Documentation |
Package: TuningGoal
Frequency-weighted gain constraint for control system tuning
Use the TuningGoal.WeightedGain object to specify a tuning requirement that limits the weighted gain from specified inputs to outputs. The weighted gain is the maximum across frequency of the gain from input to output, multiplied by weighting functions that you specify. You can use the TuningGoal.WeightedGain requirement for control system tuning with tuning commands such as systune or looptune.
After you create a requirement object, you can further configure the tuning requirement by setting Properties of the object.
Req = TuningGoal.WeightedGain(inputname,outputname,WL,WR) creates a tuning requirement. This tuning requirement specifies that the closed-loop transfer function, H(s), from the specified input to output meets the requirement:
||W_{L}(s)H(s)W_{R}(s)||_{∞} < 1.
The notation ||•||_{∞} denotes the maximum gain across frequency (the H_{∞} norm).
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:
If you are using the requirement to tune a generalized state-space (genss) model of a control system, then inputname can include:
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:
If you are using the requirement to tune a generalized state-space (genss) model of a control system, then outputname can include:
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. |
WL,WR |
Frequency-weighting functions, specified as scalars or as SISO or MIMO numeric LTI models. The functions WL and WR provide the weights for the tuning requirement. The tuning requirement ensures that the gain H(s) from the specified input to output satisfies the inequality: ||WL(s)H(s)WR(s)||_{∞} < 1. WL provides the weighting for the output channels of H(s), and WR provides the weighting for the input channels. You can specify scalar weights or frequency-dependent weighting. To specify a frequency-dependent weighting, use a numeric LTI model. For example: WL = tf(1,[1 0.01]); WR = 10; If you specify MIMO weighting functions, then inputname and outputname must be vector signals. The dimensions of the vector signals must be such that the dimensions of H(s) are commensurate with the dimensions of WL and WR. For example, if you specify WR = diag([1 10]), then inputname must include two signals. Scalar values, however, automatically expand to any input or output dimension. A value of WL = [] or WR = [] is interpreted as the identity. |
WL |
Frequency-weighting function for the output channels of the transfer function H(s) to constrain, specified as a scalar, or as a SISO or MIMO numeric LTI model. The initial value of the WL property is set by the WL input argument when you construct the requirement object. |
WR |
Frequency-weighting function for the input channels of the transfer function to constrain, specified as a scalar or as a SISO or MIMO numeric LTI model. The initial value of the WR property is set by the WR input argument when you construct the requirement object. |
Focus |
Frequency band in which tuning requirement is enforced, specified as a row vector of the form [min,max]. Set the Focus property to limit enforcement of the requirement to a particular frequency band. Express this value in the frequency units of the control system model you are tuning (rad/TimeUnit). For example, suppose Req is a requirement that you want to apply only between 1 and 100 rad/s. To restrict the requirement to this band, use the following command: Req.Focus = [1,100]; Default: [0,Inf] for continuous time; [0,pi/Ts] for discrete time, where Ts is the model sampling time. |
Stabilize |
Stability requirement on closed-loop dynamics, specified as 1 (true) or 0 (false). By default, TuningGoal.Gain imposes a stability requirement on the closed-loop transfer function from the specified inputs to outputs, in addition to the gain requirement. If stability is not required or cannot be achieved, set Stabilize to false to remove the stability requirement. For example, if the gain constraint applies to an unstable open-loop transfer function, set Stabilize to false. Default: 1(true) |
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: [] |
When you tune a control system using 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 the TuningGoal.WeightedGain requirement, f(x) is given by:
$$f\left(x\right)={\Vert {W}_{L}T\left(s,x\right){W}_{R}\Vert}_{\infty}.$$
T(s,x) is the closed-loop transfer function from Input to Output. $${\Vert \text{\hspace{0.17em}}\cdot \text{\hspace{0.17em}}\Vert}_{\infty}$$ denotes the H_{∞} norm (see norm).
evalSpec | looptune | looptune (for slTuner) | slTuner | systune | systune (for slTuner) | viewSpec