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 Weighted Passivity Goal, for a closed-loop transfer function T(s,x) from the
specified inputs to the specified outputs, and the weighted transfer function H(s,x) =
WL(s)T(s,x)WR(s), f(x) is given by:
fx = R
1+R/Rmax
, Rmax= 10^6.R is the relative sector index (see getSectorIndex) of [H(s,x); I], for the sector
represented by:
Q=
2 ρ−I
−I 2 ν,
where ρ is the minimum output passivity index and ν is the minimum input passivity index
specified in the dialog box. Rmax is fixed at 10 6 , included to avoid numeric errors for very
large R.
This tuning goal imposes an implicit minimum-phase constraint on the weighted transfer
function H + I. The transmission zeros of H + I 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.
Weighted Passivity Goal