Package: TuningGoal
Gain constraint for control system tuning
Use the TuningGoal.Gain
object to specify a constraint
that limits the gain from a specified input to a specified output. Use this tuning goal for
control system tuning with tuning commands such as systune
or
looptune
.
When you use TuningGoal.Gain
, the software attempts to
tune the system so that the gain from the specified input to the specified output does not exceed
the specified value. By default, the constraint is applied with the loop closed. To apply the
constraint to an openloop response, use the Openings
property of the TuningGoal.Gain
object.
You can use a gain constraint to:
Enforce a design requirement of disturbance rejection across a particular input/output pair, by constraining the gain to be less than 1
Enforce a custom rolloff rate in a particular frequency band, by specifying a gain profile in that band
creates a tuning goal that constrains the gain from Req
=
TuningGoal.Gain(inputname
,outputname
,gainvalue
)inputname
to
outputname
to remain below the value gainvalue
.
You can specify the inputname
or outputname
as
cell arrays (vectorvalued signals). If you do so, then the tuning goal constrains the largest
singular value of the transfer matrix from inputname
to
outputname
. See sigma
for more information about singular
values.
specifies the maximum gain as a function of frequency. You can specify the target gain profile
(maximum gain across the I/O pair) as a smooth transfer function. Alternatively, you can sketch a
piecewise error profile using an Req
= TuningGoal.Gain(inputname
,outputname
,gainprofile
)frd
model.

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. 

Maximum gain (linear). The gain constraint


Gain profile as a function of frequency. The gain constraint
If you are tuning in discrete time (that is, using a 

Maximum gain as a function of frequency, expressed as a SISO The software automatically maps 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 scaling, specified as a vector of positive real values. Use this property to specify the relative amplitude of each
entry in vectorvalued input signals when the choice of units results
in a mix of small and large signals. This information is used to scale
the closedloop transfer function from Suppose T(s) is the closedloop
transfer function from The default value, Default: 

Output signal scaling, specified as a vector of positive real values. Use this property to specify the relative amplitude of each
entry in vectorvalued output signals when the choice of units results
in a mix of small and large signals. This information is used to scale
the closedloop transfer function from Suppose T(s) is the closedloop
transfer function from The default value, Default: 

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 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
object, the software
converts the tuning goal into a normalized scalar value
f(x), where 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.Gain
, f(x) is given
by:
$$f\left(x\right)={\Vert {W}_{F}\left(s\right){D}_{o}^{1}T\left(s,x\right){D}_{i}\Vert}_{\infty},$$
or its discretetime equivalent, for discretetime tuning. Here,
T(s,x) is the closedloop transfer
function from Input
to Output
.
D_{o} and D_{i}
are diagonal matrices with the OutputScaling
and
InputScaling
property values on the diagonal, respectively. $${\Vert \text{\hspace{0.17em}}\cdot \text{\hspace{0.17em}}\Vert}_{\infty}$$ denotes the H_{∞} norm (see
getPeakGain
).
The frequency weighting function W_{F} is the
regularized gain profile, derived from the maximum gain profile you specify. The gains of
W_{F} and 1/MaxGain
roughly match
inside the frequency band Focus
. W_{F}
is always stable and proper. Because poles of W_{F} close
to s = 0 or s = Inf
might lead to poor
numeric conditioning of the systune
optimization problem, it is not
recommended to specify maximum gain profiles with very lowfrequency or very highfrequency
dynamics.
To obtain W_{F}, use:
WF = getWeight(Req,Ts)
where Req
is the tuning goal, and Ts
is the sample
time at which you are tuning (Ts = 0
for continuous time). For more
information about regularization and its effects, see Visualize Tuning Goals.
looptune
 systune
 TuningGoal.LoopShape
 TuningGoal.Tracking
 viewGoal
 makeweight
(Robust Control Toolbox)  looptune (for slTuner)
(Simulink Control Design)  slTuner
(Simulink Control Design)  systune (for slTuner)
(Simulink Control Design)