree of the digraph G .Assume,without loss of generality,`is the root node of G s .By rules (B )and (C ),split each edge (i;j )in G s into edges (i;n +j );(n +j;j )and add edge (n +`;`)for the root node `,then we canget a directed spanning tree for ~G.Sufficiency:Let ~Gs be a directed spanning tree of ~G .Note that by the definition of ~G,the digraph G can be obtained by contracting all the edges (n +i;i );i 2V in the digraph ~G.Thus,the operation of the edge contraction on ~Gs will result in a directed spanning tree,say G s ,of the digraph G .Based on the above lemma,now we have the following result.Lemma 3:Suppose that and T satisfy the inequality in (4).Let f z 1;z 2;...;z q g be any finite subsetof +.If the union of the digraphs 0(A (z 1));0(A (z 2));...;0(A (z q ))has a directed spanning tree,then the union of digraphs 0(4(z 1));0(4(z 2));...;0(4(z q ))also has a directed spanning tree.Proof:The union of the digraphs 0(4(z 1));0(4(z 2));...;0(4(z q ))hereby is exactly the digraph0(q l =14(z l )).Because and T satisfy (4),it follows that 4(z l ),l =1;2;...;q ,is a row-stochastic (and hence nonnegative)matrix with positive diagonal entries.Note that L (z l )=diag L (z l )0A (z l ).By observing the equation in (5),we get that there exists a positive number ,say =min f q (( =2)T 0( 2=4)T 2);(2= )T +(1=2)T 2g ,such that we get (7),as shown at the bottom of the page.It thus follows from ~M 12=I n that (n +i;i )20(q l =14(z l ))for any i 2V .On the other hand,~M 21=q l =1A (z l )implies that(j;i )20(q l =1A (z l ))if and only if (j;n +i )20(ql =14(z l ))for any i;j 2V ;i =j .Combining these arguments,we knowthat the digraphs0(q l =14(z l ))and0(ql =1A (z l ))correspondto the digraphs ~G and G ,respectively,as described in Lemma 2.Note that the digraph0(q l =1A (z l ))is just the union of digraphs 0(A (z 1));0(A (z 2));...;0(A (z q )).It then follows from Lemma 2that the digraph0(q l =14(z l ))has a directed spanning tree,which proves the Lemma.Let P be the set of all n by n row-stochastic matrices.Given any row-stochastic matrix P =[p ij ]2P ,define (P )=10mini;j k min f p ik ;p jk g [25].Lemma 4: (1)is continuous on P .40(k )=102T +4T2I n 0T2(diag L (k )0A 0(k))2T 04T2In2T +4T2I n 02T +12T 2(diag L (k )0A 0(k))102T 04T2I nql =14(z l )q2T 04T2I n2T +12T 2diag q l =1L (z l )0q l =1L (z l )0Inql =1A (z l )0= ~M 11~M12~M 21~M22:(7)Proof:2:P can be viewed as a subset of metricspace n .All the functions involved in the definition of (1)are continuous,and since the operations involved are sums and mins,it readily follows that (1)is continuouson n .The restriction of a continuous function is con-tinuous,so (1)is also continuous on P .Two nonnegative matrices M and N are said to be of the same type,denoted by M N ,if they have zero elements and positive elements in the same places.To derive the main result,we need the fol-lowing classical results regarding the infinite product of row-stochastic matrices.Lemma 5:([25])Let M =f M 1;M 2;...;M q g be a finite set of n 2n ergodic matrices with the property that for each se-quence M i ;M i ;...;M i of positive length,the matrix productM i M i111M i is ergodic.Then,for each infinite sequence M i ;M i ;...there exists a column vector c2n such thatlim j !1M i M i111M i =1c T :(8)In addition,when M is an infinite set, (W )<1,where W =S k S k 111Sk,S k 2M ,j =1;2;...;N (n )+1,and N (n )(which may depend on n )is the number of different types of all n 2n ergodic matrices.Furthermore,if there exists a constant 0 d <1satisfying (W ) d ,then (8)still holds.Let d=(n 01) .Assume,in the sequel,that ;T satisfy (4= T )0 T >2and T 01 (2= )T d.Then,by Lemma 1,all possible 4(k )must be nonnegative with positive diagonal elements.In addition,since the set of all 2n ( max +1)22n ( max +1)matrices can be viewed as the metricspace [2n (+1)],for each fixed pair ;T ,all possible 4(k )compose a compact set,denoted by 7( ;T ).This is because all the nonzero and hence positive entries of 4(k )are both uniformly lower and upper bounded,which can be seen by observing the form of 4(k )in (5).Let 3(A )=f B =[b ij ]22n 22n :b ij =a ij or b ij =0;i;j =1;2;...;2n g ,and denote by 5( ;T )the set of matricesM (40;41;...;4)=40411114014I 2n 0111000I 2n 11100 0111I 2nsuch that 40;41;...;423(4(k ))and 40+41+...+4=4(k ),where 4(k )27( ;T ).The set 5( ;T )is compact,since givenany 4(k )27( ;T ),all possible choices of 40;41;...;4are finite.Let (k )=[ 1(k ); 2(k );111; 2n (+1)(k )]T =[y T (k );y T (k 01);111;y T (k 0 max )]T22n (+1).Then,there exists a matrix M (40(k );41(k );...;4(k ))25( ;T )such that system (3)is rewritten as(k +1)=M (40(k );41(k );...;4(k )) (k ):(9)Clearly,the set 5( ;T )includes all possible system matrices of system (9).2Weare indebted to Associate Editor,Prof.Jorge Cortes,for his help with a simpler proof of this lemma.Given any positive integer K,define ~5(;T )=i =1M (4i 0;4i 1;...;4i):M (1)25( ;T )and there exists a integer ;1 K suchthat the union of digraphsj =04ij ;i =1;...; ;has a directed spanningtree :~5(;T )is also a compact set,which can be derived by noticing the following facts:1)5( ;T )is a compact set;2)all possible choices of are finite since is bounded by K;3)all possible choices of the directed spanning trees are finite;and 4)given the directed spanning tree and ,the followingset:i =1M (4i 0;4i 1;...;4i):M (1)25( ;T )and the union of the digraphsj =04ij;i =1;...; ;hasthe speci ed directed spanningtreeis compact (this can be proved by following the similar proof of [27,Lemma 10]).Note that the set ~5(;T )includes all possible products of ; K ,consecutive system matrices of system (9).The following lemma is presented to prove that all the possible prod-ucts of consecutive system matrices of system (9)satisfy the result as stated in Lemma 5,which in turn allow us to use the properties of in-finite products of row-stochastic matrices from an infinite set to derive our main result.Lemma 6:If 81;...;8k 2~5(;T ),where k =N (2n ( max +1))+1,then there exists a constant 0 d <1such that(k i =18i ) d .Proof:We first prove that for any 82~5(;T );8is an er-godic matrix.According to the definition of ~5(;T ),there exist pos-itive integer (1 K),M (4i 0;4i 1;...;4i )25( ;T ),i =1;...; ,such that 8= i =1M (4i 0;4i 1;...;4i)and the union of digraphs0(j =04ij ),i =1;...; ,has a directed span-ning tree.Since M (4i 0;4i 1;...;4i )25( ;T ),j =04ij must be nonnegative matrices with positive diagonal elements.Furthermore,there exists a positive number 1such that diag(j =04ij ) I 2n ,for any M (4i 0;4i 1;...;4i )25( ;T ).Specifically,by observing (5),we can choose as=min 1;10 2T + 24T20T 22(n 01) ;10 2T 0 24T2:Combining this with the condition that the union of digraphs0(j =04ij ),i =1;...; ,has a directed spanning tree,we can prove that matrix 8is ergodic by following the proof of [26,Lemma 7].Letd =max 82~5(;T )ki =18i :From Lemma 5,we know that(k i =18i )<1.This,together withthe fact that ~5( ;T )is a compact set and (1)is continuous (Lemma4),implies d must exist and 0 d <1,which therefore completing the proof.For notational simplicity,we shall denote M (40(k );41(k );...;4(k ))by M (k )if it is self-evident from the context.Based on the preceding work,now we can present our main result as follows.Theorem 1:Assume that and T satisfy (4= T )0 T >2andT 01 (2= )T d.Then,employing algorithm (2),consensus is reached for all the agents if there exists an infinite sequence of con-tiguous,nonempty,uniformly bounded time intervals [k j ;k j +1),j =1;2;...,starting at k 1=0,with the property that the union of the di-graphs 0(A (k j ));0(A (k j +1));...;0(A (k j +101))has a directed spanning tree.Proof:We first prove that consensus can be reached for system (9)using algorithm (2).Let 8(k;k )=I 2n (+1),k 0,and 8(k;l )=M (k 01)111M (l +1)M (l ),k >l 0.Assume,without loss of generality,that the lengths of all the time intervals [k j ;k j +1),j =1;2;...,are bounded by K.It follows from Lemma 3and the condition that the union of the digraphs 0(A (k j ));0(A (k j +1));...;0(A (k j +101))has a directed spanning tree that the union of the digraphs 0(4(k j ));0(4(k j +1));...;0(4(k j +101))also has a directed spanning tree for each j2+,which,together with the proof ofLemma 6,implies that 8(k j +1;k j )=k 01k =k M (k )2~5(;T ).Since 8(k j ;0)=8(k j ;k j 01)8(k j 01;k j 02)1118(k 2;k 1),it then follows from Lemma 5and Lemma 6thatlim j !18(k j ;0)=12n (+1)wT(10)where w22n (+1)and w 0.For each m >0,let k l be the largest nonnegative integer such that k l m .Note that matrix 8(m;k l )is row stochastic,thus we have8(m;0)012n w T =8(m;k l)8(k l ;0)012n wT :The matrix 8(m;k l )is bounded because it is the product of fi-nite matrices which come from a bounded set ~5(;T ).By using (10),we immediately have lim m !18(m;0)=12n (+1)w T .Combining this with the fact that (m )=8(m;0) (0)yields lim m !1 (m )=(w T (0))12n (+1)which,in turn,implies lim m !1x (m )=(w T (0))1n and lim k !1v (m )=0,and there-fore completing the proof.Remark 3:Matrix A (k )is a somewhat complex object to study compared with the adjacency matrix A (k )(see Remark 1).It is worth noting that more general results in which the sufficient conditions for guaranteeing the final consensus are presented in terms of G (k )instead of the interaction matrix in the presence of delays can be provided if some additional conditions are imposed.For example,if in addition to the conditions on and T as that required in Theorem 1,it is further required that a certain communication topology which takes effect at some time will last for at least max +1time steps,then we can get that consensus can be reached if there exists an infinite sequence of contiguous,nonempty,uniformly bounded time intervals [k j ;k j +1),j =1;2;...,starting at k 1=0,with the property that the union of the digraphs G (k j );G (k j +1);...;G (k j +101)has a directed spanning tree.This can be observed by reconstructing a new sequence of con-tiguous,nonempty and uniformly bounded time intervals which satis-fies the condition in Theorem 1by using similar technique as that in in [26,Theor.3].IV .I LLUSTRATIVE E XAMPLEConsider a group of n =6agents interacting between the possible digraphs f Ga;Gb;Gc g (see Fig.2),all of which have 0–0.2weights.Fig.2.Digraphs which model all the possible communicationtopologies.Fig.3.Position and velocity trajectories for agents.Take and T as =2and T =0:6respectively.Assume that the communication delays ij (k )satisfies 21(k )= 32(k )= 43(k )=1T s , 52(k )= 54(k )=2T s ,while 65(k )= 61(k )=3T s ,for any k2+.Moreover,we assume the switching signal is periodically switched,every 3T s in a circular way from Ga to Gb ,from Gb to Gc ,and then from Gc to Ga .Obviously,the union of the digraphs 0(A (k ))across each time in-terval of 9T s is precisely the digraph G d in Fig.2,which therefore has a directed spanning tree.Fig.3shows that consensus is reached for algorithm (2),which is consistent with the result in Theorem 1.V .C ONCLUSIONS AND F UTURE W ORKIn this technical note,we have investigated a discrete-time second-order consensus algorithm for networks of agents with nonuniform and time-varying communication delays under dynamically changing com-munication topologies in a sampled-data setting.By employing graphic method,state argumentation technique as well as the product proper-ties of row-stochastic matrices from an infinite set,we have presented a sufficient condition in terms of the associated digraph of the interac-tion matrix in the presence of delays for the agents to reach consensus.Finally,we have shown the usefulness and advantages of the proposed result through simulation results.It is worth noting that the case with input delays is an interesting topic which deserves further investigation in our future work.。

