G.J. Autonomous controller design for unmanned aerial vehicles using multi-objective geneti

第41卷第2期2024年2月控制理论与应用Control Theory&ApplicationsV ol.41No.2Feb.2024大时滞不确定系统的滞后时间削弱与自抗扰控制李向阳1,高志强2,田森平1,哀薇1†(1.自主系统与网络控制教育部重点实验室,华南理工大学自动化科学与工程学院,广东广州510640;2.克里夫兰州立大学电气工程与计算机科学系,俄亥俄克里夫兰44115,美国)摘要:针对具有变时滞、变参数和扰动的大时滞不确定系统的控制问题,本文提出了滞后时间削弱与自抗扰控制方法,综合应用了前馈控制、反馈控制和自抗扰补偿控制.为了提高系统的稳定性,在前馈控制器的设计中采用了系统的边界模型确定控制器参数取值范围;采用系统边界模型输出与系统实际输出的动态加权和作为反馈控制器的输入.为了提高系统控制的性能,自抗扰补偿控制回路的设计基于标称模型的补偿控制器.理论证明和仿真结果表明,所提出的方法是有效的,其在具有模型参数变化、滞后时间变化和外部扰动情况下,能保证系统的稳定性和良好的控制性能.关键词:大时滞系统;不确定系统;自抗扰控制;滞后时间削弱;补偿控制器引用格式:李向阳,高志强,田森平,等.大时滞不确定系统的滞后时间削弱与自抗扰控制.控制理论与应用, 2024,41(2):249–260DOI:10.7641/CTA.2023.20135Time-delay influence reducing and active disturbance rejection control of uncertain systems with large time-delayLI Xiang-yang1,GAO Zhi-qiang2,TIAN Sen-ping1,AI Wei1†(1.Key Laboratory of Autonomous Systems and Network Control,Ministry of Education,School of Automation Science and Engineering,South China University of Technology,Guangzhou Guangdong510640,China; 2.Center for Advanced Control Technologies,Department of Electrical Engineering and Computer Science,Cleveland State University,Cleveland,OH44115,USA)Abstract:For the control problem of uncertain systems with variant large time-delay,variant parameters and distur-bance,a time-delay influence reducing(TDIR)and active disturbance rejection control method(ADRC)is presented.The proposed TDIR-ADRC method integrates feedforward control,feedback control and active disturbance rejection compen-sating control.In order to enhance the system’s stability,the system’s border model is used in the design of feedforward control and the input of feedback controller is the dynamic weighted sum of the outputs of the system’s border model and the real system.In order to enhance the system’s control performance,the active disturbance rejection compensating control loop is based on the nominal model,a special compensating controller is designed.The theoretical analysis and simulation research results verify the effectiveness of the proposed TDIR-ADRC methods,the TDIR-ADRC shows nice performance of system output tracking reference input when there exist model parameter and time-delay variation and disturbance.Key words:large time-delay system;uncertain system;active disturbance rejection control;time-delay influence reduc-ing;compensation controllerCitation:LI Xiangyang,GAO Zhiqiang,TIAN Senping,et al.Time-delay influence reducing and active disturbance rejection control of uncertain systems with large time-delay.Control Theory&Applications,2024,41(2):249–2601引言在实际工业过程控制中,被控过程常采用具有纯滞后的一阶或者二阶模型,这些模型是经过机理分析和系统辨识试验获得的近似模型,缺乏精确的被控对象模型,导致现代控制理论的许多算法难以在实际中获得良好的控制效果,实践工程中大量应用的仍是比例–积分–微分(proportional-integral-derivative,PID)控制方法.我国著名学者韩京清敏锐注意到PID不依收稿日期:2022−02−24;录用日期:2023−03−14.†通信作者.E-mail:**************.cn;Tel.:+8620-87111289.本文责任编委:夏元清.国家自然科学基金项目(61773170,62173151),广东省自然科学基金项目(2021A1515011850)资助.Supported by the National Natural Science Foundation of China(61773170,62173151)and the Natural Science Foundation of Guangdong Province of China(2021A1515011850).250控制理论与应用第41卷赖精确数学模型,而是采用基于误差来消除误差的思想,提出非线性状态误差反馈律(state error feedback,SEF);他同时利用现代控制理论中状态观测器的思想发明了扩张状态观测器(extended state observer,ESO),实现对系统总扰动的估计和补偿,以克服PID其对信号利用率低的缺点;为了解决快速和超调的矛盾,他提出了跟踪微分器(tracking differentiator,TD),并用它来安排过渡过程,最终形成了自抗扰控制(activedisturbance rejection control,ADRC)[1–2].之后,AD-RC在严格理论证明和工程应用的参数整定等方面取得了重要突破[3–14],ADRC被理论界和工业界广泛认可,ADRC算法已经被TI等多家公司固化到其DSP芯片和控制软件中[15].由于ADRC只要求知道被控对象的相对阶和控制增益的粗略估计,而对被控对象的模型信息依赖很少,因此得到大量应用.但是,对于滞后过程控制系统,ADRC的无视时滞法和提高阶次法只适合小时滞系统;对于大时滞系统,ADRC必须与其他专门针对时滞系统的方法结合一起,主要有3种改进方法:延时设计型自抗扰控制(delayed designed ADRC,DDADR-C)、基于Smith预估器的自抗扰控制(Smith predictorbased ADRC,SP-ADRC)、基于预测观测器的自抗扰控制(predictor observer based ADRC,PO-ADRC)[16].本文受现有方法的启发,以一阶纯滞后系统为例,从基本的Smith预估原理出发,建立综合前馈控制和滞后时间削弱法的大时滞过程系统的ADRC方法.本文的后续内容安排如下:第2节描述了研究的问题和现有解决方法;第3节提出了一种新型的滞后时间削弱与自抗扰控制(time-delay influence reducingand ADRC,TDIR-ADRC)方法;第4节对所提出的方法进行了稳定性分析;第5节给出了仿真研究和推广;第6节是本文的结论.2问题的提出实际工业过程一般为高阶非线性系统,但是往往采用一阶纯滞后(first order plus dead time,FOPDT)或者二阶纯滞后(second order plus dead time,SOPDT)来近似[17],这除了FOPDT或者SOPDT与实际过程数据有较好的拟合关系外,还可以从时滞环节的高阶近似来理解.在复频域中,利用Pade近似,可以把时滞e−sτ近似表示为有理分式的形式[18],即e−τs≈b0+b1(τs)+···+b l(τs)la0+a1(τs)+···+a k(τs)k,(1)其中a i=(l+k−i)!k!i!(k−i)!,i=0,···,k,b j=(−1)j(l+k−j)!l!j!(l−j)!,j=0,···,l,(2)式(1)中l和k为近似的阶次,它们越大,近似精度越高;时滞τ越小,式(1)左右两边相同频带区域的相位误差越小.式(1)右边的高阶分式表示可以用左边的纯滞后来近似等效,因此,FOPDT或者SOPDT两类模型在过程控制的教科书和文献中的大量出现,反过来也说明具有纯滞后的系统特别是大滞后系统的控制一直是工业控制领域的难点.本文基于FOPDT模型研究大时滞过程的滞后时间削弱与自抗扰控制问题,并推广到SOPDT系统中.考虑如下典型的FOPDT被控对象:G pt(s)=G p(s)e−sτp=KT s+1e−sτp,(3)式中:K为过程增益;T为过程时间常数;τp为过程纯滞后时间.系统(3)的标称模型为G mt(s)=G m(s)e−sτm=K mT m s+1e−sτm,(4)式中K m,T m和τm为相应的标称参数.当τp τm时,经典的Smith预估(Smith predictor,SP)控制方法如图1所示,其反馈量为Y f(s)=Y m(s)+(Y(s)−Y mt(s)),(5)其中:Y m(s)=G m(s)U(s),(6)Y(s)=G p(s)e−τp s U(s)+D(s),(7)Y mt(s)=G m(s)e−τm s U(s).(8)图1Smith预估控制系统Fig.1Control system structure with SP从式(5)可以看出,图1的反馈量是无滞后标称模型Y m(s)的输出和有滞后实际系统与标称模型之差Y(s)−Y mt(s)的和.当标称系统等于实际系统时,即当下列条件成立:K m=K,T m=T,τm=τp,(9)有Y f(s)=Y m(s).(10)当式(10)成立时,反馈量Y f(s)只有标称模型的输出Y m(s),图1中的时滞环节移到了闭环系统的外面了,整个闭环控制系统变成了一个没有时滞的控制系统,此时达到很好的控制效果.但是条件(9)一般是不第2期李向阳等:大时滞不确定系统的滞后时间削弱与自抗扰控制251成立的,此时控制性能难以保证.为此,出现了许多Smith预估控制系统的改进形式,包括Astrom改进型和增益自适应改进型,分别如图2和图3所示.图2Astrom改进型Smith预估控制系统Fig.2Control system structure with Astrom’s modified SP图3增益自适应Smith预估补偿控制系统Fig.3Gain adaptive SP compensation control system图1的经典Smith预估控制系统是把G m,G pt和G mt分别在3个不同时刻t,t−τp和t−τm的系统输出混合在一起作为反馈量,采用一个控制器G c进行控制;图2中的Astrom改进型Smith预估控制系统把Y m(s)和Y(s)−Y mt(s)分别用2个不同控制器G c1和G c2进行控制,提供控制器设计和参数整定的灵活性,控制器G c1的目标是使Y m跟随R,控制器G c2的目标是克服扰动的影响使系统输出Y跟随Y mt,控制器G c2的整定受控制器G c1的影响,图2的Astrom改进型Smith预估控制系统比图1的经典Smith预估控制在控制器类型选择和参数整定方面更加灵活,可以获得更好的性能.与经典Smith预估控制方法一样,Astrom改进型Smith预估控制在式(9)–(10)条件成立且无外部扰动时,图2的G c2的输入为0,其输出U2也等于0,此时为开环控制,被控对象的控制输入是通过控制不含纯延时的标称模型产生的控制信号U1.U1是当标称模型G m为被控对象和R为参考输入的控制信号,也可以把U1称之为标称模型G m在输出为参考信号R时的逆输入信号,U1在应用时相当于一个前馈信号.当存在模型误差和外部扰动时,式(9)–(10)条件不成立时,图1是采用同一控制器G c来减少模型误差和外部扰动对输出的影响,而图2采用第2个控制器G c2来抗模型和外部扰动.图3是增益自适应Smith预估补偿控制系统[19],把图1的经典Smith预估控制系统中对应位置的减法运算变成了除法运算,加法运算变成了乘法运算.图3的除法运算模块A1/B1把G p相对于G m的增益变化求出,并在控制器G c中进行补偿,实现控制器增益自适应调节,保持环路增益不变.该方法削弱了过程增益变化对控制性能的影响,但是不能削弱过程滞后变化对输出的影响.图3中还增加了一个微分先行模块提高预测能力,乘法运算模块A2×B2用于抵消除法运算模块的作用,重新恢复反馈信号.图4是Smith预估器与ADRC相结合的用于滞后系统控制的SP-ADRC方法[16],该方法把图1的y f(t)经过ESO后得到系统输出的各阶导数和总扰动估计,该方法跟图1的方法类似,对滞后时间的估计误差比较敏感,还需进一步提高其性能.图4SP-ADRC结构图Fig.4Diagram of SP-ADRC structure图5是图1中从U到Y f的改造方框图,通过把被控对象中无滞后的标称模型与实际过程(含滞后)的输出进行加权的方法来构造反馈信号.根据图4的加权平均取反馈信号有Y f(s)=1L m+1Y(s)+L mL m+1Y m(s),(11)式中:当L m→0时,y f(t)→y(t),反馈信号取具有纯滞后环节的实际过程输出,滞后时间为τp;当L m→∞时,y f(t)→y m(t),反馈信号取无纯滞后环节的标称模型输出,滞后时间为0;当L m∈(0,∞)时,y f(t)是y m(t)和y(t)的加权平均,等效的滞后时间在0与τp之间,通过调节L m的大小可以调节滞后时间,起到了削弱滞后时间的作用,提高了系统的稳定性.但是,由于只有当L m→0时,才有y f(t)→y(t),真正的反馈量不是y(t),因此最后的控制效果存在稳态误差,L m的调节范围受到限制.文献[18]把L m设计成(2l m−2)/ (τm s+2)的形式,其中l m 1为可调参数,虽然提高了动态性能,但由于L m稳态时还是不为零的常数,仍然没有解决存在稳态误差的问题.本文在ADRC的框架下,综合Smith预估、解耦控制、增益自适应和滞后削弱的思想,用Smith预估中模型产生的控制量作为前馈控制量,提高响应速度;用ADRC的总扰动补偿机制代替增益自适应算法,克服增益自适应算法在除法计算中的数值稳定性问题;改进现有滞后削弱中的权函数,实现无稳态误差的控制.252控制理论与应用第41卷图5滞后时间削弱结构Fig.5Time-delay influence reducing structure3大滞后过程的ADRC方法在ADRC的框架下,大滞后过程的ADRC控制方案如图6所示,同样可以用经典ADRC的TD,ESO和SEF这3个组成部分来理解其工作原理;不同的是增加了基于系统边界模型的前馈环节,ESO被分离成两部分,一部分在等效被控对象G et(s)中,用于总扰动估计和补偿控制,另一部分合并到反馈控制器G fb(s)中, SEF的基于误差的控制律也在G fb(s)中实现.图6中的虚线框中的G pu(s)为系统输入进入ESO之前的预处理器,G cc(s)为补偿控制器,经典ADRC中补偿控制器为1;图6的前馈环节相当于图1中经典Smith预估控制或者Astrom的改进Smith预估控的预估部分,不同的是本方法采用的是被控系统的边界模型,而不是被控系统的标称模型,而且增加一个衰减系数γff,用于减少超调.u1本质上是TD之后的参考信号v关于边界模型G0的近似逆信号.图6具有前馈和滞后时间削弱结构的ADRC系统Fig.6ADRC system with feedforward and modified time-delay influence reducing structure图6中对削弱滞后时间的加权系统设计为一个动态传递函数.本文的系统边界模型是在真实模型变化的边界上取值,按照对系统稳定性最不利的参数来取值,能够保证所设计的控制系统在大范围内稳定.系统标称模型实际系统参数变化的中间取值,用于参数整定.而在前馈控制器和反馈控制器的设计中采用边界模型确定控制器的参数范围,而在参数优化过程中采用标称模型确定控制器的参数取值(在保证稳定性的参数范围内取值).下面按照频域来设计和时域来实现的方式进一步阐述图6的控制原理.对于式(3)的FOPDT被控对象,有如下假设1.假设1a=1/T,b=K/T;a∈[a min,a max],a min>0;b∈[b min,b max],b min>0;取a0=a min,b0=b max;a min a m a max,b min b m b max.由假设1,系统的边界模型为G0(s)=b0s+a0,G0t(s)=b0s+a0e−sτp,(12)系统的标称模型为G m(s)=b ms+a m,G mt(s)=b ms+a me−sτp.(13)3.1前馈控制器Gff(s)的设计Gff(s)的目的是给控制系统提供一个合适的前馈控制量u1,该前馈量的存在并不影响整个控制系统的稳定性,只要求由Gff(s)和G0(s)组成的回路本身是稳定的,且满足一定的性能.