Simulink Control Design™ - MathWorks

Loop Shape and Stability Margin Specifications

This example shows how to specify loop shapes and stability margins when tuning control

systems with systune or looptune.

Background

The systune and looptune commands tune the parameters of fixed-structure control

systems subject to a variety of time- and frequency-domain requirements. The

TuningGoal package is the repository for such design requirements.

Loop Shape

The TuningGoal.LoopShape requirement is used to shape the open-loop response

gain(s), a design approach known as loop shaping. For example,

s = tf('s');

R1 = TuningGoal.LoopShape('u',1/s);

specifies that the open-loop response measured at the location "u" should look like a pure

integrator (as far as its gain is concerned). In MATLAB, use an AnalysisPoint block to

mark the location "u", see the "Building Tunable Models" example for details. In Simulink,

use the addPoint method of the slTuner interface to mark "u" as a point of interest.

As with other gain specifications, you can just specify the asymptotes of the desired loop

shape using a few frequency points. For example, to specify a loop shape with gain

crossover at 1 rad/s, -20 dB/decade slope before 1 rad/s, and -40 dB/decade slope after 1

rad/s, just specify that the gain at the frequencies 0.1,1,10 should be 10,1,0.01,

respectively.

LS = frd([10,1,0.01],[0.1,1,10]);

R2 = TuningGoal.LoopShape('u',LS);

bodemag(LS,R2.LoopGain)

legend('Specified','Interpolated')

13 Control System Tuning Examples