Simulink Control Design™ - MathWorks

Finally, capture the design requirements using TuningGoal objects. We use the following

requirements for this example:

• Tracking requirement: The response of theta, phi, r to step commands
  theta_ref, phi_ref, r_ref must resemble a decoupled first-order response with a
  one-second time constant


• Stability margins: The multivariable gain and phase margins at the plant inputs u
  and plant outputs y must be at least 5 dB and 40 degrees


• Fast dynamics: The magnitude of the closed-loop poles must not exceed 25 to prevent
  fast dynamics and jerky transients

% Less than 20% mismatch with reference model 1/(s+1)

TrackReq = TuningGoal.StepTracking({'theta-ref','phi-ref','r-ref'},{'theta','phi','r'},1);

TrackReq.RelGap = 0.2;

% Gain and phase margins at plant inputs and outputs

MarginReq1 = TuningGoal.Margins('u',5,40);

MarginReq2 = TuningGoal.Margins('y',5,40);

% Limit on fast dynamics

MaxFrequency = 25;

PoleReq = TuningGoal.Poles(0,0,MaxFrequency);

You can now use systune to jointly tune all controller parameters. This returns the tuned

version ST1 of the control system ST0.

AllReqs = [TrackReq,MarginReq1,MarginReq2,PoleReq];

ST1 = systune(ST0,AllReqs);

Final: Soft = 1.11, Hard = -Inf, Iterations = 124

The final value is close to 1 so the requirements are nearly met. Plot the tuned responses

to step commands in theta, phi, r:

T1 = getIOTransfer(ST1,{'theta-ref','phi-ref','r-ref'},{'theta','phi','r'});

step(T1,5)

13 Control System Tuning Examples