可以把Gff(s)和G0(s)组成回路的闭环传递函数设计成可调参数的滤波器形式.设为Φff(s),则有Φff(s)=G0(s)Gff(s)1+G0(s)Gff(s),(14)则前馈控制器为Gff(s)=Φff(s)G0(s)(1−Φff(s)).(15)为了使前馈控制量在起始时刻也平滑,把Φff(s)设第2期李向阳等:大时滞不确定系统的滞后时间削弱与自抗扰控制253计成二阶阻尼传递函数,有Φff(s)=1T2ffs2+2ξffTffs+1,(16)式中:ξff为前馈回路的阻尼比;Tff为前馈回路的自然周期.前馈控制器需要根据系统参考输入快速给出前馈控制量,为了实现快读、无超调和平滑,取ξff 1和0<Tff τp.前馈控制器的输出经过一个衰减系数γff之后得到u1,0 γff 1,通过适当衰减后的前馈控制量有利于减少控制系统的超调.由于采用了衰减系数,前馈控制器可以采用边界模型或者标称模型,采用不同模型,衰减系数取不同值.当采用边界模型时,把式(12)(16)代入式(15)有Gff(s)=s+a0b0(T2ffs2+2ξffTffs).(17)3.2总扰动估计器ESO和补偿控制器G cc(s)设计ESO的目的是估计总扰动,G cc(s)实现经过补偿后的等效被控对象(图6中的虚线框)近似为G et(s)≈G0t(s)=G0(s)e−τp s.(18)根据实际过程的纯滞后时间τp的变化情况可以设计不同类型ESO.当τp为固定时,取τ0=τp,则由式(3)和式(13)有˙x1(t)=−a0x1+f1(t)+b0u(t−τ0),f1(t)=−(a−a0)x1+(b−b0)u(t−τ0)+d(t−τ0),y(t)=x1(t).(19)系统(19)的ESO设计为˙ˆx1(t)=−a0ˆx1+β1(y−ˆx1)+ˆx2+b0u(t−τ0),˙ˆx2=β2(y−ˆx1),(20)其中β1>0和β2>0为二阶ESO的增益,是Hurwitz多项式的系数.此时,G pu(s)=1,ESO的输出ˆf d=ˆx2即为前τp时刻的总扰动.实际中,当τp在一定范围变化时,可以通过试验获得纯滞后的变化范围,τp∈[τmin,τmax],取{τ0=τmin>0,τ1=τmax−τmin>0,(21)实际中一般τ1要比τ0要小得多,则根据式(3)有G pt(s)=b e−sτps+a≈b e−sτ0s+a1(τm−τ0)s+1,(22)上式推导中利用了近似公式e−s(τp−τ0)≈e−s(τm−τ0)≈1(τm−τ0)s+1,(23)则预处理器设计为G pu(s)=1(τm−τ0)s+1.(24)采用预处理器进行变时滞的处理方法就是ADRC中的提高阶次法来处理时滞系统的总扰动估计,本文用于在固定延时之外的可变延时.此时,ESO(19)的输入为u e和系统输出y,ESO的输出ˆf d为系统当前时刻以前(约为前τp时刻)的总扰动,与当前时刻的总扰动在时间上并不同步,很难完全抵消,因此需要一个补偿控制器确保补偿后的系统是稳定的.经典ADRC系统中G cc(s)为1,按照频域稳定理论,当存在较大滞后相位时,可以采用超前校正或者要求|G cc(jω)|<1,而当外界扰动中含有较大噪声时,总扰动的估计值中很可能含有部分噪声,此时可以采用滞后校正或者惯性滤波器.为了保证补偿控制回路有足够的稳定裕度,补偿控制器设计为G cc(s)=βccτcf s+1τcd s+1,(25)式中:0 βcc 1;0 τcf τ0;0.1<τcd 1.3.3滞后时间削弱的动态权重设计由于大滞后环节会产生严重的相位滞后,为了保证稳定性,需要限制闭环系统的带宽.当图6中参考信号的高频成分较大时,要求W1/(1+W2)取较大的值,减少系统输出在反馈信号y f(t)中所占的比例,保证系统稳定性;当参考输入信号处于平缓时,要求W1/(1+W2)接近0,加大实际系统输出在反馈信号y f(t)中所占的比例,保证稳定误差足够小,满足控制精度要求.根据这一思想,设计权重系数为W1(s)=L1τmax s=L1(τ0+τ1)s,L1>0,W2(s)=L2τmax s=L2(τ0+τ1)s,L2>0,W3(s)=L3τmin s=L3τ0s,L3 0,(26)则1+W3(s)1+W2(s)=1+L3τ0s1+L2(τ0+τ1)s,(27)W1(s)1+W2(s)=L1(τ0+τ1)s1+L2(τ0+τ1)s.(28)由式(27)–(28)可知,不含纯滞后的边界模型G0(s)输出信号的权重为一个近似微分(dirty derivative),而含纯滞后的被控系统输出的权重为一个超前–滞后校正环节,其分子具有微分先行作用,可以提高系统输出反馈的快速性和稳定性,静态时只有系统输出反馈量,保证了稳态精度.3.4TD和反馈控制器G fb(s)的设计TD用来安排闭环系统参考输入的过渡过程,采用如下的线性TD形式:˙v1(t)=v2,˙v2(t)=v3,˙v3=−3T rv3−3T2rv2−1T3r(v1−r),(29)254控制理论与应用第41卷式中r和T r分别为系统参考输入和TD时间常数.由于本文的ESO的标称模型并非积分串联模型,为了减少稳态误差,需要在反馈控制器G fb(s)中加入积分环节.先不考虑G et(s)和y的影响,只考虑y w对y f的贡献,由W1/(1+W2),G fb(s),γfb和G0(s)构成的闭环系统来设计G fb(s),设该闭环系统的传递函数为Φfb(s),则有Φfb(s)=γfb G fb(s)G0(s)W1(s)(1+W1(s))+G fb(s)G0(s)W1(s),(30)γfb为反馈控制器的增益系数,则反馈控制器为G fb(s)=(1+W2(s))Φfb(s)γfb G0(s)W1(s)(1−Φfb(s)).(31)对于含有纯滞后的系统,把Φfb(s)设计成二阶阻尼传递函数,有Φfb(s)=1T2fbs2+2ξfb T fb s+1,(32)式中:ξfb为反馈回路的阻尼比;T fb为反馈回路的自然周期.把式(12)(26)(32)代入式(31)有G fb(s)=(s+a0)(L2τ0s+1)γfb b0L1(τ0+τ1)s2(T2fbs+2ξfb T fb),(33)可调参数γfb初始值可取为1/b0,最终的控制量为{u0=u1+u2,U(s)=U0(s)−G cc(s)ˆF d(s),(34)式中ˆF d(s)为ESO估计的总扰动.4大滞后过程的ADRC的稳定性分析图6的控制系统结构,一共有3个闭环,包括产生前馈控制量u1的闭环、具有ESO的补偿控制闭环和具有滞后削弱的整个控制系统的闭环.产生前馈的闭环是一个确定系统,不影响整个系统的稳定性,可以不在系统的稳定性分析中考虑.在ADRC的理论体系中已完成了对其ESO的分析和证明,本文直接用引理给出.下面讨论具有削弱时间控制回路的反馈控制回路和总扰动补偿控制回路的稳定性.4.1削弱滞后时间控制回路的稳定性分析假如被控对象通过补偿控制后,从反馈控制器的角度看,其等效的被控对象为G0(s)e−τp s,则有如下定理.定理1当G et(s)经过ESO和补偿控制作用变为G0(s)e−τp s时,采用式(31)反馈控制器和式(32)的Φfb,采用式(26)的削弱滞后时间权重方法,并按照如下参数配置时,可以实现闭环系统稳定,即2 L1 10,0 L3 1.5,L2=α1L1,α1∈[0.01,0.3],ξfb 1,0<T fb τ0+τ1.(35)证当等效的被控对象为G0(s)e−τp s时,暂时不考虑前馈作用.W3(s)起微分先行作用,主要用于减少超调量,可以先不考虑其对稳定性的影响,即L3=0,则从U2到Y f的传递函数G f(s)为G f(s)=G0(s)W1(s)1+W2(s)+G0(s)e−τp s1+W2(s),(36)则相应闭环系统的传递函数Φf为Φf(s)=G fb(s)G f(s)b0+G fb(s)G f(s).(37)由式(36)–(37)和G0(s)与W1(s)的表达式有Φf(s)=M1(s)N1(s)=(G0W1+G0e−τp s)ΦfbG0W1(1−Φfb)+(G0W1+G0e−τp s)Φfb,(38)N1(s)=L1(τ0+τ1)s2(T2fbs+2ξfb T fb)+(L1(τ0+τ1)s+e−τp s),(39)M1(s)=L1τm s+e−τp s,(40)只要N1(s)的零点全部在左半平面,则Φf是稳定的.对N1(s)采用如下近似:e−sτp≈1−sτp,(41)则有N1(s)≈¯N1(s)=K10s3+K11s2+K12s+K13,(42)其中K10=L1(τ0+τ1)T2fb,K11=2L1(τ0+τ1)ξfb T fb,K12=L1(τ0+τ1)−τp,K13=1.(43)由于纯滞后环节e−sτp的奈奎斯特曲线为单位圆,而1−sτp的奈奎斯特曲线在单位圆的外部,因此¯N1(s)稳定,则N1(s)稳定.由式(35)有K12>L1(τ0+τ1)/2,0<T fb τ0+τ1,和ξfb 1,可以验证K11K12>K10K13,(44)因此闭环系统Φf是稳定的,定理1成立.证毕.由式(38)(40)可知,其阶跃响应的稳态误差为0,即有lims→0(sΦf1s)=1.(45)当被控对象未进行补偿控制时,有如下定理.定理2当G et(s)没有补偿控制时,即为G p(s)e−τp s时,采用式(31)反馈控制器和式(32)的Φf,取γfb=1/b0,采用式(26)的削弱滞后时间权重,并按照式(35)配置系统参数,可以实现闭环系统稳定.第2期李向阳等:大时滞不确定系统的滞后时间削弱与自抗扰控制255证当G et (s )=G p (s )e −τp s 时,为了简化,暂不考虑前馈和微分先行的作用,从U 2到Y f 的传递函数G f (s )为G f (s )=G 0(s )W 1(s )1+W 2(s )+G p (s )e −τp s1+W 2(s ).(46)与定理1相同的推导有Φf (s )=M 2(s )N 2(s )=(G 0W 1+G p e −τp s )ΦfbG 0W 1(1−Φfb )+(G 0W 1+G p e −τp s )Φfb ,(47)N 2(s )=b (s +a 0)e −τp s +b 0(s +a )L 1(τ0+τ1)s +L 1(τ0+τ1)s 2(T 2fb s+2ξfb T fb )b 0(s +a ),(48)M 2(s )=b (s +a 0)e −τp s +b 0(s +a )L 1(τ0+τ1)s.(49)采用式(41)近似公式有N 2(s )≈¯N2(s )=K 10s 4+K 11s 3+K 12s 2+K 13s +K 14,(50)其中K 20=b 0L 1(τ0+τ1)T 2fb ,K 21=b 0L 1(τ0+τ1)(2ξfb T fb +aT 2fb ),K 22=b 0L 1(τ0+τ1)2aξfb T fb +b 0L 1(τ0+τ1)−bτp ,K 23=ab 0L 1(τ0+τ1)−a 0bτp +b,K24=a 0b.(51)由假设参数取值范围,有K 2i >0,i =0,···,4,且根据条件(35)可以验证λ22=K 21K 22−K 20K 23K 21>0,(52)λ23=λ22K 23−K 21K 24λ22>0,(53)即劳斯表的第1列全部大于零,根据劳斯判据,N 2(s )的零点全部在复平面的左半平面.因此定理的闭环系统Φf 是稳定的,定理2成立.证毕.同理Φf 的阶跃响应为lim s →0(sΦf 1s )=a 0ba 0b =1.(54)当存在等效到U 2(s )侧的扰动D 2(s )时,有Y f (s )=G f (s )G fb (s )b 0+G f (s )G fb (s )V 1(s )+b 0G f (s )b 0+G f (s )G fb (s )D 2(s ).(55)当U 2(s )和D 2(s )都为阶跃信号时,根据终值定理有y (∞)=y f (∞)=lim s →0sY f (s )=1.(56)定理1和定理2说明:1)在获得确保系统稳定的参数范围时,采用了边界模型,对实现纯滞后系统的控制是有利的.由于ADRC 的模型并非积分串联模型[20],为了实现对阶跃输入的零稳态误差,因此需要在反馈控制律中增加积分项使其成为Ⅰ型系统.2)当广义被控对象为G 0W 1/(1+W 2)和不同的G f 合成时,当存在常值扰动时,反馈控制器式(33)都能保持闭环系统的稳定性和对阶跃信号的跟踪能力.3)从证明过程可以看出,当考虑W 3(s )的作用时,定理证明中的稳定性判定方法也是适用的.从式(43)中的系数表达式看出,增大ξfb 有利用提高系统的稳定裕度,减小T fb 有利于提高系统的快速性,可以根据实际过程需求灵活调节.4.2ESO 补偿控制回路的稳定性分析在ADRC 的理论框架中,ESO 对系统总扰动含有纯滞后项的估计中,当纯滞后时间变化不大时,有如下引理.引理1当过程纯滞后τp 已知且基本不变时,取τ0为τp ,采用式(20)形式的ESO,取ESO 的增益参数为β1=2ωo ,β2=ω2o ,ωo >0,(57)若f 1(t )及其导数有界时,则当ωo 充分大时,扩张状态ˆx 2可以实现对总扰动f 1(t )的准确估计[7,13,21].当τp 在一定范围变化时,先对系统控制输入进行式(24)的惯性环节的处理,然后再按照式(20)形式的ESO 进行处理获得系统总扰动.设当前时刻为t ,则当前实时总扰动为f 1(t ),而此时估计的总扰动为ˆf 1(t −τp ).由引理1有|f 1(t −τp )−ˆf 1(t −τp )|<σ1,(58)式中σ1>0为估计误差,是1/ωo 的高阶无穷小.在经典的ADRC 实时补偿中,是要用ˆf 1(t −τp )来抵消f 1(t )的影响,当没有纯滞后项时,两者的滞后时间只差一个采样周期和ESO 本身的延时,当ωo 充分大时,可以认为两者在时间上近似同步.对于纯滞后的系统,当f 1(t )变化较快时,两者相位可能大于180◦,可能造成|f 1(t )−ˆf 1(t −τp )|比f 1(t )还要大,此时,不仅没有补偿效果,甚至造成系统不稳定.因此,对于纯滞后系统,一方面要尽量获得较准确的系统模型,另一方面要专门设计补偿控制器保证补偿回路稳定.补偿控制器本质是要通过ˆf 1(t −τp )及其导数信息,获得f 1(t )的估计值⌣f 1(t )并进行补偿.由于对f 1(t )的模型信息知道较少,因此采用线性预测方法,线性预测对f 1(t )256控制理论与应用第41卷的要求或者假设是其在τp时间范围内,不要剧烈变化,是一个慢变过程,使得下式成立:|f1(t)−⌣f1(t)|<2σ1+|f1(t)|,(59)否则没有必要采用补偿控制,只采用削弱滞后时间的控制方法.定理3设f1(t)的最大频率含量为ωp,当选择补偿控制器式(25)的参数满足如下条件时:max 0 ω ωp |1−βcc1+jτcfω1+jτcdωe−jτpω|<1,(60)式中ω为扰动频率,则式(59)成立,补偿控制有效.证由绝对值的性质有|f1(t)−⌣f1(t)||f1(t)−ˆf1(t)|+|ˆf1(t)−⌣f1(t)|<σ1+|ˆf1(t)−⌣f1(t)|,(61)应用频域理论对上式最后一项进行处理,有⌣F1(s)=G cc(s)ˆF1(s)e−τp s,(62)ˆF1(s)−⌣F1(s)=ˆF1(s)(1−G cc(s)e−τp s)=ˆF 1(s)(1−β3τcf s+1τcd s+1e−τp s),(63)因此,当式(60)成立时,由式(63)有|f1(t)−⌣f1(t)|<σ1+|ˆf1(t)|<2σ1+|f1(t)|,(64)即式(59)成立,补偿控制是有效的.证毕.定理3的说明:1)定理3中,条件(60)中第2项的相角ψ(ω)= arctan(τcfω)−arctan(τcfω)−τpω,因此通过限制ωp 和减小β3,该条件是能够满足的,但是需要考虑扰动的频率范围,对于具有纯滞后的系统,过高频率范围的扰动是无法补偿的;2)增加ESO的带宽只能保证对其从输入信号u(t)和y(t)中提取总扰动的快速性,有利于减少ESO本身的延时,并不能解决补偿控制中被控对象本身的延时问题,补偿控制的稳定性是要考虑包括被控对象在内的整个回路.要实现基于ESO的补偿控制,需要考虑控制量补偿点(等效到被控系统输入端)的实时总扰动与被估计的总扰动在时间上的同步性(相位误差),当相位误差较大时,应该适当降低补偿控制器的增益,这一点在经典ADRC中往往是通过调节b0来实现,本文把总扰动的估计和补偿分离,分别按照估计精度和补偿控制的稳定性两个不同目标来设计,因此不需要调节b0,减少了调节b0对估计精度和反馈控制回路性能的副作用,实现了参数的解耦调节,方便实际工程应用,也为ADRC研究中如何确定b0及其物理意义提供了一个新的研究思路[22].4.3具有前馈和滞后时间削弱结构的ADRC系统虽然图6由多个部分组成,下面就每个部分的物理意义进行进一步说明,方便在实际的控制系统如DCS 中实现.TD部分是一个三阶低通滤波器,用于平滑参考输入信号,由式(29)有V1(s)=G TD(s)R(s)=R(s)(T r s+1)3.(65)前馈环节的传递传递函数为U1(s)=γffGff(s)Gff(s)+G−1(s)G−1(s)V1(s).(66)其中:G−10(s)是被控对象无滞后环节时的边界模型的逆模型;Gff(s)具有积分环节,是求G0(s)输出为V1(s)时的逆信号;系统γff是为了减少过前馈补偿.自抗扰补偿控制环节的作用是使得等效的被控系统G et(s)近似为G m(s)e−τm s(当ESO的模型取标称模型时).滞后削弱环节的作用是使得反馈控制器G fb(s)的反馈信号取实际被控对象的输出与其边界模型输出的加权平均值,高频时以边界模型为主,低频是以实际被控对象输出为主.Y f(s)=1+W31+W2Y(s)+W11+W2Y w(s),(67)式(67)保证了即使在系统输出有纯滞后时,反馈控制器G fb(s)一直有反馈信号Y f(s),且按照边界模型G0(s)来产生控制输出U2,从而确保整个控制系统的稳定.5仿真研究首先对FOPDT系统进行仿真研究,之后推广到SOPDT系统中.5.1FOPDT系统的滞后时间削弱和自抗扰控制考虑如下典型的FOPDT被控对象:G pt(s)=G p(s)e−sτp=bs+ae−sτp,(68)式中:a,b和τp的标称值分别为a m=0.3,b m=3和τm= 9,其中参数a和b上下变化20%,而τp上下变化1,有a∈[0.24,0.36],b∈[2.4,3.6].τp∈[8,10].则{a0=a min=0.24,b0=b max=3.6,τ0=8,τ1=2.(69)纯滞后时间与惯性时间常数之比为τm a m=2.7,显然这是一个大滞后系统.前馈控制器根据参考信号快速给出系统控制量的动态工作点,且不影响反馈控制器的动态调节过程,取前馈控制器的参数ξff=4, Tff=τ0/8=1和γff=0.5,前馈控制器为Gff(s)=s+a0b0(T2ffs2+2ξffTffs)=s+0.243.6(s2+4s).(70)确定控制器的参数范围是按照边界模型参数来确定,保证足够的鲁棒性,为了保证系统控制性能,整定。

