Tracking vs. Rejection
To gain insight into the trade-off between tracking and disturbance rejection, increase the
minimum loop gain in the frequency band [0,0.1] rad/s by a factor. Re-tune the PID
gains for the values.
% Increase loop gain by factor 2
alpha = 2;
R3.MinGain = alpha*wc/s;
T2 = systune(T0,R1,[R2 R3]);
Final: Soft = 1.17, Hard = 0.9994, Iterations = 115
% Increase loop gain by factor 4
alpha = 4;
R3.MinGain = alpha*wc/s;
T3 = systune(T0,R1,[R2 R3]);
Final: Soft = 1.25, Hard = 0.99993, Iterations = 183
Compare the responses to a step command r and to a step disturbance d entering at the
plant input u.
figure, step(T1,T2,T3,3)
title('Setpoint tracking')
legend('\alpha = 1','\alpha = 2','\alpha = 4')
PID Tuning for Setpoint Tracking vs. Disturbance Rejection