自动原理控制专业英语词汇线性反馈系统的稳定性辅助多项式：Auxiliary polynomial相对稳定性：Relative stabilityRouth-Hurwitz判据：Routh-Hurwitz criterion稳定性：Stability稳定系统：Stable system根轨迹法出射角：Angle of departure渐近线：Asymptote渐近中心：Asymptote centroid分离点：Breakaway point轨迹：Locus根轨迹的条数：Number of separate loci参数设计：Parameter design根轨迹：Root locus根轨迹法：Root locus method实轴上的根轨迹段：Root locus segments on the real axis根灵敏度：Root sensitivity频率响应方法带宽：BandwidthBode 图：Bode plot截止频率：Break frequency转折频率：Corner frequency分贝(db)：Decibel (DB)Fourier变换：Fourier transform频率响应：Frequency response对数幅值：Logarithmic magnitude对数坐标图：Logarithmic plot频率响应的最大值：Maximum value of the frequency最小相位：Minimum phase固有频率：Natural frequency非最小相位：Nonminimum phase极坐标图：Polar plot谐振频率：Resonant frequency频率特性函数：Transfer function in the frequency domain频域稳定性Cauchy定理：Cauchy thorem闭环频率响应：Closed-loop frequency response保角映射：Conformal mapping围线映射：Conrour map增益裕度：Gain marginNichols图：Nichols chartNyquist 稳定性判据：Nyquist stability criterion相角裕度：Phase margin幅角原理：Principle of the argument时延：Time delay反馈控制系统设计串联校正网络：Cascade compensation network校正：Compensation数字控制系统幅值量化误差：Amplitude quantization error数字计算机校正网络：Digital computer compensator数字控制系统：Digital control system采样数据：Sampled data数据采样系统：Sampled-data system式样周期：Sampling period数据采样系统的稳定性：Stability of a sampled-data system z平面：z-planez变换：z-transforma. c .balance indicator,交流平衡指示器a. c. bridge,交流电桥a. c. current calibrator,交流电流校准器a. c. current distortion,交流电流失真a. c. induced polarization instrument,交流激电仪a. c. potentiometer,交流电位差计a. c. resistance box,交流电阻箱a. c. standard resistor,交流标准电阻器a. c. voltage distortion,交流电压校准器a. c. voltage distortion,交流电压失真Abbe comparator,阿贝比长仪aberration,象差ability of anti prereduced component,抗先还原物质能力ablative thickness transducer [sensor],烧蚀厚度传感器abrasion testing machine,磨损试验机absolute calibration,绝对法校准absolute coil,独立线圈absolute error,绝对误差(absolute)error of measurement,测量的（绝对）误差absolute gravimeter,绝对重力仪absolute gravity survey,绝对重力测量absolute ,绝对分辨率absolute salinity,绝对盐度absolute stability,绝对稳定性absolute stability of a linear system,线性系统的绝对稳定性absolute static pressure of the fluid,流体绝对静压absolute temperature scale,绝对温标absorbance,吸光度absorbed current image,吸收电流象absorptance,吸收比absorptiometer,吸收光度计absorption cell,吸收池absorption coefficient,吸收系数absorption correction,吸收修正absorption edges,吸收边absorption factor,吸收系数absorption spectrum,吸收光谱absorption X-ray spectrometry,吸收X射线谱法absorptivity,吸收率absorptivity of an absorbing,吸引材料的吸收率abstract system,抽象系统abundance sensityivity,丰度灵敏度AC-ACLVDT displacement transducer,交流差动变压器式位移传感器accelerated test,加速试验accelerating voltage,加速电压acceleration,加速度acceleration error coefficient,加速度误差系数acceleration of gravity,重力加速度acceleration simulator,加速度仿真器acceleration transducer[sensor],加速度传感器accelerometer,加速度计acceptance of the mass filter,滤质器的接收容限acceptance test,验[交]收检验access,存取 access time,存取时间accessibility,可及性accessories of testing machine,试验机附件accessory(for a measuring instrument),（测量仪表的）附件accessory ,水声信标acoustic current meter,声学海流计acoustic element,声学元件acoustic emission,声发射acoustic emission amplitude,声发射振幅acoustic emission analysis system,声发射分析系统acoustic emission detection system,声发射检测系统acoustic emission detector,声发射检测仪acoustic emission energy,声发射能量acoustic emission event,声发射事件acoustic emission preamplifier,声发射前置放大器acoustic emission pulser,声发射脉冲发生器acoustic emission rate,声发射率acoustic emission signal processor[conditioner],声发射信号处理器acoustic emission rate,声发射信号acoustic emission source location and analysis system,声发射源定位及分析系统acoustic emission source location system,声发射源定位系统acoustic emission source,声发射源acoustic emission spectrum,声发射频谱acoustic emission technique,声发射技术acoustic emission transducer[sensor],声发射换能器acoustic fatigue,声疲劳acoustic impedance,声阻抗acoustic logging instrument,声波测井仪acoustic malfunction,声失效acoustic matching layer,声匹配层acoustic(quantity)transducer[sensor],声（学量）传感器acoustic ratio,声比acoustic releaser,声释放器acoustic resistance,声阻acoustic thermometer,声学温度计；声波温度表acoustic tide gauge,回声验潮仪acoustic transponder,声应答器acoustical frequency electric,声频大地电场仪acoustical -beam scanning,电子束扫描声全息acoustical ,布拉格衍射声成像acoustical impedance method,声阻法acoustical lens,声透镜acoustically transparent pressure vessel,透声压力容器acquisition time,取数据时间actinometer,光能计；直接日射强度表；日射表(active)energy meter,（有功）电度表active gauge length,有效基长active gauge width,有效基宽active metal indicated electrode,活性金属指示电极active remote sensing,主动遥感active transducer[sensor],有源传感器activity,活度 activity coefficient,活度系数actual material calibration,实物校准actual time of observation,实际观测时间actual transformation ratio of voltage transformer,电压互感器的实际变化actral transformation ratio of current transformer,电流互感器的实际变化actual value,实际值actual voltage ratio,实际电压比actuator,执行机构；驱动器actuator bellows,执行机构波纹管actuator load,执行机构负载actuator power unit,执行机构动力部件actuator sensor interface(ASI),执行器传感器接口actuator shaft,执行机构输出轴actuator spring,执行机构弹簧actuator stem,执行机构输出杆actuator stem force,执行机构刚度actuator travel characteristic,执行机构行程特性adaptation layer,适应层adaptive control,（自）适应控制adaptive control system,适应控制系统adaptive controller,适应控制器adaptive prediction,适应预报adaptive telemetering system,适应遥测系统adder,加法器addition method,叠加法additional correction,补充修正additivity of mass spectra,质谱的可迭加性address,地址 adiabatic calorimeter,绝热式热量计adjust buffer total ion strength,总离子强度调节缓冲剂adjustable cistern barometer,动槽水银气压表adjustable relative time,调整保留时间adjusted retention volume,调整保留体积adjuster,调整机构；调节器adjustment,调整adjustment bellows,调节波纹管adjustment device,调整装置adjusting pin,校正针adsorbent,吸附剂adsorption chromatography,吸附色谱法aerial camera,航空照相机aerial remote sensing,航空遥感aerial surveying camera,航摄仪aerodynamic balance,空气动力学天平aerodynamic noise,气体动力噪声aerograph,高空气象计aerogravity survey,航空重力测量aerometeorograph,高空气象计aerosol,县浮微料；气溶胶aging of column,柱老化agitator,搅拌器agricultural analyzer,农用分析仪air-borne gravimeter,航空重力仪air capacitor,空气电容器air consumption,耗气量air damper,空气阻尼器air-deployable buoy,空投式极地浮标air-drop automatic station,空投自动气象站air duct,风道air gun,空气枪air inlet,进风口air lock,气锁阀air-lock device,锁气装置air outlet,回风口air pressrue balance,空气压力天平air pressure test,空气压力试验air sleeve,风（向）袋air temperature,气温air-tight instrument,气密式仪器仪表air to close,气关air to open,气开airborne electromagnetic system;AEM system,航空电磁系统airborne flux-gate magnetometer,航空磁通门磁力仪airborne gamma radiometer,航空伽玛辐射仪airborne gamma spectrometer,航空伽玛能谱仪airborne infrared spectroradiometer,机载红外光谱辐射计airborne optical pumping magnetometer,航空光泵磁力仪airborne proton magnetometer,航空甚低频电磁系统airborne XBT,机载投弃式深温计airgun controller,气控制器airmeter,气流表alarm summery panel,报警汇总画面alarm unit,报警单元albedograph,反射计alcohol thermometer,酒精温度表algorithm,算法 algorithmic language,算法语言alidade,照准仪alignment instrument,准线仪alkali flame ionization detector(AFID),碱焰离子化检测器alkaline error,碱误差alkalinity of seawater,海水碱度all-sky camera,全天空照相机all-weather wind vane and anemometer,全天候风向风速计allocation problem,配置问题；分配问题allowable load impedance,允许的负载阻抗allowable pressure differential,允许压差allowable unbalance,许用不平衡量alpha spectrometer,α粒子能谱仪alternating[exchange]load,交变负荷alternating-current linear variable differential transformer(AC-ACLVDT), 交流极谱仪alternating temperature ,环境振动ambiguity error,模糊误差ammeter,电流表ammonia(pressure)gauge,氨压力表amount of precipitation,雨量amount of unbalance,不平衡量amount of unbalance indicatior,不平衡量指示器ampere-(AM),幅度调制；调幅amplitude-phase error,幅相误差amplitude ratio-phase difference instrument,振幅比—相位差仪amplitude response,幅值响应analog computer,模拟计算机analog control,模拟控制analog data,模拟数据analog deep-level seismograhp,模拟深层地震仪analog input,模拟输入analog magnetic tape record type strong-motion instrument,模拟磁带记录强震仪analog model,模拟模型analog output,模拟输出analog seismograph tape recorder,模拟磁带地震记录仪analog simulation,模拟仿真analog stereopotter,模拟型立体测图仪analog superconduction magnetometer,模拟式超导磁力仪analog system,模拟系统analog telemetering system,模拟遥测系统analog-to-digital conversion accuracy,模-数转换精确度analog-to-digital conversion rate,模-数转换速度analog transducer[sensor],模拟传感器analogue computer,模拟计算单元analogue date,模拟数据analogue measuring instrument,模拟式测量仪器仪表analogue representation of a physical quantity,物理量的模拟表示analogue signal,模拟试验analogue-digital converter;AD converter,模-数转换器；AD转换器analogue-to-digital conversion,模数转[变]换analysis of simulation experiment,仿真实验分析analytical balance,分析天平analytical electron microscope,分析型电子显微镜analytical gap,分析间隙analytical instrument,分析仪器analytical line,分析线analytical plotter,解析测图仪analyzer tube,分析管anechoic chamber,消声室；电波暗室anechoic