2024学年上师闵分高三上英语月考1I. Listening comprehension1. A. At a grocery store. B. At a florist’s stand.C. At a bank counter.D. At an electronic shop.2. A. Sign up for a fitness class. B. Shop for fitness equipment.C. Have a fitness test.D. Watch a fitness video.3. A. Pay the ticket right away. B. Challenge the ticket.C. Ignore the ticket.D. Apologize to the parking officer.4. A. She is available on Saturday. B. She will cancel her dentist appointment.C. She can not cover the man’s shift.D. She forgot about the shift.5. A. The woman had better give him an extension on the deadline.B. The woman had better draft the proposal by herself.C. The woman had better approve the proposal.D. The woman had better give insights on the budget section.6. A. She doesn’t like animals from the shelter.B. She prefers buying pets from breeders.C. She thinks adopting a pet is a bad idea.D. She supports the idea of adopting a pet.7. A. Either of them is an experienced chef.B. Both of them have experienced failures in the kitchen.C. Neither of them are fond of cooking.D. Both of them are concerned about the new recipe.8. A. Bungee jumping is safe.B. Bungee jumping is thrilling.C. Bungee jumping might have risks.D. Bungee jumping is sure to be regrettable.9. A. The man should borrow the book several days later.B. The woman urgently needs the book back.C. The man does not need to return the book quickly.D. The woman is unwilling to lend the man the book.10. A. The woman’s parents will not appreciate a surprise party.B. The woman should prioritize her parents’ preferences for the party.C. The man dislikes the idea of a surprise party.D. The woman should plan a party based on her own preferences.Section BQuestions 11 through 13 are based on the following speech.11. A. A pupil in need of help. B. A person promising to donate money.C. A member from a charity.D. A teacher in the Semira Region.12. A.10%. B.35%. C.50%. D.65%.(13. A. To train teachers for the disabled. B. To help a pupil with special needs.C. To pay for a walking holiday.D. To organize a charity club for the disabled.Questions 14 through 16 are based on the following passage.14. A. To distract other students from doing well.B. To impress his friends with the shining ring.C. To improve his chances in the exam.D. To honor his grandfather by wearing a ring.15. A. By having enough time for breaks.B. By breaking down learning into portions.C. By informing teachers of the study habits.D. By wearing lucky objects.16. A. Start revision ahead of time.B. Reward oneself during revision.C. Consider different learning styles.D. Stay up late for the exam.Questions 17 through 20 are based on the following conversation.17. A. To inquire about travel recommendations.B. To discuss cultural festivals in Southeast Asia.C. To plan a solo travel adventure to Thailand.D. To learn about Mr. Patel’s travel experiences.18. A. Europe and Africa. B. Thailand and Vietnam.C. South America and Australia.D. Japan and China.19. A. Solely cultural exploration.B. Primarily outdoor adventures.C. A mix of cultural and outdoor experiences.D. Luxurious and private accommodations.20. A. It is ideal for meeting fellow travelers.B. It offers exclusive travel experiences.C. It is a more comfortable and secure stay.D. It offers authentic cultural immersion.II. Grammar and vocabularySection ADocumentary Shares Moving Story of POWs’ RescueAs the documentary The Sinking of Lisbon Mar u ended in the British Film Institute’s Southbank theater in London, England on Tuesday, long- lasting applause erupted, and tears welled up in the eyes of many in the audience.The Lisbon Maru was 21 armed Japanese cargo ship that participated in World WarII, and thedocumentary told the lesser- known story of hardship, horror, tragedy, and courage 22 surrounded its sinking while transporting more than 1,800 British prisoners of war, or POWs, from Hong Kong toward Japan.The sinking by a US submarine happened 23 the vessel did not bear a sign indicating it was carrying POWs, who were battened(封住底舱)down below deck at the time and who were left to drown by the Japanese soldiers on the ship.When the Lisbon Mar u went down off the coast of East China’s Zhejiang province on Oct 2, 1942, local Chinese fishermen 24 ( spring) into action, pulling 384 POWs from the water. 25 800 went down with the ship.Fang Li, 26 produced the documentary, said:“ It’s an untold history. We see the bravery of our Chinese fishermen. We hear heart- breaking stories of individual British families, one after another. And we are angered by Japan’s attempt 27 ( cover) up the brutal crime.”Wearing a T- shirt with the coordinates(坐标) 122°45’31.14”E, 30°13’44.42”N, which are those of the 28 (sink) Lisbon Maru, Fang said he first heard about the incident from a ferry captain while shooting another film in 2013. Moved by the story, Fang surveyed the area in2016 and, 29 sonar detectors installed on drones, located the wreck.In the following years, he and his team contacted more than 380 relatives of the POWs and interviewed 120 of them, 30 ( include) the only two British survivors still alive at the time.“While I was doing this, I was totally touched by those young boys, the age of my son. So many of them lost their lives there,” he told the BBC in 2018 after posting adverts in British newspapers seeking descendants of the POWs.Section BA. quicklyB. analyzeC. programmedD. adoptionE. drawbacksF. runG. dramatic H. transform I. distracted J. peacefully K. prospectImagine an urban neighborhood where most of the cars are self- driving. What would it be like to be a pedestrian?Actually, pretty good. In fact, pedestrians might end up with the 31 of the place.In a new study published in the Journal of Planning Education and Research, Millard- Ball looks at the 32 of urban areas where a majority of vehicles are“ autonomous” or self- driving. It’s a phenomenon that’s not as far off as one might think.“Autonomous vehicles have the potential to 33 travel behavior,” Millard- Ball says. He uses game theory to 34 the interaction between pedestrians and self- driving vehicles, with a focus on yielding(让行)at crosswalks.Because autonomous vehicles are designed to avoid risks, Millard- Ball’s model thinks autonomous vehicles may bring about a shift towards pedestrian- oriented urban neighborhoods. However, Millard- Ball also finds that the 35 of autonomous vehicles may be influenced by their strategic disadvantage that slows them down in urban traffic.“Pedestrians routinely play the game of chicken,” Millard- Ball writes. Crossing the street, even at a marked crosswalk without a traffic signal, requires a probability calculation: what are the odds of survival?The benefit of crossing the street 36 , instead of waiting for a gap in traffic, is traded off against theprobability of injury or even death. Pedestrians know that drivers are not interested in running them down-usually. But there is the chance a driver may be 37 or drunk.Self- driving cars are 38 to obey the rules of the road, including waiting for pedestrians to cross. They could provide the most 39 transformation in urban transportation systems. Parking, street design, and transportation service networks are likely to be revolutionized. In his latest study, Millard- Ball suggests that the potential benefits of self- driving cars-avoiding boredom of traffic and traffic accidents-may be outweighed by the 40 of an always play- it- safe vehicle that slows traffic for everybody.“From the point of view of a passenger in an automated car, it would be like driving down a street filled with unaccompanied five- year- old children,” Millard- Ball writes.Alternatively, planners could seize the opportunity to create more pedestrian- oriented streets. Autonomous vehicles could start a new era of pedestrian domination.II. Reading ComprehensionsSection AWhy some brilliant ideas get overlooked?In 1928, Karl Jansky, a young radio engineer at Bell Telephone Laboratories, began researching static interference that might obscure voice transmissions. Five years later, after building a large rotating antenna(天线) and investigating every possibility he could think of, he published his remarkable 41 : some of the static was coming from the Milky Way.Jansky’s theory was eye- catching enough to be published in The New York Times but scientists were 42 . Radio signals from outer space? Surely, they were too weak to detect. Jansky’s ideas were largely 43 for about a decade. He died at the age of 44.Thankfully, he lived long enough to see his ideas blossom into field of radio astronomy.Jansky’s story resonates with us: we all like the idea of the researcher who is so far ahead of their 44 that it takes years for the rest of the world to catch up. Gregor Mendel’s research into plant genetics is a famous example-published in 1866, it was only verified and taken seriously in 1900.The stories of Jansky and Mendel hold out some hope to anyone who feels that the world has not quite 45 their brilliance. There is even a name for such cases, coined by Anthony van Raan of Leiden University:“ Sleeping Beauties”, scientific papers that receive almost no citations for years, before finding wide 46 . (Some scholars argue that the term is sexist and prefer “delayed recognition”.)So what is it about an idea that delays recognition? One view is that brilliant ideas are overlooked when delivered by obscure messengers. Jansky and Mendel were somewhat detached from (离开) the scientific 47 . In 1970, the sociologist Stephen Col e published an analysis arguing that the obstacle tended to lie in the 48 of the idea itself, rather than the prestige of the scientist behind it. Ideas fell asleep for a hundred years because they were radical, or confusing, or both.It is difficult to be sure. Two scholars of the field, Eugene Garfield and Wolfgand Glanzel, have argued that such 49 of delayed recognition are so rare as to be hard to analyze. Studying papers published in 1980 from the vantage (优势) point of 2004, they looked for articles that were barely cited for five years, then subsequently 50 . They found just 60 examples in 450,000 cases. There are plenty of examples of research that is barely cited; what is rare istheir subsequent popularity.Why, then, is this myth such a compelling one? One explanation, of course, is that we all love a story of the underdog(黑马) who triumphs against 51 . Immediate and sustained success is as boring as immediate and sustained failure.Another is that scientists themselves are fond of the thought that their ideas are 52 . In an essay on delayed recognition, Garfield notes mildly that one historian of science, Derek Price, believed one of his own papers was suffering delayed recognition. It is easy to chuckle, but it is also easy to empathize.Delayed recognition is rare. Much more 53 is for people simply to reach their prime late in life. David Galenson is an economist who studies the creative output of musicians, artists, directors and others. Galenson has found that while it is quite possible to 54 as a radical young conceptual artist, there are many examples of“ old masters” whose later works are more admired than their youthful ones.We all need to be able to hold on to the idea that the best is yet to come. But it is too tempting to hope that what we have already produced will, one day, be recognized for its brilliance. Good things do not come to those who wait, if 55 is all they do. It is wiser to get back to work and make something better.41. A. paper B. device C. invention D. conclusion42. A. unreliable B. unimpressed C. unsatisfactory D. uncomfortable43. A. ignored B. kept C. criticized D. inspected44. A. mission B. goal C. schedule D. time45. A. caught up with B. taken advantage of C. made good use of D. had a good command of46. A. space B. platform C. attention D. vision47. A. data B. mainstream C. kingdom D. proof48. A. content B. origin C. popularity D. presence49. A. reports B. examples C. letters D. supporters50. A. broke off B. paid off C. switched off D. took off51. A. the authorities B. the wrong C. the opposite D. the odds52. A. underappreciated B. underdeveloped C. underequipped D. underperformed53. A. challenging B. complicated C. common D. difficult54. A. get through B. break through C. make ends meet D. make sense55. A. waiting B. complaining C. thinking D. socializingSection B(A)After some blood tests, Dr Stubs stood before me, a tall man, but short on personality and sporting a cold expression. You have systemic lupus, he said matter- of- factly. “Lupus,” he continued,“ is an auto- immune disease and …”I remember certain details but mostly I remember him talking about children.“ Children are no harm. But childbirth would jumpstart additional symptoms that could be life threatening. You already have two kids anyway.”As I got up to leave, shaken and drained, he said his parting words, “I would discourage any further research. There is no cure and nothing can prevent its progression.”Still, I did research lupus and its symptoms of tiredness and joint pain were both consistent with what I wasexperiencing. And eventually some major organs could be affected, causing shutdown and possibly death.I studied and found out that echinacea had a record in making immune system stronger. I decided that along with the plant I would strengthen my mindset by immersing myself in my family with my one- year- old son and three- year- old daughter.After another visit, I decided never to go back to Dr. Stubs. How could one endure repeatedly hear desperate words coming from an emotionless mouth even though they were truth? The years passed. When I would feel tired and achy I pulled support from my children and their laughter.Finally, after eight years, I went to Dr. Kirstein who was recommended by a friend. She stood there holding my hand and looking into my eyes warmly,“So, let’s talk a little.”Instantly my defenses were down. Before I knew it, she had me running on and on about my children, my husband, my life and dreams. I told her about all the meaningful activities I was involved in, those things I might have never done without the disease.After several follow- up tests, and greater research into my family history, Dr. Kirsteincame came to conclusive answer. I did not have systemic lupus. There must be something wrong with the initial tests 8 years before.I didn’t know whether I should jump for joy or scream because I had been living the last eight years in fear of a fatal disease. But then I realized that I had been living every day, not so much in fear, but in happiness. Every day wasa gift and I knew it.56. Dr. Strubs warned the author against having more children because ______.A. The process of giving birth put her life in dangerB. Taking care of children will gradually worsen her diseaseC. Her disease will threaten the health of her childrenD. She already has enough children57. Why did the author stop seeing doctor Strubs after two visits?A. Because she was not qualified to treat her disease.B. Because he recommended Dr. Kirkstein to her.C. Because his cold attitude upset the author.D. Because she suspected his diagnosis about her disease.58. How did the author deal with the disease?A. She calmly waited for major organs to shut down.B. she took effective medicine regularly to fight the disease.C. She turned to Dr. Kirstein to get cure for the disease.D. She tried to strengthen immune system and drew strength from family.59. Why did the author think every day in the past 8 years was a gift?A. Because systemic lupus was no longer a deadly disease.B. Because she made every day valuable in spite of disease.C. Because she received a gift every day from her family.D. Because she only occasionally felt pain and tiredness.(B)The data behind the push for a four- day weekDe- StressStaff at PerpetualGuardian reportedtheir stress levelsdecreased from 45 percent to 38 per centafter a four- day week.9-New working hours5After the Industrial Revolution, our working day decreasedTHE SLACKERS OF THE G7According to the Office for National Statistics, the UK’s GrossDomestic Product per hour worked is 15.1 per cent lower than therest of the G7, ( labelled G7exUK in graph).ways, in the tail end of a post- manufacturing industry style of working.“I think we have an overemphasis(B)Pursuit Marketing, based in Glasgow, declared Fridays to be voluntary for all staff in September2016. Following an initial 37 per cent productivity increase, which operations director Lorraine Gray owes to the novelty factor, total productivity settled to almost 30 percent higher than before the change.“I think it works really well here because it’s part of an overall culture of wellbeing,” says Gray.” Everyone is really clear that the focus is on the work- life balance and making sure everyone can be the best version of themselves.”Having less time to complete the same tasks drives staff to work efficiently. “Just shifting to thinking about’ How can I do my work in less time?’ focuses people’s attention on what it is important for them to do. They make slightly more strategic decisions over the actions that are going to result in higher levels of productivity,” explains Prof Paul Redford, an occupational psychologist at the University of the West of England.The 9 to 5, five- day week is a relatively recent invention in the history of human work. It was the result of muchcampaigning to reduce working hours once the Industrial Revolution had provided technology to vastly improve productivity. The Trades Union Congress (TUC) believes that we should once more take advantage of the rewards of our technological boom, in particular AI and automation, and shorten our working week further.“The Industrial Revolution, with the promotion of factory- based working, shifted the nature of work to this 9 to 5,’ says Redford. “We’re still, in some on productivity. Sometimes the focus on wellbeing is saying that it’s good to have high level of wellbeing because it’s more productive; I think that wellbeing is not a bad aim in and of itself.”60. What does “the novelty factor”( paragraph 1) refer to?A. Productivity increased by 38%.B. Workers needn’t work on Fridays.C. Pursuit Marketing was based in Glasgow.D. Total productivity settled to almost 30% higher.61. What conclusion can be drawn from the column of“ The data behind the push for a four- day week”?A. G7exUK in graph refers to the members of the G7 inclusive of the UK.B. The working hours per week decreased greatly in the decade from 1920 to 1930.C.38% of the staff members at Perpetual Guardian were against the four- day week.D. Workers in Germany were about 35% more productive than those in the UK in 2016.62. In terms of a four- day work week, which of the following statements is Prof Paul Redford most likely to agree with?A. Everyone can become the best decision maker.B. High productivity can improve workers’ wellbeing.C. Workers may ignore the importance of productivity.D. AI and automation has resulted in a shorter working week.(C)Imagine a world in which your life is filled with intelligent advertisements. Jaron Lanier, who was an adviser on “Minority Report”, asci- fi film, worries that this could be the future. A few platform firms, he fears, will control what consumers see and hear and other companies will have to use some of their profits (by buying ads) to gain access to them.That may sound ridiculous, but it is increasingly what investors are banking on. The total market value of a basket of a dozen American firms that depend on ad revenue, or are designing their strategies around it, has risen by 126% over the past five years. The part of America’s economy that is ad- centric has become systematically important, with a market value that is larger than the banking industry.The huge sums being bet on advertising raise a question: how much of it can America take?A back- of- the- envelope calculation by Schumpeter suggests that stock prices currently imply that American advertising revenues will rise from 1% of GDP today, to as much as 1.8% of GDP by 2027-a massive-mp. Since 1980 the average has been 1.3%, according to Jonathan Barnard of Zenith, a media agency, and in the past few years the advertising market relative to GDP has been shrinking.There are reasons why it might go on, points out Bob Norman of Group M, another media agency. In the old days advertisers in Time magazine or on billboards in Times Square were what only giant firms could afford. But techplatforms have done a brilliant job of persuading smaller companies to spend money targeting customers.Adverts could become even more effective at identifying customers and attracting them to spend money, using data that have been gathered to anticipate their needs. As commerce shifts online, firms will cut back on conventional marketing, freeing up budgets to spend more on digital ads.Yet there is a logical limit to the size of the advertising market: the irritation factor, or how much consumers can absorb without being put off. The golden rule used to be that ads could comprise no more than 33-50% of TV or radio programming, or of a magazine’s pages, says Rishad Tobacco wala, of Publicis, an advertising firm. The digital world is already showing signs of saturation. More people are using ad- blocking software. Tech brands that avoid bombarding(狂轰滥炸) customers with ads, such as Apple and Netflix, are wildly popular.63. What can be learned from paragraph 2?A. Some decisions that investors make are ridiculous.B. Investors are optimistic about intelligent advertising.C. The banking industry itself has been shrinking greatly.D. More American firms devote themselves to advertising.64. According to Bob Norman, why might American advertising revenues account for a larger part of GDP?A. Conventional marketing is losing its appeal.B. Giant firms will spend much more on advertising.C. Advertising will be available to more and more firms.D. Customers are becoming more willing to spend money.65. By “The digital world is already showing signs of saturation”( paragraph 6), the writer means that ______.A. ad- blocking software needs to be used more widelyB. customers can hardly skip a website filled with advertisementC. the digital world is not as advanced as commonly thoughtD. the online advertising market may have reached its limit66. What is the passage mainly about?A. The limits of intelligent advertising.B. The prospects of intelligent advertising.C. The advantages of intelligent advertising.D. The dominance of intelligent advertising.Section CA. Making only mindful purchases, and looking for ways to recycle my clothes makes me a better consumer.B. Its modern simplicity really appeals to me.C. Some fibres simply do not recycle and do not de- compose in landfill at the end of their usefulness.D. It switches the make-wear-and- dispose cycle of fashion into a circular one.E. One of my favourites is this burnt orange lightweight, unlined wool coat.F. I only wish I’d learned this lesson about shopping a lot sooner than I did!Full Circle FashionAutumn’s cooler temperature and beautiful colours never cease to excite me. I love reaching deep into mywardrobe and rediscovering the soft wool items that have served me well for many years. 67 Every October, I decide it’s time for it to make its yearly appearance. The loose style allows for lots of layering, so I’m able to wear it now and throughout the colder winter weather. It was a carefully considered purchase, and one I’ve not regretted for a moment. I always find the more time and thought I put into my wardrobe investments, the better they pay off.An item currently under consideration is this one that caught my eye last winter - a recycled cashmere poncho(羊绒斗篷). I’ve tried on this long poncho a few times and a year later, I still love it. 68 Also the cashmere itself is superb quality. The flexibility of a long poncho makes it even more irresistible. It would be ideal for a chilly office or aeroplane. It layers perfectly under loose long coat like my orange one. I love how it modernizes a odernizesr blouse. It feels like a wise investment for my wardrobe; supporting a business that facilitates sustainable fashion feels like a wise direction of my money.“Circular fashion”, where no longer used items are re- crafted into new clothes (like this poncho) is a new way of consuming that will be with us forever. 69 Every aspect of the process ensures tons of clothing do not end up in landfill each year. In general, circular fashion opts for wool, cotton, cashmere, and silk- all of which can be re- used or mixed with new natural fibres. These materials are more expensive, but if they are used in several circular cycles of clothing in the future, they pollute and waste less of our natural resources. 70 And innovative circular fashion brands will soon be giving us many more incredible options.IV. Summary Writing71.How to make resolutions stickHow are those New Year’s resolutions going? If you’re persisting, good for you. Many people do not. Given that the real challenge seems to be not making resolutions, but keeping them, I would like to understand more about that challenge.There is a revealing story at the end of How to Change in which Milkman and her colleague Angela Duckworth discuss the success of a large experiment. This experiment was run with a national gym chain and aimed to get people exercising more. Had it been a success? While the experimental persuasions were demonstrably effective at getting people to go to the gym during the four- week experimental period, they were far less effective at getting people to maintain their gym- going habit. If you hope for persistent results, one possible answer is persistent persuasion.There are other approaches. David Epstein, for example, had been struggling to quit his late- night snacking habit. When moving house, he simply decided that he would leave the old habit in the old house. This approach, he writes, was completely successful. Epstein also made a clear plan, something that is often missing from resolutions. Your resolutions to exercise more? Great! Where and how will you exercise, and when will you do it? It is better to sign up for a particular exercise class than for a generic gym membership, because you’ re forced to be specific about how you will achieve your goal.Another idea that has stuck in my mind is that our actions are influenced both by driving forces and by restraints -the accelerator(加速器) and the brake, if you like. When we want to move, we instinctively stamp harder on the accelerator, but we often get better results from releasing the brake. If you’re thinking of embracing a new resolution, ask yourself, “Why haven’t I been doing this already? What has been stopping me?” Answer those questions, and you might learn something that will help make your new resolution stick.V. Translation72.一到公司，他就被告知由于台风来袭电力中断。

