All the closed loops are stable, but the overshoots of the loops with unstable plants (C =
4 , through 7 ) are too large. To improve the results, increase the target open-loop
bandwidth to 10 rad/sec.
Design updated controllers for the unstable plant models.
Controllers = pidtune(Plants,'pidf',10);
Display the controller for C = 4.
Controllers(:,:,4)
ans =
1 s
Kp + Ki --- + Kd --------
s Tf*s+1
with Kp = -283, Ki = -151, Kd = -128, Tf = 0.0183
Continuous-time PIDF controller in parallel form.
Construct the closed-loop systems, and plot the closed-loop step responses for the new
controllers.
clsys = feedback(Plants*Controllers,1);
figure
hold on
for ct = 1:length(C)
% Select a system from the LTI array
sys = clsys(:,:,ct);
set(sys,'Name',['C=',num2str(C(ct))],'InputName','Reference');
% Plot step response
stepplot(sys,20);
end
legend('show','location','southeast')
Design Family of PID Controllers for Multiple Operating Points