Package: TuningGoal
Frequencyweighted gain constraint for control system tuning
Use TuningGoal.WeightedGain
to limit the weighted
gain from specified inputs to outputs. The weighted gain is the maximum
across frequency of the gain from input to output, multiplied by weighting
functions that you specify. You can use the TuningGoal.WeightedGain
tuning
goal for control system tuning with tuning commands such as systune
or looptune
.
After you create a tuning goal, you can configure it further by setting Properties of the object.
creates
a tuning goal that specifies that the closedloop transfer function, H(s),
from the specified input to output meets the requirement:Req
=
TuningGoal.WeightedGain(inputname
,outputname
,WL,WR
)
W_{L}(s)H(s)W_{R}(s)_{∞} < 1.
The notation •_{∞} denotes the maximum gain across frequency (the H_{∞} norm).

Input signals for the tuning goal, specified as a character vector or, for multipleinput tuning goals, a cell array of character vectors.
For more information about analysis points in control system models, see Mark Signals of Interest for Control System Analysis and Design. 

Output signals for the tuning goal, specified as a character vector or, for multipleoutput tuning goals, a cell array of character vectors.
For more information about analysis points in control system models, see Mark Signals of Interest for Control System Analysis and Design. 

Frequencyweighting functions, specified as scalars, matrices, or SISO or MIMO numeric LTI models. The functions WL(s)H(s)WR(s)_{∞} < 1. WL provides the weighting for
the output channels of H(s),
and WR provides the weighting for the input channels.
You can specify scalar weights or frequencydependent weighting. To
specify a frequencydependent weighting, use a numeric LTI model.
For example:
WL = tf(1,[1 0.01]); WR = 10; If you specify MIMO weighting functions, then If you are tuning in discrete time (that is, using a A value of 

Frequencyweighting function for the output channels of the
transfer function to constrain, specified as a scalar, a matrix, or
a SISO or MIMO numeric LTI model. The initial value of this property
is set by the 

Frequencyweighting function for the input channels of the transfer
function to constrain, specified as a scalar, a matrix, or a SISO
or MIMO numeric LTI model. The initial value of this property is set
by the 

Frequency band in which tuning goal is enforced, specified as
a row vector of the form Set the Req.Focus = [1,100]; Default: 

Stability requirement on closedloop dynamics, specified as
1 ( By default, Default: 1( 

Input signal names, specified as a cell array of character
vectors that identify the inputs of the transfer function that the
tuning goal constrains. The initial value of the 

Output signal names, specified as a cell array of character
vectors that identify the outputs of the transfer function that the
tuning goal constrains. The initial value of the 

Models to which the tuning goal applies, specified as a vector of indices. Use the Req.Models = 2:4; When Default: 

Feedback loops to open when evaluating the tuning goal, specified as a cell array of character vectors that identify loopopening locations. The tuning goal is evaluated against the openloop configuration created by opening feedback loops at the locations you identify. If you are using the tuning goal to tune a Simulink model
of a control system, then If you are using the tuning goal to tune a generalized statespace
( For example, if Default: 

Name of the tuning goal, specified as a character vector. For example, if Req.Name = 'LoopReq'; Default: 
This tuning goal imposes an implicit stability constraint
on the weighted closedloop transfer function from Input
to Output
,
evaluated with loops opened at the points identified in Openings
.
The dynamics affected by this implicit constraint are the stabilized
dynamics for this tuning goal. The MinDecay
and MaxRadius
options
of systuneOptions
control the bounds on these
implicitly constrained dynamics. If the optimization fails to meet
the default bounds, or if the default bounds conflict with other requirements,
use systuneOptions
to change
these defaults.
When you tune a control system using a TuningGoal
,
the software converts the tuning goal into a normalized scalar value f(x). 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 TuningGoal.WeightedGain
, f(x)
is given by:
$$f\left(x\right)={\Vert {W}_{L}T\left(s,x\right){W}_{R}\Vert}_{\infty}.$$
T(s,x)
is the closedloop transfer function from Input
to Output
. $${\Vert \text{\hspace{0.17em}}\cdot \text{\hspace{0.17em}}\Vert}_{\infty}$$ denotes
the H_{∞} norm (see getPeakGain
).
evalGoal
 looptune
 systune
 viewGoal
 looptune
(for slTuner)
(Simulink Control Design)  slTuner
(Simulink Control Design)  systune (for slTuner)
(Simulink Control Design)