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 Tracking Goal, f(x) is given by:
fx = WFs Ts,x−I ∞,or its discrete-time equivalent. Here, T(s,x) is the closed-loop transfer function between
the specified inputs and outputs, and ⋅ ∞ denotes the H∞ norm (see getPeakGain). WF
is a frequency weighting function derived from the error profile you specify in the tuning
goal. The gain of WF roughly matches the inverse of the error profile for gain values
between –20 dB and 60 dB. For numerical reasons, the weighting function levels off
outside this range, unless you specify a reference model that changes slope outside this
range. This adjustment is called regularization. Because poles of WF close to s = 0 or s =
Inf might lead to poor numeric conditioning of the systune optimization problem, it is
not recommended to specify error 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.
Reference Tracking Goal