Simulink Control Design™ - MathWorks

consider increasing the scaling order. See “Stability Margins in Control System

Tuning” on page 10-216.

• Apply goal to

Use this option when tuning multiple models at once, such as an array of models

obtained by linearizing a Simulink model at different operating points or block-

parameter values. By default, active tuning goals are enforced for all models. To

enforce a tuning requirement for a subset of models in an array, select Only Models.

Then, enter the array indices of the models for which the goal is enforced. For

example, suppose you want to apply the tuning goal to the second, third, and fourth

models in a model array. To restrict enforcement of the requirement, enter 2:4 in the

Only Models text box.

For more information about tuning for multiple models, see “Robust Tuning

Approaches” (Robust Control Toolbox).

Algorithms

When you tune a control system, the software converts each tuning goal into a normalized

scalar value f(x). Here, x is the vector of free (tunable) parameters in the control system.

The software then adjusts the parameter values to minimize f(x) or to drive f(x) below 1 if

the tuning goal is a hard constraint.

For Margins Goal, f(x) is given by:

fx = 2 αS−αI∞.

S = D–1[I – L(s,x)]–1D is the scaled sensitivity function.

L(s,x) is the open-loop response being shaped.

D is an automatically-computed loop scaling factor.

α is a scalar parameter computed from the specified gain and phase margin.

This tuning goal imposes an implicit stability constraint on the closed-loop sensitivity

function measured at the specified, evaluated with loops opened at the specified loop-

opening locations. The dynamics affected by this implicit constraint are the stabilized

dynamics for this tuning goal. The Minimum decay rate and Maximum natural

frequency tuning options control the lower and upper bounds on these implicitly

constrained dynamics. If the optimization fails to meet the default bounds, or if the

10 Control System Tuning