For more information about tuning for multiple models, see “Robust Tuning
Approaches” (Robust Control Toolbox).Algorithms
Evaluating Tuning Goals
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 Gain Goal, f(x) is given by:
fx = WFsDo−^1 Ts,xDi∞,or its discrete-time equivalent. Here, T(s,x) is the closed-loop transfer function between
the specified inputs and outputs, evaluated with parameter values x. Do and Di are the
scaling matrices described in “Options” on page 10-87. ⋅ ∞ denotes the H∞ norm (see
getPeakGain).
The frequency weighting function WF is the regularized gain profile, derived from the
maximum gain profile you specify. The gain of WF roughly matches the inverse of the gain
profile you specify, inside the frequency band you set in the Enforce goal in frequency
range field of the tuning goal. WF is always stable and proper. Because poles of WF(s)
close to s = 0 or s = Inf might lead to poor numeric conditioning for tuning, it is not
recommended to specify maximum gain profiles 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 also imposes an implicit stability constraint on the closed-loop transfer
function between the specified inputs to outputs, 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.
Gain Goal