ex8_3c.m

离散控制系统设计的MATLAB 代码

%%%%%%%%%%%%%%%%% Example 8.3(c) %%%%%%%%%%%%%%%%
%   Discrete-Time Control Problems using        %
%       MATLAB and the Control System Toolbox   %
%   by J.H. Chow, D.K. Frederick, & N.W. Chbat  %
%         Brooks/Cole Publishing Company        %
%                September 2002                 %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   ---- Root locus for final KD & KI gains for PID Control  ----
%
clear
disp('Example 8.3(c)')
 
Ts = 0.1;			                % sampling period
Gp_s = tf(4,conv([2 1],[0.5 1]));   % continuous process
H_s = tf(1,[0.05 1]);		        % continuous sensor
HGp_s = H_s*Gp_s                    % continous plant
HGp_z = c2d(HGp_s,Ts,'zoh')         % discrete plant, using ZOH option
 
KI = 0.5; 
KD = 0.45;

%----- PID controller with KP = 1 -------
Gc = (tf(1,1,Ts) ...                         % porportional = 1
        + tf([KI*Ts  0],[1 -1],Ts) ...       % integral
        + tf(KD*[1 -1],[Ts 0],Ts));          % derivative
 
%----- open-loop system, with KP = 1 
Gol = HGp_z*Gc

%---- first, show large area ------
figure, ucircle, hold on
rlocus(Gol), hold off
axis([-6 2 -4 4])
text('Units','norm','Pos',[0.1,0.10],'Str',['KI = ',num2str(KI)])
text('Units','norm','Pos',[0.1,0.05],'Str',['KD = ',num2str(KD)])

disp('******>'), pause

%---- then show smaller area ------
figure, ucircle, hold on
rlocus(Gol)
zgrid(0.8,[]), hold off
axis([-1.2 1.2 -1.2 1.2])
text('Units','norm','Pos',[0.1,0.10],'Str',['KI = ',num2str(KI)])
text('Units','norm','Pos',[0.1,0.05],'Str',['KD = ',num2str(KD)])
 
disp('******>'), pause

%---- then show smaller area for use with rlocfind cmd ------

figure
ucircle, hold on
rlocus(Gol)
dzline(0.6), hold off
axis([0.0 1.2 -0.1 1.1])
text('Units','norm','Pos',[0.1,0.1],'Str',['KI = ',num2str(KI)])
text('Units','norm','Pos',[0.1,0.05],'Str',['KD = ',num2str(KD)])

disp('select point for marginal stablity')
[kk,pCL] = rlocfind(Gol)
[mag_pCL,theta_pCL] = xy2p(pCL);
[kk,pCL] = rlocfind(Gol)
[mag_pCL,theta_pCL] = xy2p(pCL);
[kk,pCL] = rlocfind(Gol)
[mag_pCL,theta_pCL] = xy2p(pCL);
[kk,pCL] = rlocfind(Gol)
[mag_pCL,theta_pCL] = xy2p(pCL);
[kk,pCL] = rlocfind(Gol)
[mag_pCL,theta_pCL] = xy2p(pCL);
[kk,pCL] = rlocfind(Gol)
[mag_pCL,theta_pCL] = xy2p(pCL);
[kk,pCL] = rlocfind(Gol)
[mag_pCL,theta_pCL] = xy2p(pCL);
disp('Click on root locus curve to find gain, pole, ')
disp('damping ratio, overshoot, and frequency.')
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