自动化专业英语讲义(2010-2011第２学期)
课前要求：通读课文1遍、将生词查出。
课后要求：独立完成作业。
预习下次课的内容
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答疑地点：杰德控制系统工程研究中心（一校西门南三层楼305室）
答疑时间：每周工作日上午10:00～11:30、下午3:00～5:00(周四除外)之间,请先电话联系
办公电话：2554
参考书：
《工业自动化专业外语》，王树青，韩建国编，化学工业出版社，2001年。
《自动化专业英语教程》王宏文，机械工业出版社，2007年。
《Modern Control System》，R.C. Dorf, R.H. Bishop，科学出版社，2004年。
《自动化专业英语》，李国厚，王春阳，北京大学出版社，2006年。
《自动化专业英语》，任金霞,任金霞,何小阳，华中科技大学出版社，2008年。
《自动化专业英语》，王旸,原驰,哈尔滨工业大学，2008年。
《自动化专业英语》，王建国,陈东淼，中国电力出版社，2005年。
《自动控制专业英语》，沈宏，电子工业出版社，2003年。
《自动控制专业英语》，李国厚，清华大学出版社，2005年。
《自动化专业英语》，戴文进，章卫国，武汉理工大学出版社，2006年。
《自动化与电子信息专业英语》，杨植新，周劲，孙江波，电子工业出版社，2009年。
No.1 Pronunciation of mathematical expressions; Major catalogue; Periodicals and journals
1.1 Pronunciation of Mathematical Expressions
The pronunciations of the most common mathematical expressions are given in the list below. In general, the shortest versions are preferred (unless greater precision is necessary).
3、Real numbers
1+x x plus one 1-x x minus one 1±x
x plus or minus one xy
xy / x multiplied by y
))((y x y x +- x minus y , x plus y
y
x x over y / x on y
＝the equals sign
x x equals 5 / x is equal to 5
=
5
x x (is) not equal to 5
5
≠
x≡x is equivalent to (or identical with) y
y
x≠y x is not equivalent to (or identical with) y y
x>x is greater than y
x≥x is greater than or equal to y
y
x<x is less than y
y
y
x≤x is less than or equal to y
<x zero is less than x is less than 1
0<
1
≤x zero is less than or equal to x is less than or equal to 1 1
0≤
x mod x / modulus x / absolute value of x
2
x x squared / x (raised) to the power 2
3
x x cubed
4
x x to the fourth / x to the power four
n
x x to the nth / x to the power n
n
x-x to the (power) minus n
x(square) root x / the square root of x
3x cube root (of) x
4x fourth root (of) x
n x n th root (of) x
2)(y x +
x plus y all squared
2
⎪⎪⎭
⎫ ⎝⎛y x x over y all squared
!n n factorial x
ˆ x hat x x bar x ~
x tilde
i x
xi / x subscript i / x suffix i / x sub i
i x
xi / x superscript i / x superfix i / x super i
∑=n
i i
a
1
the sum from i equals one to n a i / the sum as i runs from 1 to n of the a i
4、Linear algebra
x
the norm (or modulus) of x
OA / vector OA
OA
OA / the length of the segment OA T A A transpose / the transpose of A 1-A
A inverse / the inverse of A
5、Functions
)(x f
f x / f of x / the function f of x
T S f →:
a function f from S to T
y x
x maps to y / x is sent (or mapped) to y
)(x f '
f prime x / f dash x / the (first) derivative of f with respect to x )(x f ''
f double –prime x / f double –dash x / the second derivative of f with respect to x
)(x f ''' f triple –prime x / f triple –dash x / the third derivative of f with respect to x
)()4(x f
f four x / the fourth derivative of f with respect to x
F x ∂∂ partial F on partial x / partial differential F on x
1
x f ∂∂ the partial (derivative) of f with respect to x 1
2
1
2x f
∂∂ the second partial (derivative) of f with respect to x 1
⎰
∞
the integral from zero to infinity
lim →x
the limit as x approaches zero
lim +→x
the limit as x approaches zero from above
lim -→x
the limit as x approaches zero from below
y e log
log y to the base e / log to the base e of y / natural log (of) y
y ln
log y to the base e / log to the base e of y / natural log (of) y
Individual mathematicians often have their own way of pronouncing mathematical expressions and in many cases there is no generally accepted “correct” pronunciation.
