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musynOptions

Options for musyn

Since R2019b

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Syntax

opts = musynOptions
opts = musynOptions(Name,Value)

Description

example

opts = musynOptions returns the default options for performing μ synthesis with the musyn command.

example

opts = musynOptions(Name,Value) creates an option set with the options specified by one or more name-value pair arguments.

Examples

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Open Live Script

Create an options set for musyn that turns on mixed-μ analysis for real uncertainty, restricts the D and G scalings for repeated ureal blocks so they are diagonal, and limits the maximum number of D-K iterations to 20. 

opts = musynOptions('MixedMU','on','FullDG',false,'MaxIter',20)
opts = 
  musyn with properties:

          Display: 'short'
          MaxIter: 20
       TargetPerf: 0
          TolPerf: 0.0100
          MixedMU: 'on'
           FullDG: [0 0]
         FitOrder: [5 2]
    FrequencyGrid: [0x1 double]
        AutoScale: 'on'
       Regularize: 'on'
        LimitGain: 'on'
      RandomStart: 0
      UseParallel: 0
         MinDecay: 1.0000e-07
     MaxFrequency: Inf

Alternatively, start with the default options set, and use dot notation to change option values.

opts = musynOptions;
opts.MixedMu = 'on';
opts.FullDG  = false;
opts.MaxIter = 20;

You can now use opts as an input argument to musyn to perform μ synthesis using the specified options.

Input Arguments

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Name-Value Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Before R2021a, use commas to separate each name and value, and enclose Name in quotes.

Example: opts = musynOptions('MaxIter',20,'MixedMU','on') creates an option set for musyn to specify that the function take into account the presence of real uncertainty and to stop the D-K iteration process after at most 20 iterations.

General Options

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Flag to display progress of D-K iterations and generate report in the command window, specified as the comma-separated pair consisting of 'Display' and 'short', 'full', or 'off'.

  • 'short' — Display a brief summary after each iteration.

  • 'full' — Pause after each iteration and display detailed results, including plots of D and G scaling data and the frequency dependence of μ.

  • 'off' — Turn off the display.

For details on how to interpret the default 'short' display and the 'full' display, see Robust Performance Measure for Mu Synthesis.

Example: opts = musynOptions('Display','off') creates an option set for musyn that turns the display off.

Maximum number of D-K iterations, specified as the comma-separated pair consisting of 'MaxIter' and a positive integer. musyn stops after the specified number of iterations or when the stopping tolerance specified by the 'TolPerf' option is reached, whichever is fewer.

Example: opts = musynOptions('MaxIter',20) creates an option set for musyn that specifies a maximum of 20 iterations.

Target robust H∞ performance, specified as the comma-separated pair consisting of 'TargetPerf' and a nonnegative scalar. By default, musyn tries to drive the robust H∞ performance (PeakMu in the default display) to zero in each iteration. If you set 'TargetPerf' to a nonzero value, then D-K iteration terminates when the robust H∞ performance drops below this target value. If you know your system can tolerate worse values of this performance metric, increasing this value can speed up the H∞ part of the D-K iteration. For details about this performance metric, see musynperf.

Example: opts = musynOptions('TargetPerf',1) creates an option set for musyn that specifies a target H∞ performance value of 1.

Stopping tolerance, specified as the comma-separated pair consisting of 'TolPerf' and a nonnegative scalar. The musyn computation terminates when the robust H∞ performance improves by less than this value over two consecutive iterations. Because of the limited accuracy of fitting the D and G scalings, reducing 'TolPerf' below the default does not necessarily yield more precise results.

If 'TolPerf' = 0, then musyn always performs the number of iterations specified by 'MaxIter', regardless changes in the robust performance from iteration to iteration.

Example: opts = musynOptions('TolPerf',0) creates an option set for musyn that causes the function to always perform the number of iterations specified by MaxIter.

Options for D Step (μ Analysis)

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Option to specify real or complex μ analysis, specified as the comma-separated pair consisting of 'MixedMU' and 'off' or 'on'. By default, musyn treats all uncertainties as complex, which can result in overly conservative estimates for the upper bound on μ. If your plant has real uncertain parameters, try setting 'MixedMu' to 'on' to see if musyn returns a controller with better performance.

