Simulink Control Design™ - MathWorks

Fro = tf(wn^2,[1 2*zeta*wn wn^2]); % parametric transfer function

setBlockParam(ST0,'RollOff',Fro) % use Fro to parameterize "RollOff" block

Design Requirements

The autopilot must be tuned to satisfy three main design requirements:

1. Setpoint tracking: The response to the command should closely match the
   response of the reference model:

This reference model specifies a well-damped response with a 2 second settling time.

2. High-frequency roll-off: The closed-loop response from the noise signals to should
   roll off past 8 rad/s with a slope of at least -40 dB/decade.


3. Stability margins: The stability margins at the plant input should be at least 7 dB
   and 45 degrees.

For setpoint tracking, we require that the gain of the closed-loop transfer from the

command to the tracking error be small in the frequency band [0.05,5] rad/s (recall

that we cannot drive the steady-state error to zero because of the plant zero at s=0).

Using a few frequency points, sketch the maximum tracking error as a function of

frequency and use it to limit the gain from to.

Freqs = [0.005 0.05 5 50];

Gains = [5 0.05 0.05 5];

Req1 = TuningGoal.Gain('Nzc','e',frd(Gains,Freqs));

Req1.Name = 'Maximum tracking error';

The TuningGoal.Gain constructor automatically turns the maximum error sketch into a

smooth weighting function. Use viewGoal to graphically verify the desired error profile.

viewGoal(Req1)

13 Control System Tuning Examples