Distinctions made in writing are often not made explicit in speech; thus the sounds fx may be interpreted as any of: fx ,
,,,),(FX FX FX f x f x The difference is usually made clear by the context; it is only when confusion
may occur, or where he/she wishes to emphasize the point, that the mathematician will use the longer forms: f
multiplied by x , the function f of x , f subscript x , line FX , the length of the segment FX , vector FX .
Similarly, a mathematician is unlikely to make any distinction in speech (except sometimes a difference in intonation or length of pauses) between pairs such as the following: )(z y x ++ and z y x ++)(
b ax + and
b ax +
1-n
a and 1
-n a
6、其它数学符号和公式例子 4/5 four fifths / 4 on 5 0.025 zero point zero two five 38.49 thirty-eight point four nine 2%
two per cent
25 the second power of five / five to the power two
x
the square root of x
7106⨯ six times the seventh power of ten +
plus ; positive -
minus ; negative ⨯ multiplied by ; times ÷; /
divided by = is equal to ; equals
( ) round brackets ; parentheses (parenthesis) i ; j
imaginary unit
!a factorial a
sin sine of x
x
arcsin arc sine of x
x
∏the product of the terms indicated
∑the sum of the terms indicated
b'b prime
b''b second prime
b b sub two
2
"
b b second prime sub m
m
dx
dy/the first derivative of y with respect to x
2/dx
2
d th
e second derivative o
f y with respect to x
y
⎰b a integral between limits a and b
x x approaches to infinity
∞
→
a=
+a plus b is equal to c
b
c
-a minus b equals c
a=
c
b
s=s equals v multiplied by t
vt
=v equals s divided by t
v/
t
s
⨯
-
+/)
(a plus b minus c multiplied by d, all divided by e equals f a=
d
b
e
f
c
C+
=C over R equals G divided by the sum of one and H times G R
1/(
)
/GH
G
1.2 Major Catalogue
根据国家教委1998年颁布的新专业目录（Major Catalogue），将原工业自动化（Industrial Automation）、自动控制（Automatic Control）、自动化（Automation）、电气技术（Electrical Technology）等专业合并统称为自动化专业（Automation）。
全国专业指导委员会对本专业本、专科生及研究生的必修课程（compulsory subjects/required subjects）和选修课程（elective subjects）做了指导性规划，除一些大学基础课程外，还应包括的主要专业基础课和专业课有：
电路（Theory of Circuit）
模拟电子技术（Analog Electronics Technology）
数字电子技术（Digital Electronics Technology）
电力电子技术（Power Electronics Technology）
电磁场（Electromagnetic Field）
电工测量（Electric Measurement）
电机学（Theory of Electric Motors）
自动控制理论（Automatic Control Theory）
现代控制理论（Modern Control Theory）
微机原理（Principle of Microcomputer）
计算机控制技术（Computer Control Techniques）
自动调节装置（Automatic Regulators）
过程控制系统（Process Control System）
电气自动控制（Electrical Automatic Control）
电力拖动基础（Fundamental of Electric Drive）
交流调速系统（AC Motor Speed Regulating System）
电力拖动自动控制系统（Automatic Control System for Electric Drive）
单片机应用（Application of Single-chip Computer）
可编程序控制器系统（Programmable Logical Controller System）
供电技术（Power Supplying Technology）
系统仿真（System Simulation）
楼宇自动化（Building Automation）
线性系统（Linear System）
自适应控制（Adaptive Control System）
系统辨识（System Identification）
模糊控制与神经元网络（Fuzzy Control and Neutral Network）电气CAD（Electrical CAD）
计算机多媒体与网络技术（Multimedia and Network Technique）运动控制（Motion Control）
网络化控制系统（Networked Control System）
1.3 Periodicals and Journals
1.3.1 国内自动化专业主要期刊
(略)