tank,消声水池anemograph,风速计anemometer,风速表anemometer meast,测风杆anemometer tower,测风塔aneroid barograph,空盒气压计aneroid barometer,空盒气压表；空盒气压计aneroidograph,空盒气压计angle,角度angle beam technique,斜角法angle beam testing,斜角法angle form,角型angle of attach,冲角angle of field of view,视场角angle of incidence,入射角angle of refraction,折射角angle of spread,指向角；半扩散角angle of view of telescope,望远镜视场角angle of X-ray projiction,X射线辐射圆锥角angle probe,斜探头angle resolved electron spectroscopy(ARES),角分辨电子谱法angle strain,角应变angle transducer[sensor],角度传感器anglg-attack transducer[sensor],迎角传感器angle valve,角形阀angular acceleration,角加速度angular acceleration transducer[sensor],角加速度传感器angular displacement,角加速度传感器angular displacement,角位移angular displacement grationg,角位移光栅angular encoder,角编码器angular sensitivity,角灵敏度angular velocity transducer[sensor],角速度传感器annular coil clearance,环形线圈间隙annular space,环形间隙annunciator,信号源anode,阳极answering,应答anti-cavitation valve,防空化阀anti-contamination device,防污染装置anti-coupling bi-frequency induced polarization instrument,抗耦双频激电仪anti-magnetized varistor,消磁电压敏电阻器antiresonance,反共振antiresonance frequency,反共振频率anti-stockes line,反斯托克线aperiodic dampong,非周期阻尼；过阻尼aperiodic vibration,非周期振动aperture,光阑aperture of pressure difference,压差光阑aperture photographic method,针孔摄影法aperture stop,孔径光栏aperture time,空隙时间apparatus for measuring d.c.magnetic characteristic with ballistic galvanometer, 冲击法直流磁特性测量装置apparent temperature,表观温度appearance potentical,出现电位appearance potential spectrometer,出现电热谱仪appearance potential spectrometer(APS),出现电热谱法application layer(AL),应用层application layer protocol specification,应用层协议规范application layer service definition,应用室服务定义application software,应用软件approval,批准approximate absolute temperature scale,近似绝对温标aqueous vapour,水汽arc suppressing varstor,消弧电压敏电阻器arctic buoy,极地浮标area effect,面积影响area location,区域定位area of cross section of the main air flow,主送风方向横截面积argon-ion gun,氩离子枪annular chamber,环室argon ionization detector,氩离子化检测器arithmetic logic unit(ALU),算术逻辑运算单元arithmetic mean,算术平均值arithmetic weighted mean,算术加权平均值arithmetical mean deviation of the(foughness)profile,(粗糙度）轮廓的算术平均偏差arm error,不等臂误差armature,动铁芯array,阵，阵列array configuration,阵排列arrester varistor,防雷用电压敏电阻器articulated robot,关节型机器人artificial defect,人工缺陷artificial environment,人工环境artificial field method instrument,人工电场法仪器artificial intelligence,人工智能artificial seawater,人工海水ash fusion point determination meter,异步通信接口适配器asynchronous input,异步输入asynchronous transmission,异步传输atmidometer,蒸发仪，蒸发表atmometer,蒸发仪；蒸发表atmoradiograph,天电强度计atmosphere,气氛atmospheric counter radiation,天气向下辐射atmospheric electricity,大气电atmospheric opacity,大气不透明度atmospheric pressure,气压atmospheric pressure altimeter,气压高度计atmospheric pressure ionization(API),大气压电离atmospherics,天电；远程雷电atom force microscope,原子力显微镜atomic absorption spectrometry,原子吸收光谱法atomic fluorescence spectrophotometer,原子荧光光度计atomic fluorescence spectrometry,原子荧光光谱法atomic mass unit,原子质量单位atomic number correction,原子序数修正atomin spectrum,原子光谱atomic-absorption spectrophotometer,原子吸收分光光度计atomization,原子化atomizer,原子化器attenuation,衰减attenuation coefficient,衰减系数attenuation length,衰减长度attenuator,衰减器attitude,姿态attitude transducer[sensor],姿态传感器audio monitor,监听器audio-frequency spectrometer,声频频谱仪audit,审核Auger electron energy spectrometer(AEES),俄歇电子能谱仪Auger electron image,俄歇电子象Auger electron spectrometer,俄歇电子能谱仪Auger electron spectroscopy(AES),俄歇电子能谱法aurora,极光auto-compensation logging instrument,电子自动测井仪auto-compound current transformer,自耦式混合绕组电流互感器auto-polarization compensator,自动极化补偿器autocorrelation function,自相关函数automatic a.c.,d.c.B-H curve tracer,交、直流磁特性自动记录装置automatic balancing machine,自动平衡机automatic control,自动控制automatic control souce of vacuum,真空自动控制电源automatic control system,自动控制系统automatic data processing,自动数据处理automatic exposure device,自动曝光装置automatic feeder for brine,盐水溶液自动补给器automatic focus and stigmator,自动调焦和消象散装置automatic level,自动安平水准仪automatic levelling compensator,视轴安平补偿器automaticmanual station;AM station,自动手动操作器automatic programming,自动程度设计automatic radio wind wane and anemometer,无线电自动风向风速仪automatic railway weigh bridge,电子轨道衡automatic scanning,自动扫查automatic spring pipette,自动弹簧式吸液管automatic testing machine,自动试验机automatic titrator,自动滴定仪automatic tracking,自动跟踪automatic vertical index,竖直度盘指标补偿器automatic weather station,自动气象站automation,自动化automaton,自动机auxiliary attachment,辅件auxiliary controller bus(ACB),辅助控制器总线auxiliary crate controller,辅助机箱控制器auxiliary devices,辅助装置auxiliary equipment(of potentiometer),(电位差计的）辅助设备auxiliary gas,辅助气体auxiliary output signal,辅助输出信号auxiliary storage,辅助存储器auxiliary terminal,辅助端auxiliary type gravimeter,助动型重力仪availability,可用性available time,可用时间average,平均值average availability,平均可用度average nominal characteristic,平均名义特性average sound level,平均声级average value of contarmination,污染的平均值average wind speed,平均风速axial clearance,轴向间隙axial current flow method,轴向通电法axial load,轴向载荷axial sensitivity,轴向灵敏度axial vibration,轴向振动axis of rotation,摆轴；旋转轴axix of strain gauge,应变计[片]轴线B-scope,B型显示back flushing,反吹background,后台，背景，本底background current,基流background mass spectrum,本底质谱background noise,背景噪声background processing,后台处理background program,后台程度Backman thermometer,贝克曼温度计backscattered electron image,背散射电子象backward channel,反向信道baffle wall,隔板balance,天平balance for measuring amount of precipitation,水量秤balance output,对称输出balance quality of rotor,转子平衡精度balance wieght,平衡块balanced plug,平衡型阀芯balancing,平衡balancing machine sensitivity,平衡机灵敏度balancing machine,平衡机balancing speed,平衡转速ball pneumatic dead wieght tester,浮球压力计ball screw assembly,滚珠丝杠副ball valve,球阀ballistic galvanometer,冲击栓流计band,频带bandwidth,带宽band width of video amplifier,视频放大器频宽bar primary bushing type current transformer,棒形电流互感器barograph,气压计barometer cistern,气压表水银槽barometer,气压表barometric correction,气压表器差修正barometrograph,空盒气压计barothermograph,气压温度计barrel distortion,桶形畸变；负畸变base,基底base line,基线base peak,基峰base unit(of measurement),基本（测量）单位baseband LAM,基带局域网baseline drift,基线漂移baseline noise,基线噪声baseline potential,空白电位baseline value,空白值basic NMR frequency,基本核磁共振频率basic standard,基础标准batch control,批量控制batch control station,批量控制站batch inlet,分批进样batch of strain gauge,应变计[片]批batch processing,成批处理batch processing simulation,批处理仿真Baud,波特beam,横梁；声速beam deflector,电子束偏转器beam path distance,声程beam ratio,声束比beam spot diameter,束斑直径beam-deflection ultrasonic flowmeter,声速偏转式超声流量计beam-loading thermobalance,水平式热天平bearing,轴承；刀承bearing axis,轴承中心线bdaring support,支承架beat frequency oscillator,拍频振荡器beat method(of measurement),差拍（测量）法Beaufort scale,蒲福风级Beckman differential thermometer,贝克曼温度计bed,机座Beer' law,比尔定律bell manometer,钟罩压力计bell prover,钟罩校准器bellows,波纹管bellows(pressure)gauge,波纹管压力表bellows seal bonnet,波纹管密封型上阀盖bench mark,水准点bending strength,弯曲强度bending vibration,弯曲振动bent stem earth thermometer,曲管地温表Besson nephoscope,贝森测云器betatron,电子回旋加速器；电子感应加速器bezel ring,盖环bias voltage,偏压bi-directional vane,双向风向标；双风信标bilateral current stabilizer,双向稳流器bimetallic element,双金属元件bimetallic instrument,双金属式仪表bimetallic temperature transducer[sensor],双金属温度传感器bimetallic thermometer,双金属温度计binary coded decimal(BCD),二-十进制编码binary control,二进制控制binary digital,二进制数字binary elastic scattering event,双弹性散射过程binary elastic scattering peak,双弹性散射峰binary element,二进制元binary signal,二进制信号biomedical analyzer,生物医学分析仪biochemical oxygen demand (BOD)microbial transducer[sensor],微生物BOD传感器 biochemical oxygen demand meter for seawater,海水生化需氧量测定仪biochemical quantity transducer[sensor],生化量传感器biological quantity transducer[sensor],生物量传感器biosensor,生物传感器bird receiving system,吊舱接收系统bit,比特；位bit error rate,误码率bit serial,位串行bit-serial transducer[sensor],血钙传感器blood carbon dioxide transducer[sensor],血液二氧化碳传感器blood chloried ion transducer[sensor],血氯传感器blood electrolyte transducer[sensor],血液电解质传感器blood flow transducer[sensor],血流传感器blood gas transducer[sensor],血气传感器blood-group immune transducer[sensor],免疫血型传感器blood oxygen transducer[sensor],血氧传感器blood PH transducer[sensor],血液PH传感器blood potassium ion transducer[sensor],血钾传感器blood-pressure transducer[sensor],血压传感器blood sodium ion transducer[sensor],血钠传感器blood-volume transducer[sensor],血容量传感器blower device,鼓风装置bluff body,阻流体Bode diagram,博德图body temperature transducer,体温传感器bolometer,辐射热计；热副射仪bomb gauge,粘贴式应变计bonnet,上阀盖boomerang grab,自返式取样器boomerang gravity corer,自返式深海取样管booster,增强器bore(of liquid-in-glass thermometer),（玻璃温度计的）内孔borehole acoustic television