For more information, see Improve Results of Mu Synthesis.

Example: opts = musynOptions('MixedMU','on') creates an option set for musyn that causes the function to take into account the presence of real uncertainty.

Structure of D and G scalings, specified as the comma-separated pair consisting of 'FullDG' and true, false, [true false], or [false true].

By default, musyn uses full scalings for uncertain blocks that appear multiple times in the control system. Full scaling matrices can have frequency-dependent entries both on and off the diagonal. The alternative, diagonal scaling, is equivalent to treating each repeated block as an independent instance of the uncertain parameter. Therefore, full scaling is less conservative than diagonal scaling, and can yield better robust performance.

However, when blocks are repeated more than about four or five times, full scaling can be impractical, leading to lengthy computation, undesirably high-order controllers, or both. In such cases, restricting scalings to diagonal can improve results. To do so, set 'FullDG' to:

  • false to limit both D and G scalings to diagonal.

  • [true false] to use full D scaling but diagonal G scaling. This option is useful because fitting full G scalings is more likely to cause high-order controllers than full D scaling.

  • [false true] to use full G scaling but diagonal D scaling. This option is useful if you need full G scaling to get a good fit, but observe that full D scaling does not improve musyn results.

For details about how the musyn algorithm uses D and G scalings, see Robust Performance Measure for Mu Synthesis.

Example: opts = musynOptions('FullDG',false) creates an option set for musyn that causes the function to use diagonal scalings for both D and G.

Maximum order for fitting D and G scaling data, specified as the comma-separated pair consisting of 'FitOrder' and a vector of two positive integers. The integers specify the maximum fit orders for the D and G scalings, respectively. (For details about how the musyn algorithm uses and fits scalings, see Robust Performance Measure for Mu Synthesis.)

For each iteration, musyn fits each entry in the D and G scaling matrices by a rational function whose order is automatically selected. By default, the maximum order is 5 for D scaling and 2 for G scaling. (G scaling is for dynamics in addition to dynamics needed to capture sign changes, so the final order of the G fit can be higher.) In general, the higher the order of these functions, the higher the order of the resulting controller.

To see whether you need to increase the maximum order, examine the musyn command-line display for a rough indication of fit quality. The Peak MU and DG Fit columns of the display give the best obtained robust performance before and after fitting, respectively. If the value for any given iteration increases drastically after fitting, you might obtain better results by increasing the maximum order.

Conversely, if the default maximum scaling order yields a good result, you can try lowering the maximum order to see if musyn returns a lower-order controller with similar performance.

Example: opts = musynOptions('FitOrder',[3 2]) creates an option set for musyn that reduces the maximum fit order to 3 for the D scaling and 2 for the G scaling.

Frequency grid used for μ analysis, specified as the comma-separated pair consisting of 'FrequencyGrid' and an empty vector or a vector of frequencies in radians per second. By default, musyn computes an appropriate frequency grid based on system dynamics and the frequency dependence of the D and G scaling data. This default generally yields better results than a custom frequency grid, which restricts the computation to the specified frequencies regardless of the actual frequency dependence of the scaling data. Therefore, specifying frequencies is not recommended unless you know the frequency range in which D and G vary.

Options for K Step with Unstructured Controller (hinfsyn Controller Design)

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Automatic plant scaling, specified as the comma-separated pair consisting of 'AutoScale' and one of the following:

  • 'on' — The underlying hinfsyn computation in the K step automatically scales the plant states, controls, and measurements to improve numerical accuracy. musyn always returns the controller in the original unscaled coordinates.

  • 'off' — hinfsyn does not change the plant scaling. Turning off scaling when you know your plant is well scaled can speed up the computation.

Example: opts = musynOptions('AutoScale','off') creates an option set for musyn that turns off automatic scaling for the underlying hinfsyn computation.