1.3.2国外自动化专业主要期刊
1.3.3 国内外自动化学术团体
1、美国电气与电子工程师学会（The Institute of Electrical and Electronics Engineers，简称IEEE）
IEEE是电气与电子工程方面目前世界上最大的学术团体。
它与100多个国家建立了人事往来和学术交流活动，并已逐渐发展成一个国际性的机构。
现有国内外会员20余万人。
IEEE活动主要是举办大量国际性或全国性会议和出版期刊和会议录，举办各种展览会，组织会员访问科研单位和工厂企业的实验室、进行职业调查并出版相应的调查报告等。
IEEE按专业活动划分为：计算机；控制系统；电介质与电气绝缘；电子器件；工业应用；工业电子学；信息理论；测试设备与测量；大功率电子学（委员会）；机器人与自
动学（委员会）；系统、人与控制论等10个部和36个技术协会和委员会。
2、英国电气工程师学会（The Institute of Electrical Engineers，简称IEE）
IEE目前有会员82 000人，主要活动也是召开学术会议和出版科技刊物。
IEE与IEEE相似，每年要组织召开许多国际会议和讨论会，多数出版会议录或论文摘要，并以连续出版物的形式出版《IEE会议出版物》（IEE Conference Publication）或《IEE讨论会论文摘要》（IEE Colloquium Digest），这类出版物均以会议名称命名，并有连续编号，如International Conference on Mobile Radio Systems and Techniques （Conf.Publ.No.238）。
IEE编辑出版的刊物中影响较大的是《IEE会报》，共分A～J 10个分辑（双月刊），均为工程学的核心期刊。
3、国内主要相关专业性学会
中国自动化学会
中国电机工程学会
中国动力工程学会
中国系统仿真学会
中国仪器仪表学会
中过电工技术学会
中国电子学会
中国系统工程学会
中国计算机学会
No.2 Specified English words and expressions for automation and thermal system
actuator 执行器
adaptive control 自适应控制
amplitude 幅值／振幅
anti-reset windup 抗积分饱和
assumption 假设
automatic control 自动控制
auto-tuning 自整定
bandwidth 带宽
black-box model 黑箱模型
white-box model 白箱模型
gray-box model 灰箱模型
boiler drum 汽包水位
capacitance 电容
capacitor 电容
characteristic equation 特征方程
closed-loop stability 闭环稳定
controller tuning 控制器整定
converge 收敛
convergence 收敛性
diode 二极管
direct-digital-control 直接数字控制distributed control 分布控制
emission 排放，散发
empirical model 经验模型
equilibrium 平衡点
feedback control 反馈控制
fuzzy control 模糊控制
fuzzification 模糊化
de-fuzzification 解模糊
generalized predictive control 广义预测控制generator 发电机
turbo-generator 汽轮发电机
turbo-generator unit 汽轮发电机组
feed-forward control 反馈控制
intelligent control 智能控制
linear quadratic regulator LQR，线性二次高斯控制
magnitude 大小，幅值
manual control 手动控制
multiple variable system 多变量系统
numerator polynomial 分子多项式
negative feedback control 负反馈控制
partial fraction expansion 部分分式展开proportional plus integral plus derivative control PID控制physical modeling 物理模型
prerequisite 先决条件
process control 过程控制
ratio control 比率控制
robustness 鲁棒性
saturation 饱和
self-tuning regulator 自校正调节器
set-point 设定值
simulation research 仿真研究
startup/start-up 启动
state space model 状态空间模型
step function 阶跃函数
step response 阶跃响应
pulse response 脉冲响应
system identification 系统辨识
s-plane s平面
z-plane z平面
theorem 定理
theoretical 理论上的thermocouple 热电偶
time delay 时延
transducer 传感器
sensor 传感器
transfer function 传递函数
transmitter 变送器
true value 真值
unit matrix 单位矩阵
valve 阀门
voltage 电压
white noise 白噪声
color noise 有色噪声
zero-order hold 零阶保持器
open-loop 开环
closed-loop 闭环
minimum-phase 最小相位
non-minimum phase system 非最小相位
coal-fired power plant 燃煤发电厂
circulating fluidized bed boiler 循环流化床锅炉
disturbance rejection 抗扰动
feed-forward plus feedback control 前馈加反馈控制
cascade control system 串级控制
steam temperature 蒸汽温度
first order system 一阶系统
second order system 二阶系统
first order plus pure time delay system 一阶加纯滞后系统(FOPDT) second order plus pure time delay system 二阶加纯滞后系统(SOPDT)
critical 临界的
sub-critical 亚临界的
super-critical 超临界的
ultra-super-critical 超临界的
carbon monoxide (CO) 一氧化碳
carbon dioxide (CO2) 二氧化碳
nitrogen oxide (NO x) 氮氧化物
板式空气预热器plate air-preheater
半无烟煤semi-anthracite
半直吹式燃烧semi-direct firing
