# systune

Tune control system parameters in Simulink using slTuner interface

## Description

systune tunes fixed-structure control systems subject to both soft and hard design goals. systune can tune multiple fixed-order, fixed-structure control elements distributed over one or more feedback loops. For an overview of the tuning workflow, see Automated Tuning Workflow.

This command tunes control systems modeled in Simulink®. For tuning control systems represented in MATLAB®, use systune for genss models.

example

[st,fSoft] = systune(st0,SoftGoals) tunes the free parameters of the control system in Simulink. The Simulink model, tuned blocks, and analysis points of interest are specified by the slTuner interface, st0. systune tunes the control system parameters to best meet the performance goals, SoftGoals. The command returns a tuned version of st0 as st. The best achieved soft constraint values are returned as fSoft.

If the st0 contains real parameter uncertainty, systune automatically performs robust tuning to optimize the constraint values for worst-case parameter values. systune also performs robust tuning against a set of plant models obtained at different operating points or parameter values. See Input Arguments.

Tuning is performed at the sample time specified by the Ts property of st0.

[st,fSoft,gHard] = systune(st0,SoftGoals,HardGoals) tunes the control system to best meet the soft goals, subject to satisfying the hard goals. It returns the best achieved values, fSoft and gHard, for the soft and hard goals. A goal is met when its achieved value is less than 1.

[st,fSoft,gHard] = systune(___,opt) specifies options for the optimization for any of the input argument combinations in previous syntaxes.

[st,fSoft,gHard,info] = systune(___) also returns detailed information about each optimization run for any of the input argument combinations in previous syntaxes.

## Examples

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Tune the control system in the rct_airframe2 model to soft goals for tracking, roll off, stability margin, and disturbance rejection.

mdl = 'rct_airframe2';
open_system(mdl);

Create and configure an slTuner interface to the model.

st0 = slTuner(mdl,'MIMO Controller');

st0 is an slTuner interface to the rct_aircraft2 model with the MIMO Controller block specified as the tunable portion of the control system.

The model already has linearization input points on the signals az ref, delta fin, az, q, and e. These signals are therefore available as analysis points for tuning goals and linearization.

Specify the tracking requirement, roll-off requirement, stability margins, and disturbance rejection requirement.

req1 = TuningGoal.Tracking('az ref','az',1);
req2 = TuningGoal.Gain('delta fin','delta fin',tf(25,[1 0]));
req3 = TuningGoal.Margins('delta fin',7,45);
max_gain = frd([2 200 200],[0.02 2 200]);
req4 = TuningGoal.Gain('delta fin','az',max_gain);

req1 constrains az to track az ref. The next requirement, req2, imposes a roll-off requirement by specifying a gain profile for the open-loop, point-to-point transfer function measured at delta fin. The next requirement, req3, imposes open-loop gain and phase margins on that same point-to-point transfer function. Finally, req4 rejects disturbances to az injected at delta fin, by specifying a maximum gain profile between those two points.

Tune the model using these tuning goals.

opt = systuneOptions('RandomStart',3);
rng(0);
[st,fSoft,~,info] = systune(st0,[req1,req2,req3,req4],opt);
Final: Soft = 1.13, Hard = -Inf, Iterations = 95
Final: Soft = 1.13, Hard = -Inf, Iterations = 78
Final: Soft = 1.13, Hard = -Inf, Iterations = 72
Final: Soft = 40, Hard = -Inf, Iterations = 87

st is a tuned version of st0.

The RandomStart option specifies that systune must perform three independent optimization runs that use different (random) initial values of the tunable parameters. These three runs are in addition to the default optimization run that uses the current value of the tunable parameters as the initial value. The call to rng seeds the random number generator to produce a repeatable sequence of numbers.

systune displays the final result for each run. The displayed value, Soft, is the maximum of the values achieved for each of the four performance goals. The software chooses the best run overall, which is the run yielding the lowest value of Soft. The last run fails to achieve closed-loop stability, which corresponds to Soft = Inf.

Examine the best achieved values of the soft constraints.

fSoft
fSoft =

1.1327    1.1327    0.5140    1.1327

Only req3, the stability margin requirement, is met for all frequencies. The other values are close to, but exceed, 1, indicating violations of the goals for at least some frequencies.

Use viewGoal to visualize the tuned control system performance against the goals and to determine whether the violations are acceptable. To evaluate specific open-loop or closed-loop transfer functions for the tuned parameter values, you can use linearization commands such as getIOTransfer and getLoopTransfer. After validating the tuned parameter values, if you want to apply these values to the Simulink® model, you can use writeBlockValue.

## Input Arguments

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Interface for tuning control systems modeled in Simulink, specified as an slTuner interface.

