TuningGoal.Rejection class
Package: TuningGoal
Disturbance rejection requirement for control system tuning
Description
Use TuningGoal.Rejection
to specify the minimum
attenuation of a disturbance injected at a specified location in a control system. This tuning
goal helps you tune control systems with tuning commands such as systune
or
looptune
.
When you use TuningGoal.Rejection
, the software attempts
to tune the system so that the attenuation of a disturbance at the specified location exceeds the
minimum attenuation factor you specify. This attenuation factor is the ratio between the open
and closedloop sensitivities to the disturbance and is a function of frequency. You can achieve
disturbance attenuation only inside the control bandwidth. The loop gain must be larger than one
for the disturbance to be attenuated (attenuation factor > 1).
Construction
creates a tuning goal for rejecting a disturbance entering at Req
=
TuningGoal.Rejection(distloc
,attfact
)distloc
. This
tuning goal constrains the minimum disturbance attenuation factor to the frequencydependent
value, attfact
.
Input Arguments

Disturbance location, specified as a character vector or, for multipleinput tuning goals, a cell array of character vectors.


Attenuation factor as a function of frequency, specified as a numeric LTI model.
attfact = frd([100 100 1 1],[0 1 10 100]); Req = TuningGoal.Rejection('u',attfact); bodemag(attfact) ylim([5,40]) When you use an If you are tuning in discrete time (that is, using a 
Properties

Minimum disturbance attenuation 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: 

Toggle for automatically scaling loop signals, specified as For multiloop or MIMO disturbance rejection tuning goals, the feedback channels are
automatically rescaled to equalize the offdiagonal (loop interaction) terms in the openloop
transfer function. Set Default: 

Location of disturbance, specified as a cell array of character vectors that identify one
or more analysis points in the control system to tune. For example, if 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
Constant Minimum Attenuation in Frequency Band
Create a tuning goal that enforces a attenuation of at least a factor of 10 between 0 and 5
rad/s. The tuning goal applies to a disturbance entering a control system at a point identified
as 'u'
.
Req = TuningGoal.Rejection('u',10); Req.Name = 'Rejection spec'; Req.Focus = [0 5]
FrequencyDependent Attenuation Profile
Create a tuning goal that enforces an attenuation factor of at least 100 (40 dB) below 1 rad/s, gradually dropping to 1 (0 dB) past 10 rad/s. The tuning goal applies to a disturbance entering a control system at a point identified as 'u'
.
attfact = frd([100 100 1 1],[0 1 10 100]);
Req = TuningGoal.Rejection('u',attfact);
These commands use a frd
model to specify the minimum attenuation profile as a function of frequency. The minimum attenuation of 100 below 1 rad/s, together with the minimum attenuation of 1 at the frequencies of 10 and 100 rad/s, specifies the desired rolloff.
attfact
is converted into a smooth function of frequency that approximates the piecewise specified profile. Display the gain profile using viewGoal.
viewGoal(Req)
The shaded region indicates where the tuning goal is violated.
Tips
This tuning goal imposes an implicit stability constraint on the closedloop sensitivity function measured at
Location
, 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). In
this case, x is the vector of free (tunable) parameters in the control system.
The parameter values are adjusted automatically to minimize
f(x) or drive f(x)
below 1 if the tuning goal is a hard constraint.
For TuningGoal.Rejection
, f(x) is
given by:
$$f\left(x\right)=\underset{\omega \in \text{\hspace{0.17em}}\Omega}{\mathrm{max}}{\Vert {W}_{S}\left(j\omega \right)S\left(j\omega ,x\right)\Vert}_{\infty},$$
or its discretetime equivalent. Here,
S(jω,x) is the closedloop sensitivity
function measured at the disturbance location. Ω is the frequency interval over which the tuning
goal is enforced, specified in the Focus
property.
W_{S} is a frequency weighting function derived from the
specified attenuation profile. The gains of W_{S} and
MinAttenuation
roughly match for gain values ranging from –20 dB to 60 dB.
For numerical reasons, the weighting function levels off outside this range, unless the specified
attenuation profile changes slope outside this range. This adjustment is called
regularization. Because poles of
W_{S} close to s = 0 or
s = Inf
might lead to poor numeric conditioning of the
systune
optimization problem, it is not recommended to specify attenuation
profiles with very lowfrequency or very highfrequency dynamics.
To obtain W_{S}, use:
WS = 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.
Compatibility Considerations
See Also
looptune
 viewGoal
 systune
 systune (for slTuner)
(Simulink Control Design)  looptune (for slTuner)
(Simulink Control Design)  TuningGoal.Tracking
 TuningGoal.LoopShape
 slTuner
(Simulink Control Design)