备件duplicate part, renewals
备品spare parts
备用reserve
备用电源reserve power supply
备用发电厂stand-by generator
备用发电机reserve feed tank
备用机组stand-by set, stand-by unit, reserve machine 备用零件spare detail
本征矢量/特征矢量eigenvector
本征值/特征值eigenvalue
泵pump
给水泵feed water pump
闭式循环closed circulating, closed cycle
表面式减温器surface type attemperator
表面式冷却器surface cooler
表面式凝汽器surface condensor
并列运行parallel operation
不灵敏区dead zone
不完全燃烧incomplete combustion
厂用电auxiliary power, station service
除氧deaeration
除氧器deaerator
除氧水箱deaerator storage tank
吹灰器soot blower
挡板baffle plate, dash
低速磨煤机low speed mill
调峰cycling loading
对流过热器convection superheater
发电成本generating cost
辐射式过热器radiant superheater
负荷分配load distribution
钢球磨煤机ball tube mill
给煤机coal feeder, pulverized coal feeder
给粉机pulverized fuel feeder, pulverized coal feeder 鼓风机blower, aerator
锅炉boiler
超临界锅炉supercritical boiler
亚临界锅炉subcritical boiler
燃煤锅炉coal-fired boiler
燃油锅炉oil-fired boiler
直流锅炉once-through boiler
回转式空气预热器rotary air-preheater
机组负荷unit load
经济负荷economic load
空气air
一次空气primary air
二次空气secondary air
三次空气tertiary air
过剩空气excess air
空气预热器air preheater, air heater
板式空气预热器plate air preheater
管式空气预热器tubular air preheater
回转式空气预热器rotary air preheater
三分仓空气预热器trisector air preheater
炉膛安全监控系统furnace safeguard supervision system (FSSS) 凝汽器condensor
排粉机pulverizer exhauster
频率frequency
额定频率normal frequency
固有频率inherent frequency
工频power frequency
自然频率natural frequency
燃烧combustion
切圆燃烧tangential combustion
四角燃烧diagonal combustion
热电联产cogeneration
热电偶thermocouple, thermopair
省煤器economizer
脱硫desulphurization
旋风分离器cyclone separator
送风机/鼓风机forced fan (FDF)
引风机/吸风机induced fan (IDF)
再热器reheater
专业词汇往往有其特殊词义(不能只记得单词的一个意思)：memory 内存；记忆
bus 总线(Field Bus Control System)；公共汽车
monitor 监视器；班长
order 阶次；命令、订货
No.3 Introduction to process control; PID control
“英译中”的关键一是理解，二是表达。
作为理解除了英语水平（阅读能力、词汇量）之外，背景知识也十分重要；所以在平时一定注意知识的积累。
作为表达，很大程度上取决于中文水平。
如果真正理解了，可以不受原文的约束。
所以翻译（表达）的技巧很多，例如可以将原来一句话分为两句话，甚至多句话。
也可以将原来两句话或者多句话合并为一句话。
可以对词性进行转换；可以将原来肯定的表达，用否定的方式表达；或者是相反；可以将原来被动的表达，用主动的方式表达；等等，等等。
3.1 Introduction to process control- The World of Control
背景知识：自动控制理论是分析和设计自动控制系统的学科。
自动控制理论可以大致分为“经典控制理论”和“现代控制理论”。
自动控制系统可以分为：开环系统和闭环系统（反馈系统）、连续系统和离散系统、线性系统和非线性系统、时不变（定常）系统和时变系统、集中参数系统和分布参数系统、确定系统和随机系统、单变量系统和多变量系统。
New Words:
abound v. 大量存在
power boost 功率助推装置
damp v.阻尼，减幅，衰减
yaw n.偏航
altitude n.海拔高度
attitude n.姿态
intuition n.直觉
trail-and-error 试凑法
domain n.域，领域
advent n.出现
state variable 状态变量
matrix algebra 矩阵代数
tedious a.令人厌烦的、冗长乏味的
proponent n.支持者、辩护者
detractor n.反对者、贬低者
in effect 在结果方面、实际上、实质上
discrete a.离散的
subsequent a.后续的
differential equation 微分方程
difference equation 差分方程
lumped parameter 集中参数
distributed parameter 分散参数
spring n.弹簧
lead n.导线
resistance n.阻抗
uniform a.一致的
ordinary differential equation 常微分方程
partial differential equation 偏微分方程
stochastic a. 随机的
probability theory 概率论
rationale n.理论，原理的阐述
先试着每段都只阅读第一句话。
看看能够获得什么信息。
时间控制在2分钟之内。
Introduction
The world control is usually taken to mean regulate, direct, or command. Control systems in our environment. In the most abstract sense it is possible to consider every physical object as a control system.