logger,超声电视测井仪borehole compensated sonic logger,补偿声波测井仪borehole gravimeter,井中重力仪borehloe gravimetry,井中重力测量borehole thermometer,井温仪bottorm echo,底面反射波bottom flange,下阀盖bottom-loading thermobalance,下皿式热天平bottom surface,底面Bouguer's law,伯格定律Bourdon pressure sensor,弹簧管压力检测元件Bourdon tube,弹簧管；波登管Bourdon tube(pressure)gauge,弹簧管压力表box gauge,箱式验潮仪BP-scope,BP 型显示Bragg's equation,布拉格方程braking time,制动时间braking torque(of an integrating instrument),（积分式仪表的）制动力矩branch,分支branch cable,支线电缆breakdown voltage rating,绝缘强度breakpoint,断点breather,换气装置bremsstrahlung,韧致辐射bridge,桥接器bridge's balance range,电桥平衡范围bright field electron image,明场电子象bridge for measuring temperature,测温电桥bridge resistance,桥路电阻brightness,亮度Brinell ,宽带随机振动broad band spectrum,宽波段broadcast,广播BT-calibrationg installation,深温计[BT]检定装置bubble,水准泡bubble-tube,吹气管bucket thermometer,表层温度表buffer,缓冲器buffer solution,缓冲溶液buffer storage,缓冲存储器built-in galvanometer,内装式检流计built-in-weigthts,挂码bulb,温包；感温泡bulb(of filled system themometer),（压力式温度计的）温包bulb(of liquid-in-glass thermometer),（玻璃温度计的）感温泡bulb length(of liquid-in-glass thermometer),（玻璃温度计的）感温泡长度bulk type semiconductor strain gauge,体型半导体应变计bulk zinc oxide varistor,体型氧化锌电压敏电阻器bump,连续冲击bump test,连续冲击试验；颠簸试验bump testing machine,连续冲击台buoy,浮标buoy array,浮标阵buoy float,浮标体buoy motion package,浮标运动监测装置buoy station,浮标站buoyancy correction,浮力修正buoyancy level measuring device,浮力液位测量装置burden(of a instrument transformer),（仪用互感器的）负载burning method,燃烧法burst acoustic emission signal,突发传输bus,总线bus line，总线bus master,总线主设备bus mother board,总线母板bus network,总线网bus slave,总线从设备bus topology,总线拓扑bus type current transformer,母线式电流互感器bushing type current transformer,套管式流互感器busy,忙busy state,忙碌状态butterfly valve,蝶阀 by-pass,旁路by-pass injector,旁通进样器by-pass manifold,旁路接头by-pass valve,旁通阀Byram anemometer,拜拉姆风速表byte,字节byte frame,字节帧byte serial,字节串行byte-serial highway,字节串行住信处公路集散控制系统——Distributed Control System（DCS）现场总线控制系统——Fieldbus Control System（FCS）监控及数据采集系统——Supervisory Control And Data Acqusition（SCADA）可编程序控制器——Programmable Logic Controller（PLC）可编程计算机控制器——Programmable Computer Controller（PCC）工厂自动化——Factory Automation（FA）过程自动化——Process Automation（PA）办公自动化——Office Automation（OA）管理信息系统——Management Information System（MIS）楼宇自动化系统——Building Automation System人机界面——Human Machine Interface（HMI）工控机——Industrial Personal Computer（IPC）单片机——Single Chip Microprocessor计算机数控（CNC）远程测控终端——Remote Terminal Unit（RTU）上位机——Supervisory Computer图形用户界面（GUI）人工智能——Artificial Intelligent（AI）智能终端——Intelligent Terminal模糊控制——Fuzzy Control组态——Configuration仿真——Simulation冗余——Redundant客户服务器——ClientServer网络——Network设备网——DeviceNET基金会现场总线——foundation fieldbus（FF）现场总线——Fieldbus以太网——Ethernet变频器——Inverter脉宽调制——Pulse Width Modulation（PWM）伺服驱动器——Servo Driver软起动器——Soft Starter步进——Step-by-Step控制阀——Control Valver流量计——Flowmeter仪表——Instrument记录仪—— Recorder传感器——Sensor智能传感器——Smart Sensor智能变送器——Smart Transducer虚拟仪器——Virtual Instrument主站从站——Master StationSlave station操作员站工程师站管理员站——Operator StationEngineer StationManager Station集散控制系统——Distributed Control System（DCS）现场总线控制系统——Fieldbus Control System（FCS）监控及数据采集系统——Supervisory Control And Data Acqusition（SCADA）可编程序控制器——Programmable Logic Controller（PLC）可编程计算机控制器——Programmable Computer Controller（PCC）工厂自动化——Factory Automation（FA）过程自动化——Process Automation（PA）办公自动化——Office Automation（OA）管理信息系统——Management Information System（MIS）楼宇自动化系统——Building Automation System人机界面——Human Machine Interface（HMI）工控机——Industrial Personal Computer（IPC）单片机——Single Chip Microprocessor计算机数控（CNC）远程测控终端——Remote Terminal Unit（RTU）上位机——Supervisory Computer图形用户界面（GUI）人工智能——Artificial Intelligent（AI）智能终端——Intelligent Terminal模糊控制——Fuzzy Control组态——Configuration仿真——Simulation冗余——Redundant客户服务器——ClientServer网络——Network设备网——DeviceNET基金会现场总线——foundation fieldbus（FF）现场总线——Fieldbus以太网——Ethernet变频器——Inverter脉宽调制——Pulse Width Modulation（PWM）伺服驱动器——Servo Driver软起动器——Soft Starter步进——Step-by-Step控制阀——Control Valver流量计——Flowmeter仪表——Instrument记录仪—— Recorder传感器——Sensor智能传感器——Smart Sensor智能变送器——Smart Transducer虚拟仪器——Virtual Instrument主站从站——Master StationSlave station操作员站工程师站管理员站——Operator StationEngineer StationManager Station battery light kit 电池式灯具lamp lens 灯玻璃landing weight 卸货重量letter of indemnity | | trust receipt 赔偿保证书(信托收据range indicator 距离指示器short shipment | | goods short shipped | | goods shut out | | shut-outs 退关SMT Inductors 表面贴电感器STM-N:Synchronous Transport Module level-N 同步传送模块(electric) resistor 电阻器(With) Best Regard 谨致问候3D coordinate measurement 三次元量床A 交流电流失真A.C.powered lamp 交流供电的灯AC adaptor 电源适配器AD；analog to digital 模拟数字转换aberration 光行差橡差abnormal low-voltage arc 反差低压电弧abnormal voltage 反常电压异常电压Abradant material 研磨材料Abrasion test 磨损试验abrasion test 耐磨损性试验abrasive action 磨损作用abrasive blast equipment 喷砂设备Abrasive blast system 喷砂清理系统ABS American Bureau of Standard 美国标准局Absolute Colorimetric 绝对色度absolute value 绝对值absolute velocity 绝对速度absolute wave meter 绝对波长表absorption tube 吸收管吸收试验管absorption wave meter 吸收式波长计absorption wavemeter 吸收式波长计absorption wavetrap 吸收陷波器absorptive 吸收的absorptive power 吸收本领absorptivity 吸收率ac induced polarization instrument 交流激电仪ac potentiometer 交流电位差仪ACalternating current 交流交流电academician，association，协会ACC Automatic Centering Control 自动控制中心accelerated life test 快速寿命测试accent lighting 重点照明Acceptability Criteria 验收Acceptable life 有效使用寿命Acceptance criteria 验收标准acceptance specification 验收规范Acceptance test specification 验收测试规范worldlightingtrade Skype即时通讯工具Access panel 罩板accommodate 调节accommodation 调适accreditation 认可accreditation of testing laboratory 测试实验室的认可accumulator 储线器补偿器accuracy 精确度准确度accuracy control 精确控制accuracy grade 精度等级accuracy life 精确度寿命accuracy rating 精确度限acid rinsing shop-stamping warehouse 酸洗工段房-冲压库Acid-proof paint 耐酸涂料耐酸油漆Acid-proof paint 耐酸涂料耐酸油漆acoustic reflection shell 声反射罩ACPI：Advanced Configuration and Power Interface 高级电源配置电源接口acquisition price 收购价Across frequency 交叉频率分频频率Acrylic fitting 压克力配件acrylic plastic glazing 丙烯酸有机玻璃ACST access time 存取时间acting area(spot) lighting 舞台前台（聚光）照明activated electrode 激活电极activated phosphor 激活荧光粉Active 主动的，有源的，有效的，运行的Active Area 可读取范围active market 买卖活跃的市场active power 有效功率active probe 有效探头active scanning time 有效扫描时间active voltage 有效电压actual life 有效寿命actual transformation ratio of a current (voltage) transformer 电流互感器的实际电流(电压)比actual transformation ratio of a current (voltage) transformer 流互感器的实际电流(电压)比adaptable automobile modestyle 适用车型KENFOR Global Lighting Sourcing Centreadaptable voltage 适用电压adaptablesuitable tube''s current 适用灯管电流adaptation 顺应adapting luminance （视觉）亮适用性adaptive control system 适应控制系统adaptive controller 适应控制器adaptive prediction 适应预报adaptive temperature 适应温度Adaptoradapters 适配器转换器ADCanalog to digital ... Voltage 压敏电阻器additional 附加的额外的补充的additional cost 额外费用additional exposure 辅助曝光additional lighting 辅助照明adiabatic 绝热的adjustable pressure conveyor 调压输送机中国灯饰商贸网中文版adjustable spot lamp 可调聚光灯Adjuster nuts 调节器adjusting 调整adjusting chromaticity 调整色度adjusting chromaticityadjusting luminance 调整亮度adjusting cursor blink rate 调整光标闪烁速度adjustment for illumination 照明调节照度调整admissible burning position （灯的）允许燃点位置advanced ignition 预热启动Advanced Programmable Interrupt Controllers APICs 高级可编程中断控制器advertising lighting 广告照明Aerogel Capacitors 气凝胶电容Aerogel Capacitors 气凝胶电容aeruginous 绿青色的AF audio frequency 音频控制AFC active field control 自动频率控制"AFC automaticfrequency control " 声场控制afterglow 余晖age 寿命老化灯老炼age 中国灯饰商贸网英文版ageing 老化处理agent，deputize，substitute，supply，surrogate，agency，agent，succedaneum 代理商、加盟商aggregate width 总宽度aging 老炼老化aging condition 老炼条件aging rack 老炼台aging rate 老化速率agreeable luminous environments 适宜的照明环境aiming of 空调工作状况air discharge 空气放电air freight 空运air 通风装置air 全玻璃结构all-glass ion gauge 周围条件ambient gas 周围气体ambient characteristic 环境光反射特性ambient light rejection characteristic 环境照明抑制特性ambient lightillumination 环境照度ambient lighting 周围照明ambient pressure 环境压力ambient pressure error 环境压力误差ambient temperature 环境温度ambient temperature range 环境温度范围ambient temperatureenvironment temperature 环境温度中国灯饰商贸网产品展厅ambient thermostatic switch 环境温度恒温ambient vibration 环境振动ambiguity error 模糊误差amethystpurple 紫色ammeter 电流表ampere 电流安培amplifiermagnifier 放大器anacamptometer 反射计anaclasimeter 屈光检查计analog circuit 等效电路模拟电路Analysis and Design of Analog Integr-ated Circuits 模拟集成电路的分析和设计analysis certificate 分析化验证书angle fitting 弯头angle lighting fitting 定向照明灯具angle of adjustment （聚光灯的）调整角度。