Automatic regularization of the plant, specified as the comma-separated pair consisting of 'Regularize' and one of the following:

  • 'on' — The underlying hinfsyn computation in the K step automatically regularizes the plant to enforce certain nonsingularity requirements (see hinfsyn). Regularization is a process of adding extra disturbances and errors to handle singular problems.

  • 'off' — hinfsyn does not regularize the plant. Turning off regularization can speed up the computation when you know your problem is far enough from singular.

Example: opts = musynOptions('Regularize','off') creates an option set for musyn that turns off regularization for the underlying hinfsyn computation.

Limit on controller gains, specified as the comma-separated pair consisting of 'LimitGain' and either 'on' or 'off'. For continuous-time plants, regularization of plant feedthrough matrices D12 or D21 (see hinfsyn) can result in controllers with large coefficients and fast dynamics. Use this option to automatically seek a controller with the same performance but lower gains and better conditioning.

Options for K Step with Structured Controller (hinfstruct Controller Design)

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Number of additional optimization starts with randomized values of tunable controller parameters, specified as the comma-separated pair consisting of 'RandomStart' and 0 or a positive integer.

By default, the underlying hinfstruct computation performs a single optimization run starting from the initial values of the tunable parameters. hinfstruct finds a local minimum of the gain minimization problem. To mitigate the risk of premature termination due to a local minimum that is not the best performing controller, you can perform multiple independent D-K iteration runs initialized from different values of controller parameters. Setting RandomStart = N > 0 runs N additional musyn optimizations starting from N randomly generated parameter values.

Randomization only affects the initialization of the overall D-K iteration run. It does not affect each call to hinfstruct within a D-K iteration run.

When all runs are complete, musyn uses the best design that results from the multiple runs.

Use with 'UseParallel' = true to distribute independent optimization runs among MATLAB® workers (requires Parallel Computing Toolbox™ software).

Example: opts = musynOptions('RandomStart',5) creates an option set for musyn that runs the underlying hinfstruct computation a total of six times, using randomized initial values for the tunable parameters.

Option to enable parallel computing, specified as the comma-separated pair consisting of 'UseParallel' and false or true.

When you use the RandomStart option to run multiple randomized optimization starts when tuning a structured controller, you can also use parallel computing to distribute the optimization runs among workers in a parallel pool. When you set this option to true, if there is an available parallel pool, then the software performs independent optimization runs concurrently among workers in that pool. If no parallel pool is available, one of the following occurs:

  • If you select Automatically create a parallel pool in your Parallel Computing Toolbox preferences (Parallel Computing Toolbox), then the software starts a parallel pool using the settings in those preferences.

  • If you do not select Automatically create a parallel pool in your preferences, then the software performs the optimization runs successively, without parallel processing.

Using parallel computing requires Parallel Computing Toolbox software.

Example: opts = musynOptions('RandomStart',8,'UseParallel',true) creates an option set for musyn that performs eight additional randomized optimization runs, and turns on parallel computing for the underlying hinfstruct computation.

Minimum decay rate for closed-loop poles, specified as the comma-separated pair consisting of 'MinDecay' and a positive scalar value. The poles of the closed-loop system are constrained to satisfy Re(p) < -MinDecay. Increase this value to improve the stability of closed-loop poles that do not affect the closed-loop gain due to pole-zero cancellations.

Specify MinDecay in units of 1/TimeUnit, relative to the TimeUnit property of the system you are tuning.

Maximum closed-loop natural frequency, specified as the comma-separated pair consisting of 'MaxFrequency' and Inf or a positive scalar value. Setting MaxFrequency constrains the closed-loop poles to satisfy |p| <  MaxFrequency. To let musyn choose the closed-loop poles without such constraint, set MaxFrequency = Inf. To prevent unwanted fast dynamics or high-gain control, set MaxFrequency to a finite value.

Specify MaxFrequency in units of 1/TimeUnit, relative to the TimeUnit property of the system you are tuning.

Output Arguments

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Options for the musyn computation, returned as a musyn options object. Use the object as an input argument to musyn. For example:

[K,CLperf,info] = musyn(P,nmeas,ncont,opts);

Version History

Introduced in R2019b

See Also

Topics