Control systems designed by humans are used to extend their physical capabilities, to compensate for their physical limitations, to relieve them of routine or tedious tasks, or to save money. In a modern aircraft, for example, the power boost controls amplify the force applied by the pilot to move the control surface against large aerodynamic forces. The reaction time of a human pilot is too slow to enable him or her to fly an aircraft with a highly damped Dutch roll mode without the addition of a yaw damper system. An autopilot (flight control system) relieves the pilot of the task of continuously operating the controls to maintain the desired heading, altitude, and attitude. Freed of this routine task, the pilot can perform other tasks, such as navigation and/or communications, thus reducing the number of crew required and consequently the operating cost of the aircraft.
In many cases, the design of control system is based on some theory rather than intuition or trail-and-error. Control theory is used for dealing with the dynamic response of a system to commands, regulations, or disturbances. The application of control theory has essentially two phases: dynamic analysis and control system
design. The analysis phase is concerned with determination of the response of a plant (the controlled object) to commands, disturbances, and changes in the plant parameters. If the dynamic response is satisfactory, there need to be no second phase. If the response is unsatisfactory and modification of the plant is unacceptable, a design phase is necessary to select the control elements (the controller) needed to improve the dynamic performance to acceptable levels.
Control theory itself has two categories: Classical and, modern. Classical control theory, which had its start during World War II, can be characterized by the transfer function concept with analysis and design principally in the Laplace and frequency domains. Modern control theory has arisen with the advent of high-speed digital computers and characterized by the state variable concept with emphasis on matrix algebra and with analysis and design principally in the time domain. As might be expected, each approach has its advantages and disadvantages as well as its proponents (supporters) and detractors (opponents).
As compared to modern approach, the classical approach hs the tutorial advantage of placing less emphasis on mathematical techniques and more emphasis on physical understanding. Furthermore, in many design situations the classical approach is not only simpler bunt may be completely adequate. In those more complex cases where it is not adequate, the classical approach solution may aid in applying the modern approach and may provide a check on the more complete and exact design. For those reasons the subsequent articles will introduce the classical approach in detail.
Classification and Terminology of Control Systems
Control systems are classified in terms that describe either the systems itself or its variables:
Open-loop and closed-loop control systems. An open-loop system is one in which the control action is independent of the output. A closed-loop system, however, the input of the plant is somehow dependent on the output. Since the output is fed back in a functional form determined by the nature of the feedback elements and then subtracted from the input, a closed-loop system is often referred to as a negative feedback system or simply as a feedback system.
Continuous and discrete system.The system that all its variables are continuous functions of time is called continuous-variable or analog system; the describing equations are differential equations. A discrete-variable or digital system has one or more variables known only at particular instants of time; the equations are difference equations. If the time intervals are controlled, the system is termed a sampled-data system. Discrete variables occur naturally, as from a scanning radar that obtains position data once per scan or a data channel that transmits
many pieces of information in turn. A discrete variable will obviously approach a continuous variable as the sampling interval is decreased. Discontinuous variables occur in “on-off” or “bang-bang” control system and are treated separately in a subsequent paper.