Control system 控制系统An interconnection of components forming a system configuration that will provide a desired response.Absolute stability 绝对稳定A system description that reveals whether a system is stable or not stable without consideration of other system attributes such as degree of stability.Relative stability 相对稳定The property that is measured by the relative real part of each root or pair of roots of the characteristic equation.Stable 稳定system A dynamic system with a bounded system response to a bounded input.Principle of superposition 叠加原理The law that states that if two inputs are scaled and summed and routed through a linear, time-invariant system, then the output will be identical to the sum of outputs due to the individual scaled inputs when routed through the same system.Decibel (dB) 分贝The units of the logarithmic gain.Phase margin 相位裕量The amount of phase shift of the L(jto) at unity magnitude that will result in a marginally stable system with intersections of the —1 + /0 point on the Nyquist diagram.Gain margin 增益裕量The increase in the system gain when phase = -180° that will result in a marginally stable system with intersection of the - 1 + /0 point on the Nyquist diagram.Bandwidth 带宽The frequency at which the frequency response has declined 3 dB from its low-frequency value.Sampled data 采样Data obtained for the system variables only at discrete intervals. Data obtained once every sampling period.Sampled-data system 采样系统A system where part of the system acts on sampled data (sampled variables). Stability of a sampled-data system 采样系统稳定性The stable condition exists when all the poles of the closed-loop transfer function T(z) are within the unit circle on the z-plane.Zero-order hold 零阶保持器A mathematical model of a sample and data hold operation whose input-output transfer func- 1 - e'sT tion is represented by G n{s) = .Sampling period 采样周期The period when all the numbers leave or enter the computer. The period for which the sampled variable is held constant.Closed-loop feedback control system 闭环反馈控制系统A system that uses a measurement of the output and compares it with the desired output to control the process.Disturbance 扰动信号An unwanted input signal that affects the output signal.Block diagrams 框图Unidirectional, operational blocks that represent the transfer functions of the elements of the system.Characteristic equation 特征方程The relation formed by equating to zero the denominator of a transfer function.Closed-loop transfer function 闭环传函A ratio of the output signal to the input signal for an interconnection of systems when all the feedback or feedfoward loops have been closed or otherwise accounted for. Generally obtained by block diagram or signal-flow graph reduction.Critical damping 临界阻尼The case where damping is on the boundary between underdamped and overdamped.Damped oscillation 阻尼震荡An oscillation in which the amplitude decreases with time.Damping ratio 阻尼比A measure of damping. A dimensionless number for the second-order characteristic equation.Frequency response 频率响应The steady-state response of a system to a sinusoidal input signal.Automation 自动化The control of a process by automatic means.Closed-loop feedback control system 闭环反馈控制系统A system that uses a measurement of the output andcompares it with the desired output to control the process.Feedback signal 反馈信号A measure of the output of the system used for feedback to control the system. Multiloop feedback control system 多回路反馈控制系统A feedback control system with more than one feedback control loop.Negative feedback 负反馈An output signal fed back so that it subtracts from the input signal.Positive feedback 正反馈An output signal fed back so that it adds to the input signal.Actuator 执行机构The device that causes the process to provide the output. The device that provides the motive power to the process.。