IndexAactuation layer, 132average brightness,102-103adaptive control, 43Badaptive cruise control, 129backpropagation algorithm, 159adaptive FLC, 43backward driving mode,163,166,168-169adaptive neural networks,237adaptive predictive model, 283Baddeley-Molchanov average, 124aerial vehicles, 240 Baddeley-Molchanov fuzzy set average, 120-121, 123aerodynamic forces,209aerodynamics analysis, 208, 220Baddeley-Molchanov mean,118,119-121alternating filter, 117altitude control, 240balance position, 98amplitude distribution, 177bang-bang controller,198analytical control surface, 179, 185BCFPI, 61-63angular velocity, 92,208bell-shaped waveform,25ARMAX model, 283beta distributions,122artificial neural networks,115Bezier curve, 56, 59, 63-64association, 251Bezier Curve Fuzzy PI controller,61attitude angle,208, 217Bezier function, 54aumann mean,118-120bilinear interpolation, 90, 300,302automated manual transmission,145,157binary classifier,253Bo105 helicopter, 208automatic formation flight control,240body frame,238boiler following mode,280,283automatic thresholding,117border pixels, 101automatic transmissions,145boundary layer, 192-193,195-198autonomous robots,130boundary of a fuzzy set,26autonomous underwater vehicle, 191braking resistance, 265AUTOPIA, 130bumpy control surface, 55autopilot signal, 228Index 326CCAE package software, 315, 318 calibration accuracy, 83, 299-300, 309, 310, 312CARIMA models, 290case-based reasoning, 253center of gravity method, 29-30, 32-33centroid defuzzification, 7 centroid defuzzification, 56 centroid Method, 106 characteristic polygon, 57 characterization, 43, 251, 293 chattering, 6, 84, 191-192, 195, 196, 198chromosomes, 59circuit breaker, 270classical control, 1classical set, 19-23, 25-26, 36, 254 classification, 106, 108, 111, 179, 185, 251-253classification model, 253close formation flight, 237close path tracking, 223-224 clustering, 104, 106, 108, 251-253, 255, 289clustering algorithm, 252 clustering function, 104clutch stroke, 147coarse fuzzy logic controller, 94 collective pitch angle, 209 collision avoidance, 166, 168 collision avoidance system, 160, 167, 169-170, 172collision avoidance system, 168 complement, 20, 23, 45 compressor contamination, 289 conditional independence graph, 259 confidence thresholds, 251 confidence-rated rules, 251coning angle, 210constant gain, 207constant pressure mode, 280 contrast intensification, 104 contrast intensificator operator, 104 control derivatives, 211control gain, 35, 72, 93, 96, 244 control gain factor, 93control gains, 53, 226control rules, 18, 27, 28, 35, 53, 64, 65, 90-91, 93, 207, 228, 230, 262, 302, 304-305, 315, 317control surfaces, 53-55, 64, 69, 73, 77, 193controller actuator faulty, 289 control-weighting matrix, 207 convex sets, 119-120Coordinate Measurement Machine, 301coordinate measuring machine, 96 core of a fuzzy set, 26corner cube retroreflector, 85 correlation-minimum, 243-244cost function, 74-75, 213, 282-283, 287coverage function, 118crisp input, 18, 51, 182crisp output, 7, 34, 41-42, 51, 184, 300, 305-306crisp sets, 19, 21, 23crisp variable, 18-19, 29critical clearing time, 270 crossover, 59crossover probability, 59-60cruise control, 129-130,132-135, 137-139cubic cell, 299, 301-302, 309cubic spline, 48cubic spline interpolation, 300 current time gap, 136custom membership function, 294 customer behav or, 249iDdamping factor, 211data cleaning, 250data integration, 250data mining, 249, 250, 251-255, 259-260data selection, 250data transformation, 250d-dimensional Euclidean space, 117, 124decision logic, 321 decomposition, 173, 259Index327defuzzification function, 102, 105, 107-108, 111 defuzzifications, 17-18, 29, 34 defuzzifier, 181, 242density function, 122 dependency analysis, 258 dependency structure, 259 dependent loop level, 279depth control, 202-203depth controller, 202detection point, 169deviation, 79, 85, 185-188, 224, 251, 253, 262, 265, 268, 276, 288 dilation, 117discriminated rules, 251 discrimination, 251, 252distance function, 119-121 distance sensor, 167, 171 distribution function, 259domain knowledge, 254-255 domain-specific attributes, 251 Doppler frequency shift, 87 downhill simplex algorithm, 77, 79 downwash, 209drag reduction, 244driver’s intention estimator, 148 dutch roll, 212dynamic braking, 261-262 dynamic fuzzy system, 286, 304 dynamic tracking trajectory, 98Eedge composition, 108edge detection, 108 eigenvalues, 6-7, 212electrical coupling effect, 85, 88 electrical coupling effects, 87 equilibrium point, 207, 216 equivalent control, 194erosion, 117error rates, 96estimation, 34, 53, 119, 251, 283, 295, 302Euler angles, 208evaluation function, 258 evolution, 45, 133, 208, 251 execution layer, 262-266, 277 expert knowledge, 160, 191, 262 expert segmentation, 121-122 extended sup-star composition, 182 Ffault accommodation, 284fault clearing states, 271, 274fault detection, 288-289, 295fault diagnosis, 284fault durations, 271, 274fault isolation, 284, 288fault point, 270-271, 273-274fault tolerant control, 288fault trajectories, 271feature extraction, 256fiber glass hull, 193fin forces, 210final segmentation, 117final threshold, 116fine fuzzy controller, 90finer lookup table, 34finite element method, 318finite impulse responses, 288firing weights, 229fitness function, 59-60, 257flap angles, 209flight aerodynamic model, 247 flight envelope, 207, 214, 217flight path angle, 210flight trajectory, 208, 223footprint of uncertainty, 176, 179 formation geometry, 238, 247 formation trajectory, 246forward driving mode, 163, 167, 169 forward flight control, 217 forward flight speed, 217forward neural network, 288 forward velocity, 208, 214, 217, 219-220forward velocity tracking, 208 fossil power plants, 284-285, 296 four-dimensional synoptic data, 191 four-generator test system, 269 Fourier filter, 133four-quadrant detector, 79, 87, 92, 96foveal avascular zone, 123fundus images, 115, 121, 124 fuselage, 208-210Index 328fuselage axes, 208-209fuselage incidence, 210fuzz-C, 45fuzzifications, 18, 25fuzzifier, 181-182fuzzy ACC controller, 138fuzzy aggregation operator, 293 fuzzy ASICs, 37-38, 50fuzzy binarization algorithm, 110 fuzzy CC controller, 138fuzzy clustering algorithm, 106, 108 fuzzy constraints, 286, 291-292 fuzzy control surface, 54fuzzy damage-mitigating control, 284fuzzy decomposition, 108fuzzy domain, 102, 106fuzzy edge detection, 111fuzzy error interpolation, 300, 302, 305-306, 309, 313fuzzy filter, 104fuzzy gain scheduler, 217-218 fuzzy gain-scheduler, 207-208, 220 fuzzy geometry, 110-111fuzzy I controller, 76fuzzy image processing, 102, 106, 111, 124fuzzy implication rules, 27-28 fuzzy inference system, 17, 25, 27, 35-36, 207-208, 302, 304-306 fuzzy interpolation, 300, 302, 305- 307, 309, 313fuzzy interpolation method, 309 fuzzy interpolation technique, 300, 309, 313fuzzy interval control, 177fuzzy mapping rules, 27fuzzy model following control system, 84fuzzy modeling methods, 255 fuzzy navigation algorithm, 244 fuzzy operators, 104-105, 111 fuzzy P controller, 71, 73fuzzy PD controller, 69fuzzy perimeter, 110-111fuzzy PI controllers, 61fuzzy PID controllers, 53, 64-65, 80 fuzzy production rules, 315fuzzy reference governor, 285 Fuzzy Robust Controller, 7fuzzy set averages, 116, 124-125 fuzzy sets, 7, 19, 22, 24, 27, 36, 45, 115, 120-121, 124-125, 151, 176-182, 184-188, 192, 228, 262, 265-266fuzzy sliding mode controller, 192, 196-197fuzzy sliding surface, 192fuzzy subsets, 152, 200fuzzy variable boundary layer, 192 fuzzyTECH, 45Ggain margins, 207gain scheduling, 193, 207, 208, 211, 217, 220gas turbines, 279Gaussian membership function, 7 Gaussian waveform, 25 Gaussian-Bell waveforms, 304 gear position decision, 145, 147 gear-operating lever, 147general window function, 105 general-purpose microprocessors, 37-38, 44genetic algorithm, 54, 59, 192, 208, 257-258genetic operators, 59-60genetic-inclined search, 257 geometric modeling, 56gimbal motor, 90, 96global gain-scheduling, 220global linear ARX model, 284 global navigation satellite systems, 141global position system, 224goal seeking behaviour, 186-187 governor valves80, 2HHamiltonian function, 261, 277 hard constraints, 283, 293 heading angle, 226, 228, 230, 239, 240-244, 246heading angle control, 240Index329heading controller, 194, 201-202 heading error rate, 194, 201 heading speed, 226heading velocity control, 240 heat recovery steam generator, 279 hedges, 103-104height method, 29helicopter, 207-212, 214, 217, 220 helicopter control matrix, 211 helicopter flight control, 207 Heneghan method, 116-117, 121-124heuristic search, 258 hierarchical approaches, 261 hierarchical architecture, 185 hierarchical fuzzy processors, 261 high dimensional systems, 191 high stepping rates, 84hit-miss topology, 119home position, 96horizontal tail plane, 209 horizontal tracker, 90hostile, 223human domain experts, 255 human visual system, 101hybrid system framework, 295 hyperbolic tangent function, 195 hyperplane, 192-193, 196 hysteresis thres olding, 116-117hIIF-THEN rule, 27-28image binarization, 106image complexity, 104image fuzzification function, 111 image segmentation, 124image-expert, 122-123indicator function, 121inert, 223inertia frame, 238inference decision methods, 317 inferential conclusion, 317 inferential decision, 317 injection molding process, 315 inner loop controller, 87integral time absolute error, 54 inter-class similarity, 252 internal dependencies, 169 interpolation property, 203 interpolative nature, 262 intersection, 20, 23-24, 31, 180 interval sets, 178interval type-2 FLC, 181interval type-2 fuzzy sets, 177, 180-181, 184inter-vehicle gap, 135intra-class similarity, 252inverse dynamics control, 228, 230 inverse dynamics method, 227 inverse kinema c, 299tiJ - Kjoin, 180Kalman gain, 213kinematic model, 299kinematic modeling, 299-300 knowledge based gear position decision, 148, 153knowledge reasoning layer, 132 knowledge representation, 250 knowledge-bas d GPD model, 146eLlabyrinths, 169laser interferometer transducer, 83 laser tracker, 301laser tracking system, 53, 63, 65, 75, 78-79, 83-85, 87, 98, 301lateral control, 131, 138lateral cyclic pitch angle, 209 lateral flapping angle, 210 leader, 238-239linear control surface, 55linear fuzzy PI, 61linear hover model, 213linear interpolation, 300-301, 306-307, 309, 313linear interpolation method, 309 linear optimal controller, 207, 217 linear P controller, 73linear state feedback controller, 7 linear structures, 117linear switching line, 198linear time-series models, 283 linguistic variables, 18, 25, 27, 90, 102, 175, 208, 258Index 330load shedding, 261load-following capabilities, 288, 297 loading dock, 159-161, 170, 172 longitudinal control, 130-132 longitudinal cyclic pitch angle, 209 longitudinal flapping angle, 210 lookup table, 18, 31-35, 40, 44, 46, 47-48, 51, 65, 70, 74, 93, 300, 302, 304-305lower membership functions, 179-180LQ feedback gains, 208LQ linear controller, 208LQ optimal controller, 208LQ regulator, 208L-R fuzzy numbers, 121 Luenburger observer, 6Lyapunov func on, 5, 192, 284tiMMamdani model, 40, 46 Mamdani’s method, 242 Mamdani-type controller, 208 maneuverability, 164, 207, 209, 288 manual transmissions, 145 mapping function, 102, 104 marginal distribution functions, 259 market-basket analysis, 251-252 massive databases, 249matched filtering, 115 mathematical morphology, 117, 127 mating pool, 59-60max member principle, 106max-dot method, 40-41, 46mean distance function, 119mean max membership, 106mean of maximum method, 29 mean set, 118-121measuring beam, 86mechanical coupling effects, 87 mechanical layer, 132median filter, 105meet, 7, 50, 139, 180, 183, 302 membership degree, 39, 257 membership functions, 18, 25, 81 membership mapping processes, 56 miniature acrobatic helicopter, 208 minor steady state errors, 217 mixed-fuzzy controller, 92mobile robot control, 130, 175, 181 mobile robots, 171, 175-176, 183, 187-189model predictive control, 280, 287 model-based control, 224 modeless compensation, 300 modeless robot calibration, 299-301, 312-313modern combined-cycle power plant, 279modular structure, 172mold-design optimization, 323 mold-design process, 323molded part, 318-321, 323 morphological methods, 115motor angular acceleration, 3 motor plant, 3motor speed control, 2moving average filter, 105 multilayer fuzzy logic control, 276 multimachine power system, 262 multivariable control, 280 multivariable fuzzy PID control, 285 multivariable self-tuning controller, 283, 295mutation, 59mutation probability, 59-60mutual interference, 88Nnavigation control, 160neural fuzzy control, 19, 36neural networks, 173, 237, 255, 280, 284, 323neuro-fuzzy control, 237nominal plant, 2-4nonlinear adaptive control, 237non-linear control, 2, 159 nonlinear mapping, 55nonlinear switching curve, 198-199 nonlinear switching function, 200 nonvolatile memory, 44 normalized universe, 266Oobjective function, 59, 74-75, 77, 107, 281-282, 284, 287, 289-291,Index331295obstacle avoidance, 166, 169, 187-188, 223-225, 227, 231 obstacle avoidance behaviour, 187-188obstacle sensor, 224, 228off-line defuzzification, 34off-line fuzzy inference system, 302, 304off-line fuzzy technology, 300off-line lookup tables, 302 offsprings, 59-60on-line dynamic fuzzy inference system, 302online tuning, 203open water trial, 202operating point, 210optical platform, 92optimal control table, 300optimal feedback gain, 208, 215-216 optimal gains, 207original domain, 102outer loop controller, 85, 87outlier analysis, 251, 253output control gains, 92 overshoot, 3-4, 6-7, 60-61, 75-76, 94, 96, 193, 229, 266Ppath tracking, 223, 232-234 pattern evaluation, 250pattern vector, 150-151PD controller, 4, 54-55, 68-69, 71, 74, 76-77, 79, 134, 163, 165, 202 perception domain, 102 performance index, 60, 207 perturbed plants, 3, 7phase margins, 207phase-plan mapping fuzzy control, 19photovoltaic power systems, 261 phugoid mode, 212PID, 1-4, 8, 13, 19, 53, 61, 64-65, 74, 80, 84-85, 87-90, 92-98, 192 PID-fuzzy control, 19piecewise nonlinear surface, 193 pitch angle, 202, 209, 217pitch controller, 193, 201-202 pitch error, 193, 201pitch error rate, 193, 201pitch subsidence, 212planetary gearbox, 145point-in-time transaction, 252 polarizing beam-splitter, 86 poles, 4, 94, 96position sensor detectors, 84 positive definite matrix, 213post fault, 268, 270post-fault trajectory, 273pre-defined membership functions, 302prediction, 251, 258, 281-283, 287, 290predictive control, 280, 282-287, 290-291, 293-297predictive supervisory controller, 284preview distance control, 129 principal regulation level, 279 probabilistic reasoning approach, 259probability space, 118Problem understanding phases, 254 production rules, 316pursuer car, 136, 138-140 pursuer vehicle, 136, 138, 140Qquadrant detector, 79, 92 quadrant photo detector, 85 quadratic optimal technology, 208 quadrilateral ob tacle, 231sRradial basis function, 284 random closed set, 118random compact set, 118-120 rapid environment assessment, 191 reference beam, 86relative frame, 240relay control, 195release distance, 169residual forces, 217retinal vessel detection, 115, 117 RGB band, 115Riccati equation, 207, 213-214Index 332rise time, 3, 54, 60-61, 75-76road-environment estimator, 148 robot kinematics, 299robot workspace, 299-302, 309 robust control, 2, 84, 280robust controller, 2, 8, 90robust fuzzy controller, 2, 7 robustness property, 5, 203roll subsidence, 212rotor blade flap angle, 209rotor blades, 210rudder, 193, 201rule base size, 191, 199-200rule output function, 191, 193, 198-199, 203Runge-Kutta m thod, 61eSsampling period, 96saturation function, 195, 199 saturation functions, 162scaling factor, 54, 72-73scaling gains, 67, 69S-curve waveform, 25secondary membership function, 178 secondary memberships, 179, 181 selection, 59self-learning neural network, 159 self-organizing fuzzy control, 261 self-tuning adaptive control, 280 self-tuning control, 191semi-positive definite matrix, 213 sensitivity indices, 177sequence-based analysis, 251-252 sequential quadratic programming, 283, 292sets type-reduction, 184setting time, 54, 60-61settling time, 75-76, 94, 96SGA, 59shift points, 152shift schedule algorithms, 148shift schedules, 152, 156shifting control, 145, 147shifting schedules, 146, 152shift-schedule tables, 152sideslip angle, 210sigmoidal waveform, 25 sign function, 195, 199simplex optimal algorithm, 80 single gimbal system, 96single point mass obstacle, 223 singleton fuzzification, 181-182 sinusoidal waveform, 94, 300, 309 sliding function, 192sliding mode control, 1-2, 4, 8, 191, 193, 195-196, 203sliding mode fuzzy controller, 193, 198-200sliding mode fuzzy heading controller, 201sliding pressure control, 280 sliding region, 192, 201sliding surface, 5-6, 192-193, 195-198, 200sliding-mode fuzzy control, 19 soft constraints, 281, 287space-gap, 135special-purpose processors, 48 spectral mapping theorem, 216 speed adaptation, 138speed control, 2, 84, 130-131, 133, 160spiral subsidence, 212sporadic alternations, 257state feedback controller, 213 state transition, 167-169state transition matrix, 216state-weighting matrix, 207static fuzzy logic controller, 43 static MIMO system, 243steady state error, 4, 54, 79, 90, 94, 96, 98, 192steam turbine, 279steam valving, 261step response, 4, 7, 53, 76, 91, 193, 219stern plane, 193, 201sup operation, 183supervisory control, 191, 280, 289 supervisory layer, 262-264, 277 support function, 118support of a fuzzy set, 26sup-star composition, 182-183 surviving solutions, 257Index333swing curves, 271, 274-275 switching band, 198switching curve, 198, 200 switching function, 191, 194, 196-198, 200switching variable, 228system trajector192, 195y,Ttail plane, 210tail rotor, 209-210tail rotor derivation, 210Takagi-Sugeno fuzzy methodology, 287target displacement, 87target time gap, 136t-conorm maximum, 132 thermocouple sensor fault, 289 thickness variable, 319-320three-beam laser tracker, 85three-gimbal system, 96throttle pressure, 134throttle-opening degree, 149 thyristor control, 261time delay, 63, 75, 91, 93-94, 281 time optimal robust control, 203 time-gap, 135-137, 139-140time-gap derivative, 136time-gap error, 136time-invariant fuzzy system, 215t-norm minimum, 132torque converter, 145tracking error, 79, 84-85, 92, 244 tracking gimbals, 87tracking mirror, 85, 87tracking performance, 84-85, 88, 90, 192tracking speed, 75, 79, 83-84, 88, 90, 92, 97, 287trajectory mapping unit, 161, 172 transfer function, 2-5, 61-63 transient response, 92, 193 transient stability, 261, 268, 270, 275-276transient stability control, 268 trapezoidal waveform, 25 triangular fuzzy set, 319triangular waveform, 25 trim, 208, 210-211, 213, 217, 220, 237trimmed points, 210TS fuzzy gain scheduler, 217TS fuzzy model, 207, 290TS fuzzy system, 208, 215, 217, 220 TS gain scheduler, 217TS model, 207, 287TSK model, 40-41, 46TS-type controller, 208tuning function, 70, 72turbine following mode, 280, 283 turn rate, 210turning rate regulation, 208, 214, 217two-DOF mirror gimbals, 87two-layered FLC, 231two-level hierarchy controllers, 275-276two-module fuzzy logic control, 238 type-0 systems, 192type-1 FLC, 176-177, 181-182, 185- 188type-1 fuzzy sets, 177-179, 181, 185, 187type-1 membership functions, 176, 179, 183type-2 FLC, 176-177, 180-183, 185-189type-2 fuzzy set, 176-180type-2 interval consequent sets, 184 type-2 membership function, 176-178type-reduced set, 181, 183-185type-reduction,83-1841UUH-1H helicopter, 208uncertain poles, 94, 96uncertain system, 93-94, 96 uncertain zeros, 94, 96underlying domain, 259union, 20, 23-24, 30, 177, 180unit control level, 279universe of discourse, 19-24, 42, 57, 151, 153, 305unmanned aerial vehicles, 223 unmanned helicopter, 208Index 334unstructured dynamic environments, 177unstructured environments, 175-177, 179, 185, 187, 189upper membership function, 179Vvalve outlet pressure, 280vapor pressure, 280variable structure controller, 194, 204velocity feedback, 87vertical fin, 209vertical tracker, 90vertical tracking gimbal, 91vessel detection, 115, 121-122, 124-125vessel networks, 117vessel segmentation, 115, 120 vessel tracking algorithms, 115 vision-driven robotics, 87Vorob’ev fuzzy set average, 121-123 Vorob'ev mean, 118-120vortex, 237 WWang and Mendel’s algorithm, 257 WARP, 49weak link, 270, 273weighing factor, 305weighting coefficients, 75 weighting function, 213weld line, 315, 318-323western states coordinating council, 269Westinghouse turbine-generator, 283 wind–diesel power systems, 261 Wingman, 237-240, 246wingman aircraft, 238-239 wingman veloc y, 239itY-ZYager operator, 292Zana-Klein membership function, 124Zana-Klein method, 116-117, 121, 123-124zeros, 94, 96µ-law function, 54µ-law tuning method, 54。

