Simulink Control Design™ - MathWorks

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 Disturbance Rejection Goal, f(x) is given by:

fx = max

ω∈Ω

WSjωSjω,x ∞,

or its discrete-time equivalent. Here, S(jω,x) is the closed-loop sensitivity function

measured at the disturbance location. Ω is the frequency interval over which the

requirement is enforced, specified in the Enforce goal in frequency range field. WS is a

frequency weighting function derived from the attenuation profile you specify. The gains

of WS and the specified profile roughly match for gain values ranging from –20 dB to 60

dB. For numerical reasons, the weighting function levels off outside this range, unless the

specified gain profile changes slope outside this range. This adjustment is called

regularization. Because poles of WS close to s = 0 or s = Inf might lead to poor numeric

conditioning for tuning, it is not recommended to specify loop shapes with very low-

frequency or very high-frequency dynamics.For more information about regularization

and its effects, see “Visualize Tuning Goals” on page 10-187.

Implicit Constraints

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

default bounds conflict with other requirements, on the Tuning tab, use Tuning Options

to change the defaults.

See Also

Related Examples

• “Specify Goals for Interactive Tuning” on page 10-39


• “Manage Tuning Goals” on page 10-177


• “Visualize Tuning Goals” on page 10-187

10 Control System Tuning