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 Loop Shape Goal, f(x) is given by:
fx =WSS
WTT∞
.
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. (If Equalize loop interactions is set
to Off, then D = I.)
T = S – I is the complementary sensitivity function.
WS and WT are frequency weighting functions derived from the specified loop shape. The
gains of these functions roughly match your specified loop shape and its inverse,
respectively, for values ranging from –20 dB to 60 dB. For numerical reasons, the
weighting functions level off outside this range, unless the specified gain profile changes
slope outside this range. Because poles of WS or WT 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.
Loop Shape Goal