英国大学电力专业排名、地址及教授介绍1 Cambridge 剑桥大学地址：英格兰剑桥镇网址：教授介绍：主要都是电力电子方向Prof Gehan Amaratunga Director of EPECResearch interests include: Nanoscale materials and device design for electronics and energy conversion. Novel materials and device structures for low cost, high efficiently solar cells. Power electronics for optimum grid connection of large photovoltaic electric generation systems. Integrated and discrete semiconductor devices for power switching and control.Dr Richard McMahon Senior LecturerCurrent research focuses on low maintenance generators for wind turbines; linear generators for wave power and energy efficient power conversion for power supplies and electric appliances such as compact fluorescent lights.Dr Timothy Coombs Heads Superconductivity GroupResearch Interests * Electrical Machines * Electromagnetic Modelling * Engineering Applications of Superconductivity * MEMS2 Southampton 南安普顿大学地址：英格兰南部海滨的Hampshire郡，主校区(Highfield Campus)距离南安普敦市中心3英里网址：教授介绍：以下为主要负责人及链接，无法打开Professor Jan SykulskiElectrical Power Engineering3 Imperial College 伦敦大学帝国理工学院地址：帝国理工主校区坐落于伦敦标准的富人区南肯辛顿网址：教授介绍：Dr Balarko ChaudhuriHis areas of interest are power systems dynamics, stability and robust control. He is actively involved with ABB Corporate Research in the area of wide-area monitoring and control of power systemsProf Goran StrbacProf Strbac's research interests include Power system optimisation and economics; Integration of distributed energy resources and Intermittency.Dr Bikash PalPower System Stability; Dynamic Equivalencing and Coherency; State estimation in power distribution system, Robust Control of Power System Oscillations; FACTS Controllers; Distributed and Renewable Energy Modelling; Grid Integration of Marine Wave Generations; and Risk modelling and assessment in distribution system operation.Dr Imad Jaimoukharobust controller design for structured and unstructured uncertainties; controller reduction; model reduction for large-scale systems; hierarchical optimization in robust controller design, robust control design for power system and fault detection and isolation.4 Surrey 萨里大学地址：位于英国伦敦市郊的吉尔福德网址：教授介绍：没有electrical engineering5 Loughborough 拉夫堡大学地址：位于英格兰中部的拉夫堡镇网址：/教授介绍：Professor Philip C EamesHis research focuses on various aspects of renewable energy systems, energy in buildings and thermal energy storage.Professor Ivor R SmithFor several years recently his research interests have been in the pused power area, where he has been concerned with the Generation, Processing and Application of High-Energy pulsed of electrical energy.Dr Murray ThomsonRenewables into existing electrical power systems. Analysis of low-voltage distribution networks and the development of flexible demand as a means of grid balancing in future low-carbon power systems incorporating high penetrations of intermittent wind, marine and solar powerDr Simon J Watson Head of Wind and Water Power ResearchCondition Monitoring of Wind Turbines; Wind Resource Assessment; Wind Power Forecasting; Wake Modelling; Wave Power Device Modelling; Climate Change Impacts.6 Edinburgh 爱丁堡大学地址：位于爱丁堡市中心，爱丁堡则位于苏格兰海滨，是苏格兰首府网址：/教授介绍：Prof Robin Wallacenetwork integration of distributed renewable energy generation and marine energyProf Janusz BialekPower system economics: Transmission pricing; Modelling electricity markets and security of supply; Congestion management.Sustainable power generation and supply: Future Network Technologies; Flexible Network; Asset Management and Performance in Energy Networks; Autonomous Regional Active Network Management System; Smart Grid Oscillation Management for a Changing Generation Mix. Power systems dynamic and stabilityProf Ian BrydenMarine Renewable EnergyDr Markus MuellerThe design of novel generator topologies for direct drive wave energy, wind energy and tidal current energy converters7 Sheffield 谢菲尔得大学地址：谢菲尔得大学位于约克郡南边的谢菲尔得市网址：教授介绍：Emeritus Professor Barry ChambersSmart electromagnetic structures. Target signature management. Passive and active radar absorbing materials. Conducting polymers and composites. Optimisation using evolutionary computing techniques. Automated microwave measurement systems. Radomes and electromagnetic windows.Emeritus Professor David HoweElectrical technologies for aerospace, automotive and marine applications. High integrity electrical drive systems. Novel electromagnetic devices. Multi-physics modelingProfessor Geraint JewellSelf-bearing electrical machines. Power dense electrical machines and actuators for aerospace and marine applications. Valve actuation. Electromagnetic modelling of novel devices8 Bristol 布里斯托大学地址：大学的几个校园分布在极具活力的现代海滨城市－布里斯托市中心，布里斯托是英格兰西南部最大的城市网址：/教授介绍：Dr Dritan KaleshiCommunications and distributed systems performance; connectivity and performance issues in access and local networks. Self-organised systems, service discovery. Specification of distributed systems; specification conformance testing. Small-device networking, and in particular home networking systems. Interoperability: standardisation and autonomic systems. ICT solutions for SmartGrids and distributed energy management.Dr Dave DruryHardware-in-the-Loop and real-time substructuring (hybrid dynamic) testing methods Aircraft generation and power management systems Hybrid automative vehicle traction and generation systems Efficient control of electric machines Distributed control methods, using industrial purpose built networks and standard ethernet9 York 约克大学地址：约克大学位于历史名城约克郡约克市网址：教授介绍：没有electrical engineering10 Essex 埃塞克斯大学地址：埃塞克斯大学位于英国有史以来最古老的市镇科尔切斯特(Colchester)的郊外两英里处，该镇也是英国的第一个首都网址：主校区：/Southend校区：/southendEast 15 校区：教授介绍：没有electrical engineering11 Bath 巴斯大学地址：巴斯市郊网址：/教授介绍：Dr Miles Alexander Redfernthe control and protection of distribution systemsthe connection of embedded generationintegration of renewable energy systems into utility networks.high speed transient based protection schemescommunications for power system control and protectionnon-invasive techniques for the location of buried utilities.Dr Furong Liall aspects of power system planning, operation, analysis and power system economics.Professor Raj AggarwalProfessor Ag garwal’s research interests are in Electrical Power and Energy Systems. His research group focuses on the technology to support the development of a secure and stable electricity supply network that is able to accommodate new and renewable forms of energy generation.12 Glasgow 格拉斯哥大学地址：格拉斯哥市以西3英里网址：教授介绍：Prof. Enrique Achapower systems analysis and power electronics applications in renewable energy systems.Prof. T.J.E. MillerActive in the Power Systems & Power Engineering research areaProf. John O'Reillyfundamental trade-offs between transient stability and oscillation stability in multi-machine power systems, distributed renewable (wind) generation systems, and distribution level energy control and management.13 Queen's, Belfast 贝尔法斯特女王大学地址：学校位于北爱尔兰首府贝尔法斯特的绿树成荫的南部郊外，步行到市中心只要15分钟网址：教授介绍：Professor Brendan FoxHis interests are in power system analysis, modelling and operation. Current interests include system integration aspects of embedded generation, including wind farms, and power system dynamic stability.Professor Haifeng Wangpower systems modelling, analysis and control with power electronics and renewable generation.14 Leeds 利兹大学地址：利兹市是英格兰北部的金融以及工业中心网址：教授介绍：没有electrical engineering15 University College London 伦敦大学学院地址：伦敦市中心的Bloomsbury广场网址：教授介绍：没有electrical engineering=15 Strathclyde 斯特拉斯克莱德大学地址：格拉斯哥是苏格兰最大的城市，地处苏格兰中部，位于克莱德河两岸网址：/教授介绍：Prof James R McDonaldPower system operation, management and control, protection system analysis, design and modelling, artificial intelligence applications in power systems, energy management systems, electricity pricing techniques, power system planning; optical sensing techniques.Prof Stephen McArthurPower engineering applications of Artificial Intelligence: condition monitoring; diagnostics and prognostics for equipment and plant; active network management and Smart Grids; and monitoring and diagnosis of nuclear reactorsIntelligent and automated power system fault analysisIntelligent system methods: knowledge based systems; model based reasoning; case based reasoningMulti-Agent Systems and Intelligent Agents: agent based condition monitoring; agent based power system fault analysis; multi-agent methods, models, techniques and architectures for power engineering applicationsModel and simulation integrationDecision support environmentsProf Kwok L LoPower systems analysis, planning, operation, monitoring and control including the application of expert systems and artificial neural networks;transmission and distribution management systems and privatisation issues.Prof William E LeitheadDynamic analysis, simulation, modelling, control, integrated drive-train design of wind turbines. Analysis and design of multivariable control system. Analysis and simulation of stochastic systems.Prof David InfieldMy research interests are with electricity generation from renewable energy sources, in particular from wind and photovoltaics (PV), and the integration of these sources into electricity systems large and small. Associated with this central challenge I take an interest in energy storage technology and application, and demand side management.Dr Andrew J CrudenHydrogen and Fuel cell systems, electric vehicles, power electronics for fuel cells and rotating machines (e.g. wind turbines), and electrical machine design.Dr Graham AultDr. Ault's research is in the general area of power system planning and operations with particular emphasis on renewables grid integration, distributed energy resources, distribution systems and long-term transitions and scenarios.17 Manchester 曼彻斯特大学地址：曼彻斯特大学位于地理位置优越的曼彻斯特市中心，曼彻斯特市是伦敦以外英国最重要的商业、教育和文化中心，也是英格兰重要的交通枢纽网址：教授介绍：Prof Daniel Kirschen Head of the Electrical Energy and Power Systems Group in the School of Electrical and Electronic Engineering.The introduction of competitive electricity markets has created a whole new set of interesting and challenging problems in the operation and development of power systems.Prof Jovica MilanovicHis research and consultancy work is equally split between the areas of Power System Dynamics and Power Quality with a common, underlying stream of probabilistic / stochastic modelling of uncertainties of events and system parameters.Prof Vladimir TerzijaMy main research interests are application of intelligent methods to power system monitoring, control, and protection, as well as power system plant, particularly switchgears.=17 Heriot-Watt 赫瑞特瓦特大学地址：主校园位于爱丁堡的郊外。

