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TuningGoal.StepRejection

Step disturbance rejection requirement for control system tuning

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Description

Use TuningGoal.StepRejection to specify how a step disturbance injected at a specified location in your control system affects the signal at a specified output location. Use this tuning goal with control system tuning commands such as systune or looptune.

You can specify the desired response in time-domain terms of peak value, settling time, and damping ratio. Alternatively, you can specify the response as a stable reference model having DC-gain. In that case, the tuning goal is to reject the disturbance as well as or better than the reference model.

To specify disturbance rejection in terms of a frequency-domain attenuation profile, use TuningGoal.Rejection.

Creation

Syntax

Req = TuningGoal.StepRejection(inputname,outputname,refsys)
Req = TuningGoal.StepRejection(inputname,outputname,peak,tSettle)
Req = TuningGoal.StepRejection(inputname,outputname,peak,tSettle,zeta)

Description

Req = TuningGoal.StepRejection(inputname,outputname,refsys) creates a tuning goal that constrains how a step disturbance injected at a location inputname affects the response at outputname. The tuning goal is that the disturbance be rejected as well as or better than the reference system. inputname and outputname can describe a SISO or MIMO response of your control system. For MIMO responses, the number of inputs must equal the number of outputs.

example

Req = TuningGoal.StepRejection(inputname,outputname,peak,tSettle) specifies an oscillation-free response in terms of a peak value and a settling time.

Req = TuningGoal.StepRejection(inputname,outputname,peak,tSettle,zeta) allows for damped oscillations with a damping ratio of at least zeta.

Input Arguments

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Input signals for the tuning goal, specified as a character vector or, for multiple-input tuning goals, a cell array of character vectors.

  • If you are using the tuning goal to tune a Simulink® model of a control system, then inputname can include:

    • Any model input.

    • Any linear analysis point marked in the model.

    • Any linear analysis point in an slTuner (Simulink Control Design) interface associated with the Simulink model. Use addPoint (Simulink Control Design) to add analysis points to the slTuner interface. Use getPoints (Simulink Control Design) to get the list of analysis points available in an slTuner interface to your model.

    For example, suppose that the slTuner interface contains analysis points u1 and u2. Use 'u1' to designate that point as an input signal when creating tuning goals. Use {'u1','u2'} to designate a two-channel input.

  • If you are using the tuning goal to tune a generalized state-space (genss) model of a control system, then inputname can include:

    • Any input of the genss model

    • Any AnalysisPoint location in the control system model

    For example, if you are tuning a control system model, T, then inputname can be any input name in T.InputName. Also, if T contains an AnalysisPoint block with a location named AP_u, then inputname can include 'AP_u'. Use getPoints to get a list of analysis points available in a genss model.

    If inputname is an AnalysisPoint location of a generalized model, the input signal for the tuning goal is the implied input associated with the AnalysisPoint block:

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 multiple-output tuning goals, a cell array of character vectors.

  • If you are using the tuning goal to tune a Simulink model of a control system, then outputname can include:

    • Any model output.

    • Any linear analysis point marked in the model.

    • Any linear analysis point in an slTuner (Simulink Control Design) interface associated with the Simulink model. Use addPoint (Simulink Control Design) to add analysis points to the slTuner interface. Use getPoints (Simulink Control Design) to get the list of analysis points available in an slTuner interface to your model.

    For example, suppose that the slTuner interface contains analysis points y1 and y2. Use 'y1' to designate that point as an output signal when creating tuning goals. Use {'y1','y2'} to designate a two-channel output.

  • If you are using the tuning goal to tune a generalized state-space (genss) model of a control system, then outputname can include:

    • Any output of the genss model

    • Any AnalysisPoint location in the control system model

    For example, if you are tuning a control system model, T, then outputname can be any output name in T.OutputName. Also, if T contains an AnalysisPoint block with a location named AP_u, then outputname can include 'AP_u'. Use getPoints to get a list of analysis points available in a genss model.

    If outputname is an AnalysisPoint location of a generalized model, the output signal for the tuning goal is the implied output associated with the AnalysisPoint block:

For more information about analysis points in control system models, see Mark Signals of Interest for Control System Analysis and Design.

Reference system for target step rejection, specified as a SISO dynamic system model, such as a tf, zpk, or ss model. refsys must be stable and proper, and must have zero DC gain. This restriction ensures perfect rejection of the steady-state disturbance.

refsys can be continuous or discrete. If refsys is discrete, it can include time delays which are treated as poles at z = 0.

For best results, refsys and the open-loop response from the disturbance to the output should have similar gains at the frequency where the reference model gain peaks. You can check the peak gain and peak frequency using getPeakGain. For example:

[gmax,fmax] = getPeakGain(refsys);

Use getIOTransfer to extract the corresponding open-loop response from the system you are tuning.

Peak absolute value of target response to disturbance, specified as a scalar value.

Target settling time of the response to disturbance, specified as a positive scalar value, in the time units of the control system you are tuning.

Minimum damping ratio of oscillations in the response to disturbance, specified as a value between 0 and 1.

Properties

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Reference system for target response to step disturbance, specified as a SISO (zpk) model. The step response of this model specifies how the output signals specified by outputname should respond to the step disturbance at inputname.

If you use the refsys input argument to create the tuning goal, then the value of ReferenceModel is zpk(refsys).

If you use the peak, tSample, and zeta input arguments, then ReferenceModel is a zpk representation of the first-order or second-order transfer function whose step response has the specified characteristics.

Input signal scaling, specified as a vector of positive real elements.

