TuningGoal.Variance class
Package: TuningGoal
Noise amplification constraint for control system tuning
Description
Use TuningGoal.Variance
to specify a tuning goal that
limits the noise amplification from specified inputs to outputs. The noise amplification is
defined as either:
The square root of the output variance, for a unitvariance whitenoise input
The rootmeansquare of the output, for a unitvariance whitenoise input
The H_{2} norm of the transfer function from the specified inputs to outputs, which equals the total energy of the impulse response
These definitions are different interpretations of the same quantity. TuningGoal.Variance
imposes the same limit on these quantities.
You can use TuningGoal.Variance
for control system
tuning with tuning commands, such as systune
or
looptune
. Specifying this tuning goal allows you to tune the system
response to whitenoise inputs. For stochastic inputs with a nonuniform spectrum (colored
noise), use TuningGoal.WeightedVariance
instead.
After you create a tuning goal, you can further configure the tuning goal by setting Properties of the object.
Construction
creates a tuning goal that limits the noise amplification of the transfer function from
Req
= TuningGoal.Variance(inputname
,outputname
,maxamp
)inputname
to outputname
to the scalar value
maxamp
.
When you tune a control system in discrete time, this tuning goal assumes that the
physical plant and noise process are continuous. To ensure that continuoustime and
discretetime tuning give consistent results, maxamp
is interpreted as a
constraint on the continuoustime H_{2} norm. If the
plant and noise processes are truly discrete and you want to constrain the discretetime
H_{2} norm to the value maxamp
,
set the third input argument to maxamp
/sqrt(Ts)
, where
Ts
is the sample time of the model you are tuning.
Input Arguments

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 noise amplification from When you tune a control system in discrete time, this tuning goal assumes that the
physical plant and noise process are continuous, and interprets

Properties

Maximum noise amplification, specified as a positive scalar value. This property
specifies the maximum value of the output variance at the signals specified in


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: 
Examples
Tips
When you use this tuning goal to tune a continuoustime control system,
systune
attempts to enforce zero feedthrough (D = 0) on the transfer that the tuning goal constrains. Zero feedthrough is imposed because the H_{2} norm, and therefore the value of the tuning goal (see Algorithms), is infinite for continuoustime systems with nonzero feedthrough.systune
enforces zero feedthrough by fixing to zero all tunable parameters that contribute to the feedthrough term.systune
returns an error when fixing these tunable parameters is insufficient to enforce zero feedthrough. In such cases, you must modify the tuning goal or the control structure, or manually fix some tunable parameters of your system to values that eliminate the feedthrough term.When the constrained transfer function has several tunable blocks in series, the software’s approach of zeroing all parameters that contribute to the overall feedthrough might be conservative. In that case, it is sufficient to zero the feedthrough term of one of the blocks. If you want to control which block has feedthrough fixed to zero, you can manually fix the feedthrough of the tuned block of your choice.
To fix parameters of tunable blocks to specified values, use the
Value
andFree
properties of the block parametrization. For example, consider a tuned statespace block:C = tunableSS('C',1,2,3);
To enforce zero feedthrough on this block, set its D matrix value to zero, and fix the parameter.
C.D.Value = 0; C.D.Free = false;
For more information on fixing parameter values, see the Control Design Block reference pages, such as
tunableSS
.This tuning goal imposes an implicit stability constraint on the closedloop transfer function from
Input
toOutput
, evaluated with loops opened at the points identified inOpenings
. The dynamics affected by this implicit constraint are the stabilized dynamics for this tuning goal. TheMinDecay
andMaxRadius
options ofsystuneOptions
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, usesystuneOptions
to change these defaults.
Algorithms
When you tune a control system using a TuningGoal
, the software
converts the tuning goal into a normalized scalar value
f(x). The vector 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.Variance
, f(x) is
given by:
$$f\left(x\right)={\Vert \frac{1}{\text{MaxAmplification}}T\left(s,x\right)\Vert}_{2}.$$
T(s,x) is the closedloop
transfer function from Input
to Output
. $${\Vert \text{\hspace{0.17em}}\cdot \text{\hspace{0.17em}}\Vert}_{2}$$ denotes the H_{2} norm (see
norm
).
For tuning discretetime control systems, f(x) is given by:
$$f\left(x\right)={\Vert \frac{1}{\text{MaxAmplification}\sqrt{{T}_{s}}}T\left(z,x\right)\Vert}_{2}.$$
T_{s} is the sample time of the discretetime transfer function T(z,x).
Compatibility Considerations
See Also
looptune
 systune
 looptune (for slTuner)
(Simulink Control Design)  systune (for slTuner)
(Simulink Control Design)  slTuner
(Simulink Control Design)  viewGoal
 evalGoal
 norm
 TuningGoal.WeightedVariance