Simulink Control Design™ - MathWorks

For robustness, require at least 6 dB of gain margin and 40 degrees of phase margin at

the plant input.

% Stability margins

req3 = TuningGoal.Margins('F',6,40);

Finally, constrain the damping and natural frequency of the closed-loop poles to prevent

jerky or underdamped transients.

% Pole locations

MinDamping = 0.5;

MaxFrequency = 45;

req4 = TuningGoal.Poles(0,MinDamping,MaxFrequency);

Control System Tuning

The closed-loop system is unstable for the initial values of the PD and state-space

controllers (1 and , respectively). You can use systune to jointly tune these two

controllers. Use the slTuner interface to specify the tunable blocks and register the

plant input F as an analysis point for measuring stability margins.

ST0 = slTuner('rct_pendulum',{'Position Controller','Angle Controller'});

addPoint(ST0,'F');

Next, use systune to tune the PD and state-space controllers subject to the performance

requirements specified above. Optimize the tracking and disturbance rejection

performance (soft requirements) subject to the stability margins and pole location

constraints (hard requirements).

rng(0)

Options = systuneOptions('RandomStart',5);

[ST, fSoft] = systune(ST0,[req1,req2],[req3,req4],Options);

Final: Soft = 1.36, Hard = 0.99949, Iterations = 296

Final: Soft = 1.44, Hard = 0.99942, Iterations = 164

Final: Soft = 1.27, Hard = 0.99966, Iterations = 293

Final: Soft = 1.27, Hard = 0.99363, Iterations = 194

Final: Soft = 1.44, Hard = 0.9996, Iterations = 234

Final: Soft = 1.26, Hard = 0.99933, Iterations = 345

The best design achieves a value close to 1 for the soft requirements while satisfying the

hard requirements (Hard<1). This means that the tuned control system nearly achieves

the target performance for tracking and disturbance rejection while satisfying the

stability margins and pole location constraints.

13 Control System Tuning Examples