「FDA-cGMP问答」实验室控制【前篇】文章来源FDA，由珐成制药系统工程（上海）有限公司范宇翻译原创文章，欢迎转帖；尊重原创，从注明出处开始转帖请注明：GMP验证及自动化“FDA-cGMP 问答系列”，该系列选取美国FDA对设备、设施、QC等方面的问题和解决方案，并按不同类型分篇章的翻译。

它山之石，可以攻玉，我们希望通过我们的翻译，让更多人了解国际通行的cGMP的问题和对策，从而学习、反思我们自己平时工作中的不足，提升质量管理意识。

不积跬步，无以至千里，我们一起努力，为制药行业而奋斗吧！中文翻译仅供参考，如有异议请以原文为准1、许多龙头生产商的分析天平都提供内置的“自动校准”功能。

这样的自动校准程序是否可以信赖，并取代外部的性能检查？如果不可以，那么校准应该如何安排？不能只依赖于分析天平内部的自动校正功能，而排除外部性能检查（211.68）。

对于有内置自动校准功能的分析天平，建议定期进行外部的性能检查，但次数少于没有此功能的分析天平。

性能检查的频率取决于天平使用的频率和工艺或分析步骤的临界点和忍受度。

要注意，如果自动校验仪有问题，那么会影响到前后两次验证之间所制造的所有批次的产品。

此外，自动校准器的校准功能应定期验证-一般情况是一年一次-使用美国国家标准与技术研究所（NIST）- 可追溯的标准或NIST认证标准-其他国家在使用的合格标准。

1. Many leading analytical balance manufacturers provide built-in 'auto calibration' features in their balances. Are such auto-calibration procedures acceptable instead of external performance checks? If not, then what should the schedule for calibration be?The auto-calibration feature of a balance may not be relied upon to the exclusion of an external performance check (211.68). For a scale with a built-in auto-calibrator, we recommend that external performance checks be performed on a periodic basis, but less frequently as compared to a scale without this feature. The frequency of performance checks depends on the frequency of use of the scale and the criticality and tolerance of the process or analytical step. Note that all batches of a product manufactured between two successive verifications would be affected should the check of the auto-calibrator reveal a problem. Additionally, the calibration of an auto-calibrator should be periodically verified--a common frequency is once a year--using National Institute of Standards and Technology (NIST)-traceable standards or NIST-accredited standards in use in other countries.2、当确认药物稳定性测试方法是否可以指示稳定性时，CGMPs 要求对药物进行强制分解研究吗？不要求。