Output regulation of a class of continuous-time Markovianjumping systemsShuping He a,b,c,Zhengtao Ding c,n,Fei Liu ba College of Electrical Engineering and Automation,Anhui University,Hefei230601,Chinab Key Laboratory of Advanced Process Control for Light Industry(Ministry of Education),Institute of Automation,Jiangnan University,Wuxi214122,Chinac Control Systems Centre,School of Electrical and Electronic Engineering,University of Manchester,Sackville Street Building,Manchester M139PL,UKa r t i c l e i n f oArticle history:Received24February2012Received in revised form20June2012Accepted3August2012Available online24August2012Keywords:Output regulationMarkovian jumping systemState feedbackError feedbacka b s t r a c tThis paper studies output regulation for continuous-time Markovian jumping systems(MJSs),for which mode-dependent regulation equations are investigated.With theextension of regulation scheme to MJSs by stochastic Lyaponov–Krasovskii functionalframework,sufficient conditions are,respectively,obtained for state feedback and errorfeedback.The resulting closed-loop system is guaranteed to be stochastically stable andthe output regulation error almost asymptotically converges to zero.A semi-definiteoptimization approach via disciplined convex programming is adopted to ensurerelaxed solutions of the regulation equations.Finally,two numerical simulations aregiven to illustrate the performance of the proposed approach.Crown Copyright&2012Published by Elsevier B.V.All rights reserved.1.IntroductionMarkovian jumping systems(MJSs)have receivedconsiderable attention in systems,circuit and controlcommunity for many years,see,for example,[1–25].MJSsoften arise in practical control systems which may experi-ence abrupt changes in structures and parameters due to,for example,sudden environment changes,subsystemswitching,system noises,failures occurred in componentsor interconnections and executor faults,etc.In this classof stochastic systems,the dynamics of jumping modesand continuous states are,respectively,modeled byfinitestate Markov chains and differential equations.In recentyears,the stability,controller design andfiltering pro-blems for MJSs have regained increasing interest andsome results are also available.On another research front,the asymptotic regulationproblem of the output of a dynamical system is one of thecentral problems in control theory.An important variantof this problem is the output regulation problem and hasbeen studied since the seventies[26,27].Basically,theoutput regulation problem is either a disturbance rejec-tion problem or a tracking problem or a combination ofthese two problems.Different with the conventionaldisturbance rejection and tracking problem,the systemdisturbances or reference signals are always infinite-energy ones and generated by an external system namedexosystem.The key feature of the output regulationproblem is tofind a measured output feedback controllersuch that the closed-loop system is asymptotically stableand the regulated output asymptotically tends to zeroregardless of the exosignals affecting the system.It can beused in areas such as set point control,reference signalstracking,disturbances rejection,and observer design forautonomous systems.However,very few reports in the literature considerthe output regulation of stochastic MJSs though there areplenty of results on output regulation of linear systemsContents lists available at SciVerse ScienceDirectjournal homepage:/locate/sigproSignal Processing0165-1684/$-see front matter Crown Copyright&2012Published by Elsevier B.V.All rights reserved.n Corresponding author.E-mail addresses:shuping.he@(S.He),zhengtao.ding@(Z.Ding),fliu@(F.Liu).Signal Processing93(2013)411–419[28–30]and nonlinear systems[31–38].For linear sys-tems,the design of the linear regulator was given in terms of certain matrix equations,for example,Francis equa-tions[27].The solution depends on the property of the exosystem signals to be observable for the system output. The extension to the nonlinearfield was given by[31], [32].It has been shown that the regulation problem is solvable by means of a set of partial differential equations henceforth named the Francis–Isidori–Byrnes equations[31].In this paper,we consider the output regulation of continuous-time MJSs.Different with the main results in [29,30],the suffcient conditions of this paper are identi-fied to guarantee solutions to output regulation via state feedback and error feedback for such stochastic systems based on stochastic Lyapunov–Krasovskii functional.The design criterions are presented in the form of linear matrix inequality(LMI)[39],which can be easily checked. And the relevant regulator problem is described as a semi-definite optimization(SDP)one via disciplined con-vex programming[40].Finally,two numerical simulations are included to illustrate the effectiveness of the devel-oped techniques.Throughout this paper,we use the following notations: R n and R nÂm stand for an n-dimensional Euclidean space and the set of all nÂm real matrices,respectively;A T and AÀ1denote the matrix transpose and matrix inverse; diag f A B g represents the block-diagonal matrix of A and B;s max(p)and s min(p)denote the maximal and minimal eigenvalues of a positive-define matrix P;99*99 denotes the Euclidean norm of vectors;E{*}denotes the mathematics statistical expectation of the stochastic pro-cess or vector;L n2ð01Þis the space of n dimensional square integrable function vector overð01Þ;;99x(t)992,E denotes the mean square norm of x(t)on time-interval½0t ,where99xðtÞ992,E ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiE f x TðtÞxðtÞgp;P o0or P40means matrix P is negative-definite or positive-define;I and0are,respectively,the unit and the zero matrices with appropriate dimensions;and‘‘*’’means the sym-metric terms in a symmetric matrix.2.Problem formulationGiven a probability space(O,G,P r)where O is the sample space,F is the algebra of events and P r is the probability measure defined on G.Let us consider a class of continuous-time MJSs defined in the probability space (O,G,P r)and described by the following differential equations,_xðtÞ¼Aðr tÞxðtÞþBðr tÞuðtÞþEðr tÞdðtÞeðtÞ¼Cðr tÞxðtÞþDðr tÞdðtÞxðtÞ¼x t0,rðtÞ¼r t,t¼t08><>:ð1Þwhere x(t)A R n is the state,u(t)A R m is the controlled input,d(t)A R p is the disturbance to be rejected,e(t)A R q is the error to be regulated x tis a vector-valued initial continuous function and r0is the initial mode. A(r t)A R nÂn,B(r t)A R nÂm,C(r t)A R qÂn,D(r t)A R qÂp, E(r t)A R nÂp are the mode-dependent matrices with from an exosystem,_dðtÞ¼SðrtÞdðtÞð2ÞThe jumping parameter r t in MJSs(1)and(2)represents a continuous-time discrete state Markov stochastic process taking values on afinite set L¼f1,2,ÁÁÁ,N g with transition rate matrix P¼{p ij},i,j A L and has the following transition probability from mode i at time t to mode j at time tþD t as P r¼P r f r tþD t¼j9r t¼i g¼p ij D tþoðD tÞ,if i a j1þp ii D tþoðD tÞ,if i¼j(ð3Þwhere limD t-0oðD tÞD-0as D t40.In this relation,p ij Z0is the transition probability rate and for i,j A L,i a j,we haveX Nj¼1,j a ip ij¼Àp ii:ð4ÞRemark1.To simplify the study,we take the initial time t0¼0and let the initial values x0and r0befixed.At each mode,we assume that the continuous-time MJSs have the same dimension.The coefficient matrices in system(1) and(2)are known mode-dependent constant ones with appropriate dimensions.For convenience,we denote A(r t), B(r t),C(r t),D(r t),E(r t),S(r t)as A i,B i,C i,D i,E i,S i,respec-tively,with r t¼i,i A L.Assume that:A1.The eigenvalues of S i,i A L are with non-negative real parts;A2.MJSs(1)are Lyapunov stochastically stable;A3.The pairA i E i0S i!ðC i D iÞ2435is detectable.Wefirst consider the following full-order state feedback controller,uðtÞ¼K i xðtÞþF i dðtÞð5Þwhere K i and F i are the state feedback controller para-meters to be designed.We can get the following closed-loop MJSs(6)by substituting(5)into MJSs(1)and(2),_xðtÞ¼ðAiþB i K iÞxðtÞþðE iþB i F iÞdðtÞeðtÞ¼C i xðtÞþD i dðtÞ_dðtÞ¼SidðtÞ:8><>:ð6ÞUnder the assumptions of A1and A2,the objective of this part is to design a feedback control law,such that: B1.The feedback system(6)formed by the feedback control law u(t)¼K i x(t)þF i d(t)is stochastically stable,i.e., almost asymptotically stable([3],[4],[7],[11]);B2.For any given initial states,the controlled state x(t) of the closed-loop system can track the desired reference signal Q i d(t),wherein Q i is the coefficient matrix,i.e.,theregulated output x(t)¼x(t)ÀQ i d(t)satisfies99xðtÞ992,E¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiE f x TðtÞxðtÞgq-0over time;B3.The regulated error tends almost asymptotically toS.He et al./Signal Processing93(2013)411–419 412Remark 2.In fact,when the eigenvalues of S i ,i A L are with negative real parts,the rejected disturbances d (t )-0as t -N .and the regulated error e (t )and the regulated output x (t )of the presented MJSs (1)and (2)almost asymptotically tend to zero obviously.In this case,it just needs to design a controller u (t )¼K i x (t )that makes the closed-loop MJSs (6)stochastically stable.Thus,this paper pays more attention to almost asymptotically tracking and almost asymptotic regulation problem when d (t )a 0as time goes on.The so-called output regulation problem of linear systems was first introduced by Smith and Davison [26]and Francis and Wonham [27].For more results of this topic,we refer readers to [28–30]and the references therein.For the linear dynamic system without Marko-vian jumping,the problem of output regulation is solvable via state feedback if and only if there exists matrices Q and R that satisfy the following linear matrix equations QS ¼AQ þBR þECQ þD ¼0:(ð7ÞIn this paper,we study the output regulation problems of continuous-time MJSs.Our aim is to design a feedback controller satisfying B1–B3under the assumptions A1-A2.Before proceeding with the study,the following defini-tions for some given initial conditions can be formalized.Definition 1.The MJSs (1)and (2)(setting u (t )¼0,d (t )¼0)are said to be stochastically stable if,for any initial x (t )¼x 0and initial mode r t ¼r 0,thenlim T -1E Z T 099x ðt ,x 0,r 0Þ992dtr 0,x ðt Þ¼x 0&'o 1:ð8ÞDefinition 2.The MJSs (1)and (2)are said to be stochas-tically stabilizable if there exists a feedback control law of form (5),then the closed-loop MJSs (6)are stochastically stable.Definition 3.Define the time differential of the regula-tion output x (t )¼x (t )ÀQ i d (t )as _xðt Þ¼_x ðt ÞÀQ i _d ðt ÞÀX N j ¼1p ij Q j d ðt Þ:ð9ÞRemark 3.It should be noted that the added term P Nj ¼1p ij Q j d ðt Þin (9)is needed based on the time-dependent modes r t ¼i in MJSs (1)and (2).When we take the time differential of regulation output function x (t ),the time-dependent modes r t ¼i will be impossible to ignore.For more details about this topic,we refer readers to the results in [1],[3–5]and [11].3.Main resultsTheorem 3.1.Under the assumptions A1-A2,the problemof output regulation is solvable via state feedback if the (a1).There exist a set of matrices Q i and R i ,satisfying thefollowing regulator equations ,Q i S i ¼A i Q i þB i R i þE i ÀP N j ¼1p ij Q jn C i Q i þD i ¼0:ð10Þ(a2).The following LMI (11)holds for a set of positive-definite and mode-dependent matrices X i and mode-dependent matrices Y i .G i M ðX i Þn N ðX i Þ"#o 0ð11Þwhere G i ¼A i X i þX i A T i þB i Y i þY T i B T i þp ii X i ,M ðX i Þ¼ffiffiffiffiffiffiffip i 1p X ÁÁÁffiffiffiffiffiffiffiffiffiffiffiffiffip i i À1ðÞp X i ffiffiffiffiffiffiffiffiffiffiffiffiffiffip i i þ1ðÞp X iÁÁÁffiffiffiffiffiffiffip iN p X i h i,N ðX i Þ¼Àdiag f X 1ÁÁÁX i À1X i þ1ÁÁÁX N g :Moreover,the state feedback controller gain matrices areK i ¼Y i X À1i ,F i ¼R i ÀK i Q i :ð12ÞProof.Let x (t )¼x (t )ÀQ i d (t ).By Definition 3and consider-ing relation (10),we have_x ðt Þ¼_x ðt ÞÀXN j ¼1p ij Q j d ðt ÞþQ i _dðt Þ2435¼ðA i þB i K i Þx ðt ÞþðE i þB i F i Þd ðt ÞÀA i Q i þB i R i þE i ÀXN j ¼1p ij Q j 0@1A d ðt ÞÀX N j ¼1p ij Q j d ðt Þ¼ðA i þB i K i Þ½x ðt ÞÀQ i d ðt Þ þB i ðK i Q i þF i ÀR i Þd ðt Þ¼ðA i þB i K i Þx ðt Þð13ÞLet the mode at time t be i ;that is r t ¼i A L .Takethe stochastic Lyapunov–Krasovskii functional V (x (t ),i ,t Z 0):R n ÂR ÂR þ-R þto be V (x (t ),i )¼x T (t )P i x (t ),wherein P i 40is a positive-definite matrix for each mode i A L .The weak infinitesimal operator I [U ]of the process (x (t ),i ,t Z 0)for closed-loop MJSs (13)at the point {t ,x (t ),i }is given by [1],[3–5]and [11]I V ðx ðt Þ,i Þ¼lim D t -01D tE V ðx ðt þD t Þ,r t þD t ,t þD t Þ9x ðt Þ,r t ¼iÈÉÂÀV ðx ðt Þ,i Þ :ð14ÞTake the time differential of V (x (t ),i )along the trajec-tories of the closed-loop MJSs (13),and it yields,I V ðx ðt Þ,i Þ¼x Tðt ÞðA i þB i K i ÞT P i þP i ðA i þB i K i ÞþX N j ¼1p ij P j 2435x ðt Þ:Thus,it concludes that I V (x (t ),i )o 0can be guaranteed byðA i þB i K i ÞTP i þP i ðA i þB i K i ÞþX N j ¼1p ij P j o 0:ð15ÞPre-and post-multiplying inequality (15)by block-diagonal matrices P À1i ,applying Schur complementformula and letting X i ¼P À1i and Y i ¼K i X i ,inequality (15)S.He et al./Signal Processing 93(2013)411–419413And if matrix inequality (15)holds,there will exist matrix X i 40,such that I V ðx ðt Þ,i Þ¼ÀE f x Tðt ÞX i x ðt Þg :Since I V (x (t ),i )o 0,we can get E f V ðx ðt Þ,i Þg o E f V ðx 0,r 0Þg ¼E f x T0X i P ðr 0Þx 0g :Then,the following relation holds,I V ðx ðt Þ,i Þx o ÀE f x Tðt ÞX i x ðt Þgx 00:Define M 1¼inf 0r d r tE f 99x ðd Þ992g ,M 2¼E {99x 0992},s 1¼min i 2Ls min ðX i Þ,s 2¼max i 2Ls max ðP ðr 0ÞÞ.Therefore,there exists a positive number s 40satisfying the following relation,I V ðx ðt Þ,i ÞE f V ððt Þ,i Þg o ÀE f x Tðt ÞX i x ðt Þg E f V ð0,r 0Þg r ÀM 1s 1M 2s 2¼Às :Since M 140,M 240,s 140,s 240and s 40,we have I V ðx ðt Þ,i Þo s E f V ðx ðt Þ,i Þg :That is,E f V ðx ðt Þ,i Þg o e Às t E f V ðx 0,r 0Þg :By letting r ¼M 2s 2,for a given small positive scalar l 40,we can getl E f x T ðt Þx ðt Þg r E f V ðx ðt Þ,i Þg o r e Às t :ð16ÞLetting t go to infinity implies thatlim t -1E 99x ðt Þ992-0:ð17Þwhich also implies that 99x (t )992,E -0as t -N by the mainresults in [1],[3–6]and [11].Taking the limit as t -N ,it follows from relation (16)thatlim t -1E Z t 099x ðt Þ992&'dt o lim t -1r 1Àe Às t Âür o 1:Recalling Definition 1,we know that MJSs (13)arestochastically stable.On the other hand,e ðt Þ¼C i x ðt ÞþD i d ðt Þ¼C i x ðt ÞþðC i Q i þD i Þd ðt Þ¼C i x ðt Þð18ÞFrom (10)and (18),we know that lim t -199e ðt Þ992,E -0.This completes the proof.Remark 4.Notice that the output regulator design in this part is under the complete access to the system states.According to the definitions in [3],[5]and [11],we know that the closed-loop MJSs (13)are mean square stable when the regulated output x (t )satisfies relation (17).By the main proof of Theorem 3.1,we can see that mean square stable implies stochastically stable.In order to obtain the output regulation condition for MJSs,the coefficient matrix Q i is selected as a mode-dependent one.By the time-differential of the selected stochastic Lyapunov–Krasovskii functional V (x (t ),i )with the defini-tion in relation (14),we can get the main results in Theorem 3.1.If the coefficient matrix Q i is selected as a mode-independent one,that is Q i ¼Q ,then we have the follow-Corollary 3.1.Under the assumptions A1and A2,theproblem of output regulation is solvable via state feedback if the following relations hold for all i A L .(b1).There exist matrices Q and R,satisfying the follow-ing regulator equations ,QS i ¼A i Q þB i R þE iC i Q þD i ¼0:(ð19Þ(b2).LMI (11)with a set of positive-definite and mode-dependent matrices X i and mode-dependent matrices Y i holds .Moreover,the state feedback controller gain matrices areK i ¼Y i X À1i ,F i ¼R i ÀK i Q :ð20ÞPractically the complete access to the states is not the fact for many reasons such as the unavailability of the sensors to measure some of the state variables,and conse-quently the previous control approach will not be feasible.To overcome such problem,we first consider the jumping observer with the following state space representation,_^x ðt Þ¼A i ^x ðt ÞþB i u ðt ÞþE i ^d ðt ÞþH 1i ½e ðt ÞÀ^e ðt Þ _^d ðt Þ¼S i ^d ðt ÞþH 2i ½e ðt ÞÀ^e ðt Þ ^e ðt Þ¼C i^xðt ÞþD i^d ðt Þ8>><>>:ð21Þwhere H 1i and H 2i are observer gains to be designed.Definethe estimation error ~xðt Þ¼x ðt ÞÀ^x ðt Þ,~d ðt Þ¼d ðt ÞÀ^d ðt Þ,then we can get the following observer error dynamic MJS (22)by substituting (21)into (1),_~x ðt Þ¼ðA i þH 1i C i Þ~x ðt ÞþðE i þH 1i D i Þ~dðt Þ_~d ðt Þ¼H 2iC i~x ðt ÞþðS iþH 2iD iÞ~dðt Þ8<:ð22ÞAnd,it can be rewritten as _z ðt Þ¼A z iz ðt Þð23Þwhere z ðt Þ¼~x ðt Þ~d ðt Þ"#,A z i ¼A iE i 0S i!þH 1i H 2i!ðC iD i Þ.It shows from assumption A3that the eigenvalues of the matrix A z i can be specified in the left-half complex plane.But it does not mean the stability of the jumping observer error dynamics in (22).For these,we can invoke the stochastic stability conditions as described in (11)in the main proof of Theorem 3.1.Stated by the following Theorem,we can get the stochastic stability results of jumping observer error dynamic MJSs (22).Theorem 3.2.Under the assumption A3,the jumping observer error dynamic MJSs (22)are stochastically stable if there exist a set of positive-definite and mode-dependent matrices P 1i and P 2i and a set of mode-dependent matrices L 1i and L 2i satisfying the following LMI :S 1S 3nS 2"#o 0ð24Þwhere S 1¼P 1i A i þA T i P 1i þL 1i C i þC T i L T1i þP Nj ¼1p ij P 1j ,S 2¼P 2i S i þS T i P 2i þL 2i D i þD T i L T 2i þP N j ¼1p ij P 2j ,S.He et al./Signal Processing 93(2013)411–419414Moreover,the jumping observer gain is given byH1i¼PÀ11i L1i,H2i¼PÀ12iL2i:ð25ÞProof.For the jumping observer error dynamic MJSs(22), we take the stochastic Lyapunov–Krasovskii functional Vð~xðtÞ,~dðtÞ,iÞas follows,Vð~xðtÞ,~dðtÞ,iÞ¼~xðtÞP1i~xðtÞþ~dðtÞP2i~dðtÞ:Then following the similar proof in Theorem3.1,we can get the main results of Theorem3.2and this completes the proof.For MJSs(22),we consider the following feedback controller by estimated error feedbackuðtÞ¼K i~xðtÞþF i~dðtÞð26Þwhere K i and F i are the error feedback controller para-meters to be designed.Then,one has the following closed-loop MJSs(27)by substituting(26)into(1)and(2), _xðtÞ¼ðAiþB i K iÞxðtÞþðE iþB i F iÞdðtÞÀB i K i~xðtÞÀB i F i~dðtÞ^eðtÞ¼Ci xðtÞþD i dðtÞ_dðtÞ¼Si dðtÞ:8><>:ð27ÞTheorem3.3.Under the Assumption A1-A3,the problem of output regulation is solvable via error feedback if the following conditions hold for all i A L.(c1).There exist a set of mode-dependent matrices Q i and R i satisfying the regulator equations in(10).(c2).The mode-dependent LMI(11)with a set of positive-definite and mode-dependent matrices X i and mode-dependent matrices Y i holds.(c3).The mode-dependent LMI(24)with a set of positive-definite and mode-dependent matrices P1i and P2i and mode-dependent matrices L1i and L2i holds.Proof.Similar to the proof in Theorem 3.1,we define x(t)¼x(t)ÀQ i d(t)and take the time-differential of x(t), then it yields,_xðtÞ¼_xðtÞÀX Nj¼1p ij Q j dðtÞþQ i_dðtÞ2 43 5:¼ðA iþB i K iÞxðtÞþðE iþB i F iÞdðtÞÀB i K i~xðtÞÀB i F i~dðtÞÀQ i S i dðtÞÀX Nj¼1p ij Q j dðtÞ¼ðA iþB i K iÞ½xðtÞÀQ i dðtÞ ÀB i K i~xðtÞÀB i F i~dðtÞþA i Q iþB iðK i Q iþF iÞþE iÀQ i S iÀX Nj¼1p ij Q j2 435dðtÞ:ð28ÞBy the relation(10)and(12),we have_xðtÞ¼ðAiþB i K iÞxðtÞÀB i K i~xðtÞÀB i F i~dðtÞ:ð29ÞBy combining(29)and the observer error dynamic MJSs(22),it follows that_xðtÞ¼ðAiþB i K iÞxðtÞÀB i K i~xðtÞÀB i F i~dðtÞ_~xðtÞ¼ðAi þH1i C iÞ~xðtÞþðE iþH1i D iÞ~dðtÞ:8>><>ð30ÞIt should be pointed out that,if both the conditions (c2)and(c3)in Theorem 3.2are satisfied,the above system is stochastically stable for99~xðtÞ992,E-0and 99~dðtÞ992,E-0as t-N.Then we have99x(t)992,E-0as t-N.Moreover,we can get the following relation by condition(c1)eðtÞ¼C i xðtÞþD i dðtÞ¼C i xðtÞþðC i Q iþD iÞdðtÞ¼C i xðtÞ:ð31ÞIt means limt-199eðtÞ992,E-0.This completes the proof. Remark5.The separation principles are used to obtain the controller design and the observer design via error feedback here.Taking into account LMI(24),one has thefact that99~xðtÞ992,E-0and99~dðtÞ992,E-0as t-N.Then wehave99xðtÞ992,E-0as t-N.Following this,the controller and the observer can be,respectively,designed by LMI (11)and(24).When there are difficulties of solving(10),we cantransform(10)into the following SDP problems viadisciplined convex programming[40],min Zsubject toZ I A i Q iþB i R iþE iÀX Nj¼1p ij Q jÀQ i S in Z I26643775Z0,Z I C i Q iþD in Z I"#Z0:ð32ÞIn fact,to make the relative terms approximate with a satisfactory precision,we can alsofirstly select a suffi-ciently small scalar Z40to meet(32).Remark6.The solutions of Theorems3.1and3.3can be obtained by solving a SDP problem via disciplined convex programming with(32)and solving LMI(11).By using the relevant Matlab Toolbox,it is straightforward to check the feasibility of the disciplined convex programming and LMI.Remark7.Indeed,the applications of output regulation are comprehensive in industrial control processes,for example,set point control,reference signals tracking, disturbances rejection,and observer design for autono-mous systems,etc.It should be observed that the con-tributions of this paper are mainly theoretical aspects. As a widely used stochastic system,the proposed methods can be considered in future research.In order to illustrate the effectiveness of the developed techniques,we will give two numerical examples in the following Section4. Remark8.As one of the central problems in control theory, output regulation control was widely investigated in theo-retical and practical aspects.In this paper,we succeeded in designing the output regulator of continuous-time stochas-tic MJSs in the cases that the system states are accessible or not completely paring with the output regulation study for piecewise-linear systems[29,30],our researches are more focused on the fact that how to simplify the output regulator design procedure of stochastic MJSs byS.He et al./Signal Processing93(2013)411–419415output regulator design schemes also adapt to the systems in which the states are not completely accessible.4.Numeral examplesExample 4.1.We consider the following continuous-time stochastic MJSs with two jumping operation modes described asA 1¼À12À2À3!,A 2¼À0:51À2À3!,B 1¼0132!,B 2¼00:532 !,C 1¼C 2¼0:1À0:1ÂÃ,D 1¼À0:20:2ÂÃ,D 1¼0:1À0:1ÂÃ,E 1¼0:10:2À0:10:1 !,E 2¼0:1À0:10:20:1 !,S 1¼S 2¼03À3!:Selecting the transition rate matrix that relates the twooperation modes as P ¼À0:50:50:3À0:3!and solving theSDP optimization problem in (32)and LMI (11),we can get the optimal Z ¼1.8274Â10À11and the solutions as follows:K 1¼À0:33470:83050:50000:0042 !,F 1¼0:58141:0126À2:8895À0:2789 !,K 2¼À0:29010:71980:43330:0036!,F 2¼3:92891:7293À5:5978À0:3418!:For the initial conditions x 1(0)¼0.8and x 2(0)¼À1.0,we can get the simulation results of the jumping modes,the tracking response of state x (t )and Q i d (t ),and the regulated error e (t )in Figs.1–3.By the simulation results,the output e (t )to be regulated almost asymptotically tends to zero and the output tracking performance is quite satisfactory although there exists obvious transient tracking errors.In fact,when the states are not available,we can also study the output regulation problems for MJSs.In this situation,it just needs to design a jumping observer system to estimate the states and disturbances of the original model.Example 4.2.We consider the following two-mode con-tinuous-time stochastic MJSsA 1¼À12À2À3 !,A 2¼À2À33À2!,B 1¼B 2¼0:2000:2 !,C 1¼0:1À0:1ÂÃ,C 2¼À0:10:1ÂÃ,D 1¼À0:20:2ÂÃ,D 1¼0:1À0:1ÂÃ,E 1¼0:10:2À0:10:1!,E 2¼0:1À0:10:20:1 !,S 1¼S 2¼03À30 !:051015202530354045500.511.522.5t/sJ u m p i n g m o d e sFig.1.Jumpingmodes.S.He et al./Signal Processing 93(2013)411–419416。

