Package: TuningGoal
Disturbance rejection requirement for control system tuning
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).
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
.

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 

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 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: 
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]
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.
This tuning goal imposes an implicit stability constraint on
the closedloop sensitivity function measured at Location
,
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).
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.