Linear and nonlinear systems. A system is linear if all its elements are linear, and nonlinear if any of elements is nonlinear.
Time-invariant and time-variant systems. A time-invariant (or stationary) system is one whose parameters do not vary with time. The output of a stationary system is independent of the time at which an input is applied, and the coefficients of the describing differential equations are constant. A time-variant (or nonstationary) system is a system with one or more parameters that vary with time. The time at which an input is applied must be known, and the coefficients of the differential equations are time-dependent.
Lumped parameter and distributed parameter systems. Lumped parameter systems are those for which physical characteristics are assumed to be concentrated in one or more ‘lumps’ and thus independent of any spatial distribution. In effect, bodies are assumed rigid and treated as point massed; springs are massless and electrical leads resistanceless, suitable corrections are made to the system mass or resistance; temperature are uniform; etc. In distributed parameter systems, the continuous spatial distribution of a physical characteristic is taken into account. Bodies are elastic, springs have a distributed mass, electrical leads have a distributed resistance, and temperatures vary across a body. Lumped parameter systems are described by ordinary differential equations; while distributed parameter systems are described by partial differential equations.
Deterministic and stochastic systems. A system or variable is deterministic if its future behavior is both predictable and repeatable within reasonable limits. If not, the system or variable is called stochastic or random. Analysis of stochastic systems and of deterministic systems with stochastic inputs are based on probability theory. Single-variable and multivariable systems. A single-variable system is defined as one with only output for one reference or command input and is often referred to as a single input single output (SISO) system. A multivariable (MIMO) system has any number of inputs and outputs.
Control System Engineering Design Problem
Control system engineering consists of analysis and design of control configurations. Analysis is the investigation of the components to perform a specific task.
Designing a control system is not a precise or well-defined process; rather, it is a sequence of interralated events.
A typical sequence might be
1.Modeling of the plant
2.Linearization of the plant model
3.Dynamic analysis of the plant
4.Nonlinear simulation of the plant
5.Establishment of the control philosophy & strategy
6.Selection of the performance criteria and indices
7.Design of the controller
8.Dynamic analysis of the complete system
9.Nonlinear simulation of the complete system
10.Selection of the hardware to be used
11.Construction and test of the development system
12.Design of the production model
13.Test of the production model
This sequence is not rigid, all-inclusive, or necessarily sequential. It is given here to establish a rationale for the techniques developed and discussed in the subsequent units.
3.2 Introduction to PID Control
Introduction
This introduction will show you the characteristics of the each of proportional (P), the integral (I), and the derivative (D) controls, and how to use them to obtain a desired response. In this tutorial, we will consider the following unity feedback system:
Plant: A system to be controlled
Controller: Provides the excitation for the plant; Designed to control the overall system behavior
The three-term controller
The transfer function of the PID controller looks like the following:
• Kp = Proportional gain • Ki = Integral gain • Kd = Derivative gain
First, let's take a look at how the PID controller works in a closed-loop system using the schematic shown above. The variable (e) represents the tracking error, the difference between the desired input value (R) and the actual output (Y). This error signal (e) will be sent to the PID controller, and the controller computes both the derivative and the integral of this error signal. The signal (u) just past the controller is now equal to the proportional gain (Kp) times the magnitude of the error plus the integral gain (Ki) times the integral of the error plus the derivative gain (Kd) times the derivative of the error.
p i d
de
u K e K edt K dt =++⎰
This signal (u) will be sent to the plant, and the new output (Y) will be obtained. This new output (Y) will be sent back to the sensor again to find the new error signal (e). The controller takes this new error signal and computes its derivative and its integral again. This process goes on and on. The characteristics of P, I, and D controllers
A proportional controller (Kp) will have the effect of reducing the rise time and will reduce ,but never eliminate, the steady-state error. An integral control (Ki) will have the effect of eliminating the steady-state error, but it may make the transient response worse. A derivative control (Kd) will have the effect of increasing the stability of the system, reducing the overshoot, and improving the transient response. Effects of each of controllers Kp, Kd, and Ki on a closed-loop system are summarized in the table shown below.