AUTO TIME97NEW ENERGY AUTOMOBILE | 新能源汽车时代汽车 纯电动汽车自动驾驶功能设计李小润　钟日敏　黄祖朋　赵小羽　沈阳上汽通用五菱汽车股份有限公司技术中心 广西柳州市 545007摘 要： 针对纯电动车自动驾驶功能，设计一种利用PID 算法对车辆的驱动扭矩进行控制的系统，使得车辆的实际速度与驾驶员的期望速度一致，实现车辆自动驾驶的功能。

通过实车验证和调试，该控制系统具有良好的响应精度。

相较于传统汽车通过控制喷油量的多少来控制车速，具有更好的鲁棒性和实时性。

关键词：纯电动车　自动驾驶　PID 控制1　引言在节能减排的法规日益严格及智能驾驶不断兴起的背景下，全球汽车行业关于纯电动车的关注和投入火速增加。

美国学者麦肯锡预测，到2025年无人驾驶汽车可以产生2000亿～1.9万亿美元的产值；市场研究公司IHS 预测， 2035年4级完全无人驾驶车每年销量可达480万辆。

对任何一个行业而言，这都具有足够的市场诱惑。

[1]当前各主机厂都投入了大量的人才及资源进行开发。

无人驾驶，是指通过给车辆装备智能软件和多种感应设备，包括车载传感器、雷达、GPS 以及摄像头等，实现车辆的自主安全驾驶，安全高效地到达目的地并达到完全消除交通事故的目标。

[2]无人驾驶的一大核心功能是实现汽车自动驾驶功能，能实现脱离油门踏板，以驾驶员通过上位机发出的任何期望速度行驶。

并使得驾驶员能脱离转向系统、制动系统、换挡装置和油门踏板等，自动实现车辆的起步、换挡、加减速、停车等功能。

如图1。

鉴于传统车在实现自动驾驶的PID 模块中，通过控制喷油量来调节车速，固然有一定的可靠性。

然而出现不同工况或路况时，相同的喷油量输出的扭矩也必然不一样。

会使得控制器缺乏精准的鲁棒性和实时性。

文章对于纯电动车，设计一种自动驾驶控制系统，直接输出对电机的扭矩请求值驱动车辆，具有更好的响应精度。

2　自动驾驶功能结构模块设计自动驾驶功能控制系统的硬件模块主要包括：1、整车控制器（Vehicle Control Unit，简称VCU）；2、电机控制器（Motor Control Unit，简称MCU）；3、驱动控制器（Drive Control Unit，简称DCU）；4、车速传感器；5、驱动电机。

1 总则为统一高速铁路设计技术标准,使高速铁路设计符合安全适用、技术先进、经济合理的要求,制定本规范。

本规范适用于旅客列车设计行车速度250～350km/h的高速铁路,近期兼顾货运的高速铁路还应执行相关规范。

高速铁路设计应遵循以下原则：〔1贯彻"以人为本、服务运输、强本简末、系统优化、着眼发展" 的建设理念；〔2采用先进、成熟、经济、实用、可靠的技术；〔3体现高速度、高密度、高安全、高舒适的技术要求；〔4符合数字化铁路的需求。

高速铁路设计速度应按高速车、跨线车匹配原则进行选择,并应考虑不同速度共线运行的兼容性。

高速铁路设计年度宜分近、远两期。

近期为交付运营后第十年；远期为交付运营后第二十年。

对铁路基础设施及不易改、扩建的建筑物和设备,应按远期运量和运输性质设计,并适应长远发展要求。

易改、扩建的建筑物和设备,可按近期运量和运输性质设计,并预留远期发展条件。

随运输需求变化而增减的运营设备,可按交付运营后第五年运量进行设计。

高速铁路建筑限界轮廓及基本尺寸应符合图1.0.6 的规定,曲线地段限界加宽应根据计算确定。

7250550040002440170017501250650③①②④⑤1700251250①轨面②区间及站内正线〔无站台建筑限界③有站台时建筑限界④轨面以上最大高度⑤线路中心线至站台边缘的距离〔正线不适用图高速铁路建筑限界轮廓及基本尺寸〔单位：mm高速铁路列车设计活载应采用ZK 活载。

ZK 活载为列车竖向静活载,ZK 标准活载如图-1 所示,ZK 特种活载如图-2 所示。

图1.0.7-1 ZK 标准活载图式图-2 ZK 特种活载图式高速铁路应按全封闭、全立交设计。

高速铁路设计应执行国家节约能源、节约用水、节约材料、节省用地、保护环境等有关法律、法规。

高速铁路结构物的抗震设计应符合《铁路工程抗震设计规范》〔GB 50111及国家现行有关规定。

高速铁路设计除应符合本规范外,尚应符合国家现行有关标准的规定。