DAT ASHEETNI 920216 AI, ±10 V, 24 bit, 10 kS/s/ch Simultaneous•DSUB or push-in spring terminal connectivity•250 V RMS, CAT II, channel-to-earth isolation (spring terminal); 60 V DC, CAT I, channel-to-earth isolation (DSUB)•-40 °C to 70 °C operating, 5 g vibration, 50 g shockNote In this document, the NI 9202 with spring terminal and the NI 9202 withDSUB are referred to inclusively as the NI 9202.The NI 9202 is an analog input module for CompactDAQ and CompactRIO systems. Each channel provides a ±10 V measurement range at a 24-bit resolution. The NI 9202 has a maximum sample rate of 10 kS/s and features programmable hardware filters. By choosing one of the 5 different filter responses, a trade-off of fast settling time for increased noise rejection can be attained.NI C Series OverviewNI provides more than 100 C Series modules for measurement, control, and communication applications. C Series modules can connect to any sensor or bus and allow for high-accuracy measurements that meet the demands of advanced data acquisition and control applications.•Measurement-specific signal conditioning that connects to an array of sensors and signals •Isolation options such as bank-to-bank, channel-to-channel, and channel-to-earth ground •-40 °C to 70 °C temperature range to meet a variety of application and environmental needs•Hot-swappableThe majority of C Series modules are supported in both CompactRIO and CompactDAQ platforms and you can move modules from one platform to the other with no modification. CompactRIOCompactRIO combines an open-embedded architecturewith small size, extreme ruggedness, and C Seriesmodules in a platform powered by the NI LabVIEWreconfigurable I/O (RIO) architecture. Each systemcontains an FPGA for custom timing, triggering, andprocessing with a wide array of available modular I/O tomeet any embedded application requirement. CompactDAQCompactDAQ is a portable, rugged data acquisition platformthat integrates connectivity, data acquisition, and signalconditioning into modular I/O for directly interfacing to anysensor or signal. Using CompactDAQ with LabVIEW, youcan easily customize how you acquire, analyze, visualize, andmanage your measurement data.2| | NI 9202 DatasheetSoftwareLabVIEW Professional Development System for Windows•Use advanced software tools for large project development•Generate code automatically using DAQ Assistant and InstrumentI/O Assistant•Use advanced measurement analysis and digital signal processing•Take advantage of open connectivity with DLLs, ActiveX, and .NETobjects•Build DLLs, executables, and MSI installersNI LabVIEW FPGA Module•Design FPGA applications for NI RIO hardware•Program with the same graphical environment used for desktop andreal-time applications•Execute control algorithms with loop rates up to 300 MHz•Implement custom timing and triggering logic, digital protocols, andDSP algorithms•Incorporate existing HDL code and third-party IP including Xilinx IPgenerator functions•Purchase as part of the LabVIEW Embedded Control and MonitoringSuiteNI LabVIEW Real-Time Module•Design deterministic real-time applications with LabVIEWgraphical programming•Download to dedicated NI or third-party hardware for reliableexecution and a wide selection of I/O•Take advantage of built-in PID control, signal processing, andanalysis functions•Automatically take advantage of multicore CPUs or setprocessor affinity manually•Take advantage of real-time OS, development and debuggingsupport, and board support•Purchase individually or as part of a LabVIEW suiteNI 9202 Datasheet| © National Instruments| 3NI 9202 CircuitryCOMAI0+AI0–AI15+AI15–•Input signals on each channel are buffered, conditioned, and then sampled by an ADC.•Each AI channel provides an independent signal path and ADC, enabling you to sample all channels simultaneously.FilteringThe NI 9202 uses a combination of analog and digital filtering to provide an accuraterepresentation of in-band signals while rejecting out-of-band signals. The filters discriminate between signals based on the frequency range, or bandwidth, of the signal.The NI 9202 represents signals within the passband, as quantified primarily by passband flatness and phase linearity.The NI 9202 has a comb frequency response, characterized by deep, evenly spaced notches and an overall roll-off towards higher frequencies. The NI 9202 provides five available filter options for every data rate. The different options provide a trade-off of noise rejection (refer to Idle Channel Noise table) for filter settling time (refer to Settling Time equation) and latency (refer to Input Delay equation). To control the response of the programmable comb filter, you can select to have the first notch at 1, 1/2, 1/4, 1/8 or 1/16 of the sampling frequency. The following figures show the overall filter response with different filter settings.4 | | NI 9202 DatasheetFrequency (Hz) / Data Rate (S/s)G a i n (d B )Figure 2.Filter Response for Filter Decimation Rate 4Frequency (Hz) / Data Rate (S/s)G a i n (d B )NI 9202 Datasheet | © National Instruments | 5–80–70–60–50–40–30–20–10Frequency (Hz) / Data Rate (S/s)G a i n (d B )Figure 4. Filter Response for Filter Decimation Rate ≥8–80–70–60–50–40–30–20–100Frequency (Hz) / Data Rate (S/s)G a i n (d B )Note Refer to the Data Rates section for more information on the FilterDecimation Rate values.PassbandThe signals within the passband have frequency-dependent gain or attenuation. The small amount of variation in gain with respect to frequency is called the passband flatness. Theprogrammable comb filters of the NI 9202 adjust the frequency range of the passband to match the data rate and filter setting. Therefore, the amount of gain or attenuation at a given frequency depends on the data rate and filter setting.6 | | NI 9202 DatasheetFrequency (Hz) / Data Rate (S/s)G a i n (d B )Figure 6. T ypical Flatness for Filter Decimation Rate 4Frequency (Hz) / Data Rate (S/s)G a i n (d B )NI 9202 Datasheet | © National Instruments | 7–12–10.5–9–7.5–6–4.5–3–1.5Frequency (Hz) / Data Rate (S/s)G a i n (d B )Figure 8. Typical Flatness for Filter Decimation Rate ≥8–12–10.5–9–7.5–6–4.5–3–1.50Frequency (Hz) / Data Rate (S/s)G a i n (d B )The NI 9202 also supports power line frequency rejection. The 60 S/s data rate rejects 60 Hz noise and all harmonics of 60 Hz. The 50 S/s data rate rejects 50 Hz noise and all harmonics.The 10 S/s data rate rejects 50 Hz and 60 Hz noise and all harmonics. The following figure shows the typical frequency response for these three data rates. Refer to the Input Characteristics section for the minimum NMRR.8 | | NI 9202 DatasheetFigure 9. Typical Frequency Response at 60 S/s, 50 S/s, and 10 S/sFrequency (Hz)G a i n (d B )The -3 dB bandwidth will also be a function of data rate and filter setting, as shown in the following figures.Figure 10. Typical -3 dB Bandwidth/Data Rate vs Data Rate and Filter Settings10.0100.01000.010000.0B a n d w i d t h /D a t a r a t eData rate (S/s)NI 9202 Datasheet | © National Instruments | 9Figure 11. Typical -3 dB Bandwidth vs Data Rate and Filter Settings10002000300040005000600070008000900010000C u t o f f f r e q u e n c y (H z )Data rate (S/s)Data RatesThe frequency of a master timebase (f M ) controls the data rate (f s ) of the NI 9202. The NI 9202includes an internal master timebase with a frequency of 12.8 MHz. Using the internal master timebase of 12.8 MHz results in data rates of 10 kS/s, 8333.3 S/s, 7142.9 S/s, 6250 S/s, and so on down to 10 S/s, depending on the decimation rates and the values of the clock dividers.However, the data rate must remain within the appropriate data rate range. Power linefrequency rejection is supported through the data rates of 60 S/s, 50 S/s and 10 S/s when using the internal master timebase or when using an external master timebase of 13.1072 MHz or 12.8 MHz.The following equation provides the available data rates of the NI 9202:=×××where a is the ADC Decimation Rate (32, 64, 128, 256, 512, 1024), b is the Timebase Clock Divider (integer between 1 and 11), c is the ADC Clock Divider (4 or 8), and d is the Filter Decimation Rate (2, 4, 5, 8, 25, 64, 71, 119, 125).Notemust be greater than or equal to 1 MHz and less than 6.575 MHz.The following table lists available data rates with the internal master timebase.10 | | NI 9202 DatasheetThe NI 9202 can also accept an external master timebase or export its own master timebase. To synchronize the data rate of an NI 9202 with other modules that use master timebases to control sampling, all of the modules must share a single master timebase source. When using an external timebase with a frequency other than 12.8 MHz, the available data rates (with the exception of 60 S/s, 50 S/s and 10 S/s1) of the NI 9202 shift by the ratio of the external 1When using an external timebase of 13.1072 MHz, this data rate does not change with the ratio of the external to internal clocks.2When using an external master timebase of 13.1072 MHz.timebase frequency to the internal timebase frequency. Refer to the software help for information about configuring the master timebase source for the NI 9202.Note The cRIO-9151 R Series Expansion chassis does not support sharingtimebases between modules.NI 9202 SpecificationsThe following specifications are typical for the range -40 °C to 70 °C unless otherwise noted.Caution Do not operate the NI 9202 in a manner not specified in this document.Product misuse can result in a hazard. You can compromise the safety protectionbuilt into the product if the product is damaged in any way. If the product isdamaged, return it to NI for repair.DefinitionsWarranted specifications describe the performance of a model under stated operating conditions and are covered by the model warranty.The following characteristic specifications describe values that are relevant to the use of the model under stated operating conditions but are not covered by the model warranty.•Typical specifications describe the performance met by a majority of models.•Nominal specifications describe an attribute that is based on design, conformance testing, or supplemental testing.Specifications are Typical unless otherwise noted.Input CharacteristicsNumber of channels16 analog input channelsADC resolution24 bitsType of ADC Delta-Sigma with analog prefiltering Sampling mode SimultaneousInternal master timebase (f M)Frequency12.8 MHzAccuracy±50 ppm maximumData rate range (f s)Using internal master timebaseMinimum10 S/sMaximum10 kS/sUsing external master timebaseMinimum 3.81 S/sMaximum10.273 kS/sData rate3=×××Overvoltage protection4±30 VInput resistance (AI x to COM)>10 GΩInput voltage range (Differential)Minimum10.50 VTypical10.58 VScaling coefficients10 kS/s, 5 kS/s2,017,990 pV/LSB60 S/s51,356,632 pV/LSB2 kS/s, 1 kS/s, 500 S/s, 250 S/s,1,614,392 pV/LSB125 S/s, 50 S/s51,291,513 pV/LSB400 S/s, 200 S/s, 100 S/s,10 S/s560 S/s62,273,791 pV/LSBAll other data rates1,261,244 pV/LSBMaximum input voltage (AI x to COM)±10.5 VInput delay7+ Settling time7+ 3The data rate must remain within the appropriate data rate range andneeds to stay within 1 MHz and 6.575 MHz.4Up to 6 channels simultaneously5When using the internal master timebase or an external master timebase of 12.8 MHz 6When using an external master timebase of 13.1072 MHz7Refer to Input Delay for the values of A, B, and C.Table 2. Input DelayNon-linearity 5 ppmStability of AccuracyGain drift10 5.3 ppm/°COffset drift34.5 μV/°CPassband, -3 dB Refer to the -3 dB graphs in the PassbandsectionPhase linearity (f in ≤ 4.9 kHz)0.07° maximum8Excludes sample rates in the 0.8 category9Excludes sample rates in 1.4 category10Includes the expected difference in measurement between using single-ended and differential sources due to finite CMRR11Range equals 10.58 VChannel-to-channel mismatch (f in ≤ 4.9 kHz)Gain0.2 dB maximumPhase0.24°/kHz maximumModule-to-module mismatch (f in ≤ 4.9 kHz)Phase0.24°/B+360°B/ Attenuation @ 2 x oversample rate (23° C)12f s = 10000.0 S/s***************f s = 4545.5 S/s***********Note The noise specifications assume the NI 9202 is using the internal mastertimebase frequency of 12.8 MHz.Note The noise is dominated by the ADC Decimation Rate.12The oversample rate is the timebase divided by Timebase Clock Divider and ADC Clock Divider in Table 1. At odd multiples of the oversample rate, the NI 9202 will have significantly higherrejection.Figure 12. Idle Channel Noise vs Data Rate and Filter Settings.N o i s e (µV r m s )f S (S/s)Crosstalk (CH to CH)NI 9202 with spring terminalf in ≤ 100 Hz 100 dB f in ≤ 1 kHz 80 dB f in ≤ 3 kHz 70 dBNI 9202 with DSUBf in ≤ 100 Hz 105 dB f in ≤ 1 kHz 85 dB f in ≤ 3 kHz 75 dBCommon mode rejection ratio (CMRR) to COM f in ≤ 60 Hz 72 dB typical, 67 dB minimum Common mode rejection ratio (CMRR) to Earth Groundf in ≤ 60 Hz125 dB minimum Normal mode rejection ratio (NMRR) using internal or external master timebase of 12.8 MHz60 S/s, f in = 60 Hz ± 1 Hz 35 dB minimum 50 S/s, f in = 50 Hz ± 1 Hz 33 dB minimum 10 S/s, f in = 50 Hz/60 Hz ± 1 Hz 34 dB minimum Normal mode rejection ratio (NMRR) using external master timebase of 13.1072 MHz60 S/s, f in = 60 Hz ± 1 Hz 34 dB minimum 50 S/s, f in = 50 Hz ± 1 Hz 33 dB minimum 10 S/s, f in = 50 Hz/60 Hz ± 1 Hz33 dB minimumPower RequirementsPower consumption from chassisActive mode0.95 W maximumSleep mode53 μW maximumThermal dissipationActive mode 1.30 W maximumSleep mode0.64 W maximumPhysical CharacteristicsIf you need to clean the module, wipe it with a dry towel.Tip For two-dimensional drawings and three-dimensional models of the C Seriesmodule and connectors, visit /dimensions and search by module number.Spring terminal wiringGauge0.14 mm2 to 1.5 mm2 (26 AWG to 16 AWG)copper conductor wireWire strip length10 mm (0.394 in.) of insulation stripped fromthe endTemperature rating90 °C, minimumWires per spring terminal One wire per spring terminal; two wires perspring terminal using a 2-wire ferrule FerrulesSingle ferrule, uninsulated0.14 mm2 to 1.5 mm2 (26 AWG to 16 AWG)10 mm barrel lengthSingle ferrule, insulated0.14 mm2 to 1.0 mm2 (26 AWG to 18 AWG)12 mm barrel lengthTwo-wire ferrule, insulated2x 0.34 mm2 (2x 22 AWG) 12 mm barrellengthConnector securementSecurement type Screw flanges providedTorque for screw flanges0.2 N · m (1.80 lb · in.)WeightNI 9202 with spring terminal138.6 g (4.9 oz)NI 9202 with DSUB149.0 g (5.3 oz)Safety VoltagesConnect only voltages that are within the following limits:Maximum voltage13Channel-to-COM±30 V DC maximum, up to 6 channels at atimeNI 9202 with Spring Terminal Isolation VoltagesChannel-to-channel NoneChannel-to-earth groundContinuous250 V RMS, Measurement Category IIWithstandup to 5,000 m3,000 V RMS, verified by a 5 s dielectricwithstand testMeasurement Category II is for measurements performed on circuits directly connected to the electrical distribution system. This category refers to local-level electrical distribution, such as that provided by a standard wall outlet, for example, 115 V for U.S. or 230 V for Europe.Caution Do not connect the NI 9202 with spring terminal to signals or use formeasurements within Measurement Categories III or IV.NI 9202 with DSUB Isolation VoltagesChannel-to-channel NoneChannel-to-earth groundContinuous60 V DC, Measurement Category IWithstandup to 2,000 m1,000 V RMS, verified by a 5 s dielectricwithstand testup to 5,000 m500 V RMSMeasurement Category I is for measurements performed on circuits not directly connected to the electrical distribution system referred to as MAINS voltage. MAINS is a hazardous live electrical supply system that powers equipment. This category is for measurements of voltages from specially protected secondary circuits. Such voltage measurements include signal levels, special equipment, limited-energy parts of equipment, circuits powered by regulated low-voltage sources, and electronics.13The maximum voltage that can be applied or output between AI and COM without creating a safety hazard.Caution Do not connect the NI 9202 with DSUB to signals or use formeasurements within Measurement Categories II, III, or IV.Note Measurement Categories CAT I and CAT O are equivalent. These test andmeasurement circuits are for other circuits not intended for direct connection to theMAINS building installations of Measurement Categories CAT II, CAT III, orCAT IV.Hazardous LocationsU.S. (UL)Class I, Division 2, Groups A, B, C, D, T4;Class I, Zone 2, AEx nA IIC T4 GcCanada (C-UL)Class I, Division 2, Groups A, B, C, D, T4; ExnA IIC T4 GcEurope (ATEX) and International (IECEx)Ex nA IIC T4 GcSafety and Hazardous Locations StandardsThis product is designed to meet the requirements of the following electrical equipment safety standards for measurement, control, and laboratory use:•IEC 61010-1, EN 61010-1•UL 61010-1, CSA C22.2 No. 61010-1•EN 60079-0:2012, EN 60079-15:2010•IEC 60079-0: Ed 6, IEC 60079-15; Ed 4•UL 60079-0; Ed 6, UL 60079-15; Ed 4•CSA C22.2 No. 60079-0, CSA C22.2 No. 60079-15Note For UL and other safety certifications, refer to the product label or the OnlineProduct Certification section.Electromagnetic CompatibilityThis product meets the requirements of the following EMC standards for electrical equipment for measurement, control, and laboratory use:•EN 61326-1 (IEC 61326-1): Class A emissions; Industrial immunity•EN 55011 (CISPR 11): Group 1, Class A emissions•AS/NZS CISPR 11: Group 1, Class A emissions•FCC 47 CFR Part 15B: Class A emissions•ICES-001: Class A emissionsNote In the United States (per FCC 47 CFR), Class A equipment is intended foruse in commercial, light-industrial, and heavy-industrial locations. In Europe,Canada, Australia and New Zealand (per CISPR 11) Class A equipment is intendedfor use only in heavy-industrial locations.Note Group 1 equipment (per CISPR 11) is any industrial, scientific, or medicalequipment that does not intentionally generate radio frequency energy for thetreatment of material or inspection/analysis purposes.Note For EMC declarations and certifications, and additional information, refer tothe Online Product Certification section.CE ComplianceThis product meets the essential requirements of applicable European Directives, as follows:•2014/35/EU; Low-V oltage Directive (safety)•2014/30/EU; Electromagnetic Compatibility Directive (EMC)•2014/34/EU; Potentially Explosive Atmospheres (ATEX)Online Product CertificationRefer to the product Declaration of Conformity (DoC) for additional regulatory compliance information. To obtain product certifications and the DoC for this product, visit / certification, search by model number or product line, and click the appropriate link in the Certification column.Shock and VibrationTo meet these specifications, you must panel mount the system.Operating vibrationRandom (IEC 60068-2-64) 5 g rms, 10 Hz to 500 HzSinusoidal (IEC 60068-2-6) 5 g, 10 Hz to 500 HzOperating shock (IEC 60068-2-27)30 g, 11 ms half sine; 50 g, 3 ms half sine;18 shocks at 6 orientations EnvironmentalRefer to the manual for the chassis you are using for more information about meeting these specifications.-40 °C to 70 °COperating temperature(IEC 60068-2-1, IEC 60068-2-2)-40 °C to 85 °CStorage temperature(IEC 60068-2-1, IEC 60068-2-2)Ingress protection IP40Operating humidity (IEC 60068-2-78)10% RH to 90% RH, noncondensing Storage humidity (IEC 60068-2-78)5% RH to 95% RH, noncondensingNI 9202 Datasheet| © National Instruments| 21Pollution Degree2Maximum altitude5,000 mIndoor use only.Environmental ManagementNI is committed to designing and manufacturing products in an environmentally responsible manner. NI recognizes that eliminating certain hazardous substances from our products is beneficial to the environment and to NI customers.For additional environmental information, refer to the Minimize Our Environmental Impact web page at /environment. This page contains the environmental regulations and directives with which NI complies, as well as other environmental information not included in this document.Waste Electrical and Electronic Equipment (WEEE) EU Customers At the end of the product life cycle, all NI products must bedisposed of according to local laws and regulations. For more information abouthow to recycle NI products in your region, visit /environment/weee.电子信息产品污染控制管理办法（中国RoHS）中国客户National Instruments符合中国电子信息产品中限制使用某些有害物质指令(RoHS)。

