ex9_2b.m

离散控制系统设计的MATLAB 代码

%%%%%%%%%%%%%%%% Example 9.2(b) %%%%%%%%%%%%%%%%%
%   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                 %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   ---- Select lag zero & calc phase margin ----
%
disp('Example 9.2(b)')
%---- Assume that variables defined in Script 9.2(a) are in workspace
%	  so run ex9_2a first, and do NOT do a clear command
w_Zlag = input('Enter corner freq for lag zero [0.157]..... ') 
Zlag = -w_Zlag                              % lag zero must be negative
Gcw = tf(Klag*[1 -Zlag],[1 -Zlag/Alag])     % lag controller
GcGHw = Gcw*GHw                             % connect lag in series with plant and sensor
disp('******>'), pause
lfg = dcgain(GcGHw)                         % low-freq gain of current design
[km,pm,wkm,wpm] = margin(GcGHw);            % open-loop frequency response
disp('Gain margin and phase crossover frequency')
disp([20*log10(km)  wkm])      % gain margin in dB & omega_gm
disp('Phase margin and gain crossover frequency')
disp([pm wpm])                 % phase margin in degrees & omega_pm
ess = 1/(1 + dcgain(GcGHw))    % verify that steady-state error is OK
Gcz = c2d(Gcw,Ts,'tustin')     % controller in z domain
disp('******>'), pause

%----------  OL frequency responses for Fig. 9.5 -----
w = logspace(-3,1);
ph180 = -180*ones(length(w));
%---- first, with gain only -----
[mag_db_K,ph_K] = bodedb(Klag*GHw,w); % bodedb returns mag in dB
%---- then with final lag design
[mag_db_lag,ph_lag] = bodedb(GcGHw,w);
%----- now plot both sets
figure
subplot(211)
semilogx(w,mag_db_lag,'-',w,mag_db_K,'--');grid;
text(0.004,7,'Proportional')
text(0.05,30,'lag')
xlabel('Frequency (rad/s)')
ylabel('Magnitude (dB)')
title('Bode plot for initial (proportional) and final (lag) design of Example 9.2')
subplot(212)
semilogx(w,ph_lag,'-',w,ph_K,'--',w,ph180,':');grid
text(0.3,-25,'Proportional')
text(0.02,-70,'lag')
xlabel('Frequency (rad/s)')
ylabel('Phase angle (deg)')
disp('******>'), pause

%---------  CL step responses for Fig. 9.6 ------
% reference response
Gz = c2d(Gp,Ts,'zoh')          % discretize plant
disp('******>'), pause
Gcz = ss(Gcz)                  % convert to ss form for better numerics
disp('******>'), pause
Tz = Gz*Gcz/(1+GHz*Gcz)        % closed-loop transfer function
disp('******>'), pause
[y,tt] = step(Tz,8);           % step response to 8 s

yss = dcgain(Tz);

figure
plot(tt,y,'o');grid
hold on
plot([0 8],[yss yss],'--')
hold off
xlabel('Time (s)')
ylabel('Amplitude')
title('Unit-step response in the reference input for the final lag design of Example 9.2')
%%%%%%%%%%