Use this property to specify the relative amplitude of each entry in vector-valued input signals when the choice of units results in a mix of small and large signals. This information is used to scale the closed-loop transfer function from Input to Output when the tuning goal is evaluated.

Suppose T(s) is the closed-loop transfer function from Input to Output. The tuning goal is evaluated for the scaled transfer function Do–1T(s)Di. The diagonal matrices Do and Di have the OutputScaling and InputScaling values on the diagonal, respectively.

The default value, [] , means no scaling.

Output signal scaling, specified as a vector of positive real values.

Use this property to specify the relative amplitude of each entry in vector-valued output signals when the choice of units results in a mix of small and large signals. This information is used to scale the closed-loop transfer function from Input to Output when the tuning goal is evaluated.

Suppose T(s) is the closed-loop transfer function from Input to Output. The tuning goal is evaluated for the scaled transfer function Do–1T(s)Di. The diagonal matrices Do and Di have the OutputScaling and InputScaling values on the diagonal, respectively.

The default value, [] , means no scaling.

Names of disturbance input locations, specified as a cell array of character vectors. This property is initially populated by the inputname argument when you create the tuning goal.

Names of locations at which response to step disturbance is measured, specified as a cell array of character vectors. This property is initially populated by the outputname argument when you create the tuning goal.

Models to which the tuning goal applies, specified as a vector of indices.

Use the Models property when tuning an array of control system models with systune, to enforce a tuning goal for a subset of models in the array. For example, suppose you want to apply the tuning goal, Req, to the second, third, and fourth models in a model array passed to systune. To restrict enforcement of the tuning goal, use the following command:

Req.Models = 2:4;

When Models = NaN, the tuning goal applies to all models.

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 Openings can include any linear analysis point marked in the model, or any linear analysis point in an slTuner (Simulink Control Design) interface associated with the Simulink model. Use addPoint (Simulink Control Design) to add analysis points and loop openings to the slTuner interface. Use getPoints (Simulink Control Design) to get the list of analysis points available in an slTuner interface to your model.

If you are using the tuning goal to tune a generalized state-space (genss) model of a control system, then Openings can include any AnalysisPoint location in the control system model. Use getPoints to get the list of analysis points available in the genss model.

For example, if Openings = {'u1','u2'}, then the tuning goal is evaluated with loops open at analysis points u1 and u2.

Name of the tuning goal, specified as a character vector.

For example, if Req is a tuning goal:

Req.Name = 'LoopReq';

Examples

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Open Live Script

Create a requirement that specifies the step disturbance response in terms of peak time-domain response, settling time, and damping of oscillations.

Suppose you want the response at 'y' to a disturbance injected at 'd' to never exceed an absolute value of 0.25, and to settle within 5 seconds. Create a TuningGoal.StepRejection requirement that captures these specifications and also specifies non-oscillatory response.

Req1 = TuningGoal.StepRejection('d','y',0.25,5);

Omitting an explicit value for the damping ratio, zeta, is equivalent to setting zeta = 1. Therefore, Req specifies a non-oscillatory response. The software converts the peak value and settling time into a reference transfer function whose step response has the desired time-domain profile. This transfer function is stored in the ReferenceModel property of Req.

Req1.ReferenceModel
ans =
 
   0.92883 s
  -----------
  (s+1.367)^2
 
Continuous-time zero/pole/gain model.

Confirm the target response by displaying Req.

figure()
viewGoal(Req1)

MATLAB figure

Suppose your application can tolerate oscillations provided the damping ratio is less than 0.4. Create a requirement that specifies this disturbance response.

Req2 = TuningGoal.StepRejection('d','y',0.25,5,0.4);
figure()
viewGoal(Req2)

MATLAB figure

Open Live Script

Create a requirement that specifies the step disturbance response as a transfer function.

Suppose you want the response to a disturbance injected at an analysis point d in your control system and measured at a point 'y' to be rejected at least as well as the transfer function

H(s)=ss2+2s+1.

Create a TuningGoal.StepRejection requirement.

H = tf([1 0],[1 2 1]);
Req = TuningGoal.StepRejection('d','y',H);

Display the requirement.

viewGoal(Req)

MATLAB figure

The plot displayed by viewGoal shows the step response of the specified transfer function. This response is the target time-domain response to disturbance.

Tips

  • This tuning goal imposes an implicit stability constraint on the closed-loop 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.

Algorithms

When you tune a control system using a TuningGoal, 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.

TuningGoal.StepRejection aims to keep the gain from disturbance to output below the gain of the reference model. The scalar value of the tuning goal f(x) is given by:

f(x)=‖WF(s)Tdy(s,x)‖∞,

or its discrete-time equivalent. Here, Tdy(s,x) is the closed-loop transfer function from Input to Output, and ‖ ⋅ ‖∞ denotes the H∞ norm (see norm). WF is a frequency weighting function derived from the step-rejection profile you specify in the tuning goal. The gains of WF and 1/ReferenceModel roughly match for gain values within 60 dB of the peak gain. For numerical reasons, the weighting function levels off outside this range, unless you specify a reference model that changes slope outside this range. This adjustment is called regularization. Because poles of WF close to s = 0 or s = Inf might lead to poor numeric conditioning of the systune optimization problem, it is not recommended to specify reference models with very low-frequency or very high-frequency dynamics.

To obtain WF, 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.

Version History

Introduced in R2016a

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See Also

| | (Simulink Control Design) | (Simulink Control Design) | | | | | (Simulink Control Design)

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