1."In most cases, these signals originate as sensory data from the real world: seismic vibrations visual images, sound waves, etc. DSP isthe mathematics, the algorithms, and the techniques used to manipulate these signals after they have been converted into a digital form." 在大多数情况下，这些信号来源于人对真实世界的感觉，比如地震的震动，视觉图像，声音波形等。

数字信号处理是一种数学工具，是一种用来处理那些将上述信号转换成数字形式后的信号的算法和技术。

2.Fourier’s representation of functionsas a superposition of sines and cosines has become Ubiquitous for both the analytic and numerical solution of differential equations and for the analysis and treatment of communication signals 函数的傅里叶表示，即将函数表示成正弦和余弦信号的叠加，这种方法已经广泛用于微分方程的解析法和数值法求解过程以及通信信号的分析和处理。

3.If f (t ) is a nonperiodic signal, the summation of the periodic functions ,such as sine and cosine, does not accurately represent the signal. You could artificially extend the signal to make it periodic but it would require additional continuity at the end points . 如果f(t)是非周期信号，那么用周期函数例如正弦和余弦的和，并不能精确的表示该信号f(t)。

raw fr 原始频率响应英文版Raw FR: The Purest Form of Frequency ResponseIn the world of audio engineering and music production, the term "Raw FR" or "Raw Frequency Response" holds a special significance. It refers to the unaltered, purest form of how a sound system reproduces sound waves across various frequencies. Understanding Raw FR is crucial for audio enthusiasts, musicians, sound engineers, and anyone seeking to capture, manipulate, or enjoy sound in its purest form.When we talk about frequency response, we are referring to how a system, such as a speaker or headphones, responds to different frequencies of sound. Ideally, a perfect system would have a flat frequency response, meaning it reproduces all frequencies equally, without any boosts or cuts. However, in reality, no system is perfect, and each has its unique characteristics that affect the way sound is perceived.Raw FR, therefore, is the frequency response before any equalization, filtering, or other forms of audio processing are applied. It's the raw, unprocessed sound that comes directly from the source, unaltered by any external factors. Listening to Raw FR gives one an accurate representation of how a sound truly sounds, without any artificial enhancements or alterations.For musicians, understanding Raw FR is essential in ensuring that their music sounds as intended. It helps them identify any frequencies that may be overpowering or lacking, allowing them to adjust their instruments or production techniques accordingly. Sound engineers, on the other hand, rely on Raw FR to calibrate audio systems and ensure that they accurately represent the sound of the original recording.In the end, Raw FR is about authenticity and purity. It's about experiencing sound in its most genuine form, without any artificial interference. For audio enthusiasts and professionals alike, understanding and appreciating Raw FR is a crucial step towards achieving the perfect soundscape.中文版原始频率响应：最纯粹的频率表现在音频工程和音乐制作领域，“Raw FR”或“原始频率响应”具有特殊的意义。