Note that these correlations may not be exactly accurate, because Kp, Ki, and Kd are dependent of each other. In fact, changing one of these variables can change the effect of the other two. For this reason, the table should only be used as a reference when you are determining the values for Ki, Kp and Kd. Example Problem
Suppose we have a simple mass, spring, and damper problem.
The modeling equation of this system is
Taking the Laplace transform of the modeling equation (1)
The transfer function between the displacement X(s) and the input F(s) then becomes
Let
• M = 1kg
• b = 10 N.s/m
• k = 20 N/m
• F(s) = 1
Plug these values into the above transfer function
The goal of this problem is to show you how each of Kp, Ki and Kd contributes to obtain
• Fast rise time
• Minimum overshoot
• No steady-state error
Open-loop step response
Let's first view the open-loop step response. Create a new m-file and add in the following code:
num=1;
den=[1 10 20];
step (num,den)
Running this m-file in the Matlab command window should give you the plot shown below.
The DC gain of the plant transfer function is 1/20, so 0.05 is the final value of the output to an unit step input. This corresponds to the steady-state error of 0.95, quite large indeed. Furthermore, the rise time is about one second, and the settling time is about 1.5 seconds. Let's design a controller that will reduce the rise time, reduce the settling time, and eliminates the steady-state error.
Proportional control
From the table shown above, we see that the proportional controller (Kp) reduces the rise time, increases the overshoot, and reduces the steady-state error. The closed-loop transfer function of the above system with a proportional controller is:
Let the proportional gain (Kp) equals 300 and change the m-file to the following:
Kp=300;
num=[Kp];
den=[1 10 20+Kp];
t=0:0.01:2;
step (num,den,t)
Running this m-file in the Matlab command window should gives you the following plot.
Note: The Matlab function called cloop can be used to obtain a closed-loop transfer function directly from the open-loop transfer function (instead of obtaining closed-loop transfer function by hand). The following m-file uses the cloop command that should give you the identical plot as the one shown above.
num=1;
den=[1 10 20];
Kp=300;
[numCL,denCL]=cloop(Kp*num,den);
t=0:0.01:2;
step (numCL, denCL,t)
The above plot shows that the proportional controller reduced both the rise time and the steady-state error, increased the overshoot, and decreased the settling time by small amount.
Proportional-Derivative control
Now, let's take a look at a PD control. From the table shown above, we see that the derivative controller (Kd) reduces both the overshoot and the settling time. The closed-loop transfer function of the given system with a PD controller is:
Let Kp equals to 300 as before and let Kd equals 10. Enter the following commands into an m-file and run it in the Matlab command window.
Kp=300;
Kd=10;
num=[Kd Kp];
den=[1 10+Kd 20+Kp];
t=0:0.01:2;
step (num,den,t)
This plot shows that the derivative controller reduced both the overshoot and the settling time, and had small effect on the rise time and the steady-state error.
Proportional-Integral control
Before going into a PID control, let's take a look at a PI control. From the table, we see that an integral controller (Ki) decreases the rise time, increases both the overshoot and the settling time, and eliminates the steady-state error. For the given system, the closed-loop transfer function with a PI control is:
Let's reduce the Kp to 30, and let Ki equals to 70. Create an new m-file and enter the following commands.
Kp=30;
Ki=70;
num=[Kp Ki];
den=[1 10 20+Kp Ki];
t=0:0.01:2;
step (num,den,t)
Run this m-file in the Matlab command window, and you should get the following plot.
We have reduced the proportional gain (Kp) because the integral controller also reduces the rise time and increases the overshoot as the proportional controller does (double effect). The above response shows that the integral controller eliminated the steady-state error.
Proportional-Integral-Derivative control
Now, let's take a look at a PID controller. The closed-loop transfer function of the given system with a PID controller is:
After several trial and error runs, the gains Kp=350, Ki=300, and Kd=50 provided the desired response. To confirm, enter the following commands to an m-file and run it in the command window. You should get the following step response.
Kp=350;
Ki=300;
Kd=50;
num=[Kd Kp Ki];
den=[1 10+Kd 20+Kp Ki];
t=0:0.01:2;
step (num,den,t)。
