>> A=[0,1;-2 -3];>>B=[0;1];C=[1,2];D=[0];X0=[1;2];>> sys=ss(A,B,C,D);>>[y1,t,x1]=initial(sys,X0,0:0.02:6);>>plot(t,xl)1.5.3 When u(t) =1 (t), calculated the response ofthe system in the period [0, 6s]%The unit step response with zero initial state:>> A=[0,1;-2 -3];>> B=[0;1];C=[1,2];D=[0];>> sys=ss(A,B,C,D);>>(=[0:0.02:6];>>[y2,t,x2]=step(sys,t);>> figure(1)>> subplot(1,2,1); plot(t,x2)>> subplot(1,2,2); plot(t,y2)%full response:>> y=y1+y2;x=xl+x2;>>figure(2)>> subplot(1,2,1); plot(t,x)>> subplot(1,2,2); plot(t,y)Ill.Requirements ofthereport1.Write the relevant programs in the experimental content and compile them in thecomputer.2.All programs, results and related graphics are written on the experiment reporttogether.4
4 >> A=[0,1;-2 -3]; >>B=[0;1];C=[1,2];D=[0];X0=[1;2]; >> sys=ss(A,B,C,D); >> [y1,t,x1]=initial(sys,X0,0:0.02:6); >> plot(t,x1) 1.5.3 When u(t) = 1 (t), calculated the response of the system in the period [0, 6s] %The unit step response with zero initial state: >> A=[0,1;-2 -3]; >> B=[0;1];C=[1,2];D=[0]; >> sys=ss(A,B,C,D); >> t=[0:0.02:6]; >> [y2,t,x2]=step(sys,t); >> figure(1) >> subplot(1,2,1); plot(t,x2) >> subplot(1,2,2); plot(t,y2) %full response: >> y=y1+y2;x=x1+x2; >> figure(2) >> subplot(1,2,1); plot(t,x) >> subplot(1,2,2); plot(t,y) III. Requirements of the report 1.Write the relevant programs in the experimental content and compile them in the computer. 2.All programs, results and related graphics are written on the experiment report together
实验二控制系统的稳定性、能控性和能观测性分析Experiment II Analysis of Stability, Controllability and Observabilityby Using MATLABI.Experimental Purpose1. Master the methods of analyzing the stability of the LTI system by the Lyapunovmethod.2. Master the methods of determining the controllability and observability of acontrol system.3. Master the methods of transforming the state space description into controllablecanonical form and observable canonical form4.Master the method of structure decomposition ofa control system5.Masterthe method ofminimal realization of theLTI systemII.ExperimentalContent2.1 Consider the state space description ofa LTI system is4.5-3.50.51X =2-4.54.5-0.5A[-1 1.50.5-2.5y=[1 o 1]xDetermine the stability by the Lyapunov 2 nd Methodclose allclear all% the state space model of a systemA=[1 -3.5 4.5;2 -4.5 4.5;-1 1.5 -2.5];%Q=IQ=eye(3,3);%Finding the sol ution matrix P of Lyapunov equation A'P +PA=-Q5
5 实验二 控制系统的稳定性、能控性和能观测性分析 Experiment II Analysis of Stability, Controllability and Observability by Using MATLAB I. Experimental Purpose 1. Master the methods of analyzing the stability of the LTI system by the Lyapunov method. 2. Master the methods of determining the controllability and observability of a control system. 3. Master the methods of transforming the state space description into controllable canonical form and observable canonical form. 4. Master the method of structure decomposition of a control system. 5. Master the method of minimal realization of the LTI system. II. Experimental Content 2.1 Consider the state space description of a LTI system is y [ ]X X X u 1 0 1 0.5 0.5 0.5 1 1.5 2.5 2 4.5 4.5 1 3.5 4.5 = − − − + − − − − = Determine the stability by the Lyapunov 2nd Method. close all clear all % the state space model of a system A=[1 -3.5 4.5;2 -4.5 4.5;-1 1.5 -2.5]; %Q=I Q=eye(3,3); % Finding the solution matrix P of Lyapunov equation T A P PA Q + =−