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# TuningGoal.Overshoot class

Package: TuningGoal

Overshoot constraint for control system tuning

## Description

Use the TuningGoal.Overshoot object to limit the overshoot in the step response from specified inputs to specified outputs of a control system. Use this requirement for control system tuning with tuning commands such as systune or looptune.

## Construction

Req = TuningGoal.Overshoot(inputname,outputname,maxpercent) creates a tuning requirement for limiting the overshoot in the step response between the specified signal locations. The scalar maxpercent specifies the maximum overshoot as a percentage.

When you use TuningGoal.Overshoot for tuning, the software maps overshoot constraints to peak gain constraints assuming second-order system characteristics. Therefore, the mapping is only approximate for higher-order systems. In addition, this requirement cannot reliably reduce the overshoot below 5%.

### Input Arguments

 inputname Input signals for the requirement, specified as a string or as a cell array of strings, for multiple-input requirements. If you are using the requirement 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 interface associated with the Simulink model. Use addPoint to add analysis points to the slTuner interface. Use getPoints to get the list of analysis points available in an slTuner interface to your model. If you are using the requirement 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 a string contained 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 requirement is the implied input associated with the AnalysisPoint block: For more information about analysis points in control system models, see Managing Signals in Control System Analysis and Design. outputname Output signals for the requirement, specified as a string or as a cell array of strings, for multiple-output requirements. If you are using the requirement 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 interface associated with the Simulink model. Use addPoint to add analysis points to the slTuner interface. Use getPoints to get the list of analysis points available in an slTuner interface to your model. If you are using the requirement 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 inputname can be a string contained in T.OutputName. Also, if T contains an AnalysisPoint block with a location named AP_y, then inputname can include 'AP_y'. 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 requirement is the implied output associated with the AnalysisPoint block: For more information about analysis points in control system models, see Managing Signals in Control System Analysis and Design. maxpercent Maximum percent overshoot, specified as a scalar value. For example, the following code specifies a maximum 5% overshoot in the step response from 'r' to 'y'. `Req = TuningGoal.Overshoot('r','y',5);` TuningGoal.OverShoot cannot reliably reduce the overshoot below 5%.

## Properties

 MaxOvershoot Maximum percent overshoot, specified as a scalar value. For example, the scalar value 5 means the overshoot should not exceed 5%. The initial value of the MaxOvershoot property is set by the maxpercent input argument when you construct the requirement object. InputScaling Reference signal scaling, specified as a vector of positive real values. For a MIMO tuning requirement, when the choice of units results in a mix of small and large signals in different channels of the response, use this property to specify the relative amplitude of each entry in the vector-valued step input. This information is used to scale the off-diagonal terms in the transfer function from reference to tracking error. This scaling ensures that cross-couplings are measured relative to the amplitude of each reference signal. For example, suppose that Req is a requirement that signals {'y1','y2'} track reference signals {'r1','r2'}. Suppose further that you require the outputs to track the references with less than 10% cross-coupling. If r1 and r2 have comparable amplitudes, then it is sufficient to keep the gains from r1 to y2 and r2 and y1 below 0.1. However, if r1 is 100 times larger than r2, the gain from r1 to y2 must be less than 0.001 to ensure that r1 changes y2 by less than 10% of the r2 target. To ensure this result, set the InputScaling property as follows. `Req.InputScaling = [100,1];` This tells the software to take into account that the first reference signal is 100 times greater than the second reference signal. The default value, [] , means no scaling. Default: [] Input Input signal names, specified as a cell array of strings. These strings specify the names of the inputs of the transfer function that the tuning requirement constrains. The initial value of the Input property is set by the inputname input argument when you construct the requirement object. Output Output signal names, specified as a cell array of strings. These strings specify the names of the outputs of the transfer function that the tuning requirement constrains. The initial value of the Output property is set by the outputname input argument when you construct the requirement object. Models Models to which the tuning requirement 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 requirement for a subset of models in the array. For example, suppose you want to apply the tuning requirement, Req, to the second, third, and fourth models in a model array passed to systune. To restrict enforcement of the requirement, use the following command: `Req.Models = 2:4;` When Models = NaN, the tuning requirement applies to all models. Default: NaN Openings Feedback loops to open when evaluating the requirement, specified as a cell array of strings that identify loop-opening locations. The tuning requirement is evaluated against the open-loop configuration created by opening feedback loops at the locations you identify. If you are using the requirement 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 interface associated with the Simulink model. Use addPoint to add analysis points and loop openings to the slTuner interface. Use getPoints to get the list of analysis points available in an slTuner interface to your model. If you are using the requirement 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. Default: {} Name Name of the requirement object, specified as a string. For example, if Req is a requirement: `Req.Name = 'LoopReq';` Default: []

## Examples

expand all

### Overshoot Constraint

Create a requirement that limits the overshoot of the step response from signals named 'r' to 'y' in a control system to 8 percent.

```Req = TuningGoal.Overshoot('r','y',8);
```

You can use Req as an input to looptune or systune when tuning the control system.

Configure the requirement to apply only to the second model in a model array to tune. Also, configure the requirement to be evaluated with a loop open in the control system.

```Req.Models = 2;
Req.Openings = 'OuterLoop';
```

Setting the Models property restricts application of the requirement to the second model in an array, when you use the requirement to tune an array of control system models. Setting the Openings property specifies that requirement is evaluated with a loop opened at the location in the control system identified by 'OuterLoop'.

## Algorithms

When you use a TuningGoal object to specify a tuning requirement, the software converts the requirement into a normalized scalar value f(x). 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 requirement is a hard constraint.

For TuningGoal.Overshoot, f(x) reflects the relative satisfaction or violation of the goal. The percent deviation from f(x) = 1 roughly corresponds to the percent deviation from the specified overshoot target. For example, f(x) = 1.2 means the actual overshoot exceeds the target by roughly 20%, and f(x) = 0.8 means the actual overshoot is about 20% less than the target.

TuningGoal.Overshoot uses ${‖T‖}_{\infty }$ as a proxy for the overshoot, based on second-order model characteristics. Here, T is the closed-loop transfer function that the requirement constrains. The overshoot is tuned in the range from 5% (${‖T‖}_{\infty }$ = 1) to 100% (${‖T‖}_{\infty }$). TuningGoal.Overshoot is ineffective at forcing the overshoot below 5%.