Disturbance rejection requirement for control system tuning
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
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 closed-loop 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
tuning goal constrains the minimum disturbance attenuation factor to the frequency-dependent
Disturbance location, specified as a character vector or, for multiple-input 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
Req.Focus = [1,100];
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 off-diagonal (loop interaction) terms in the open-loop
transfer function. Set
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.
Req.Models = 2:4;
Feedback loops to open when evaluating the tuning goal, specified as a cell array of character vectors that identify loop-opening locations. The tuning goal is evaluated against the open-loop 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 state-space
For example, if
Name of the tuning goal, specified as a character vector.
For example, if
Req.Name = 'LoopReq';
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
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
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.
The shaded region indicates where the tuning goal is violated.
This tuning goal imposes an implicit stability constraint on
the closed-loop sensitivity function measured at
evaluated with loops opened at the points identified in
The dynamics affected by this implicit constraint are the stabilized
dynamics for this tuning goal. The
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,
systuneOptions to change
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.
TuningGoal.Rejection, f(x) is
or its discrete-time equivalent. Here,
S(jω,x) is the closed-loop sensitivity
function measured at the disturbance location. Ω is the frequency interval over which the tuning
goal is enforced, specified in the
WS is a frequency weighting function derived from the
specified attenuation profile. The gains of WS 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
WS close to s = 0 or
Inf might lead to poor numeric conditioning of the
systune optimization problem, it is not recommended to specify attenuation
profiles with very low-frequency or very high-frequency dynamics.
To obtain WS, use:
WS = getWeight(Req,Ts)
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.
Behavior changed in R2016a
Prior to R2016a, this functionality required a Robust Control Toolbox™ license.