If you specify parameter variation or linearization at multiple operating points when you create st0, then systune performs robust tuning against all the plant models. If you specify an uncertain (uss (Robust Control Toolbox)) model as a block substitution when you create st0, then systune performs robust tuning, optimizing the parameters against the worst-case parameter values. For more information about robust tuning approaches, see Robust Tuning Approaches (Robust Control Toolbox). (Using uncertain models requires a Robust Control Toolbox™ license.)

Soft goals (objectives) for tuning the control system described by st0, specified as a vector of TuningGoal objects. For a complete list, see Tuning Goals.

systune tunes the tunable parameters of the control system to minimize the maximum value of the soft tuning goals, subject to satisfying the hard tuning goals (if any).

Hard goals (constraints) for tuning the control system described by st0, specified as a vector of TuningGoal objects. For a complete list, see Tuning Goals.

A hard goal is satisfied when its value is less than 1. systune tunes the tunable parameters of the control system to minimize the maximum value of the soft tuning goals, subject to satisfying all the hard tuning goals.

Tuning algorithm options, specified as an options set created using systuneOptions.

Available options include:

• Number of additional optimizations to run starting from random initial values of the free parameters

• Tolerance for terminating the optimization

• Flag for using parallel processing

See the systuneOptions reference page for more details about all available options.

## Output Arguments

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Tuned interface, returned as an slTuner interface.

Best achieved values of soft goals, returned as a vector.

Each tuning goal evaluates to a scalar value, and systune minimizes the maximum value of the soft goals, subject to satisfying all the hard goals.

fSoft contains the value of each soft goal for the best overall run. The best overall run is the run that achieved the smallest value for max(fSoft), subject to max(gHard)<1.

Achieved values of hard goals, returned as a vector.

gHard contains the value of each hard goal for the best overall run (the run that achieved the smallest value for max(fSoft), subject to max(gHard)<1. All entries of gHard are less than 1 when all hard goals are satisfied. Entries greater than 1 indicate that systune could not satisfy one or more design constraints.

Detailed information about each optimization run, returned as a data structure. The fields of info are summarized in the following table.

FieldValue
Run

Run number, returned as a scalar. If you use the RandomStart option of systuneOptions to perform multiple optimization runs, info is a structure array, and info.Run is the index.

Iterations

Total number of iterations performed during the run, returned as a scalar. If you use RandomStart, info.Iterations(j) is the number of iterations performed in the jth run before termination.

f

Best overall soft constraint value, returned as a scalar. systune converts the soft tuning goals to a function of the free parameters of the control system. The command then tunes the parameters to minimize that function subject to the hard goals. (See Algorithms.) info.f is the maximum soft goal value at the final iteration. This value is meaningful only when the hard goals are satisfied. If the value is less than 1, then the soft goals are also attained.

g

Best overall hard constraint value, returned as a scalar. systune converts the hard tuning goals to a function of the free parameters of the control system. The command then tunes the parameters to drive those values below 1. (See Algorithms.) info.g is the largest hard goal value at the final iteration. If this value is less than 1, then the hard goals are satisfied.

x

Tuned parameter values, returned as a vector. This vector contains the values of the tunable parameters at the end of the run. info.x can also include the values of additional variables such as loop scalings, if systune uses them (see info.LoopScaling).

MinDecay

Minimum decay rate of tuned system dynamics, returned as a two-element row vector.

info.MinDecay(1) is the minimum decay rate of the closed-loop poles.

info.MinDecay(2) is the minimum decay rate of the dynamics of tuned blocks with stability constraints. For more information about stabilized dynamics and decay rates, see the MinDecay option of systuneOptions.

fSoft

Individual soft constraint values, returned as a vector. systune converts each soft tuning goal to a normalized value that is a function of the free parameters of the control system. The command then tunes the parameters to minimize that value subject to the hard goals. (See Algorithms.) info.fSoft contains the individual values of the soft goals at the end of each run. These values appear in fSoft in the same order in which you specify goals in the SoftReqs input argument to systune.

gHard

Individual hard constraint values, returned as a vector. systune converts each hard tuning goal to a normalized value that is a function of the free parameters of the control system. The command then tunes the parameters to minimize those values. A hard goal is satisfied if its value is less than 1. (See Algorithms.) info.gHard contains the individual values of the hard goals at the end of each run. These values appear in gHard in the same order in which you specify goals in the HardReqs input argument to systune.

Blocks

Tuned values of tunable blocks and parameters in the tuned control system, returned as a structure whose fields are the names of tunable elements and whose values are the corresponding tuned values.

When you perform multiple runs by setting the RandomStart option to a positive value, you can use this field to examine control system performance with the results from other runs. For instance, use the following code to apply the tuned values from the jth run.

stj = setBlockValue(st0,info(j).Blocks)

LoopScaling

Optimal diagonal scaling for evaluating MIMO tuning requirements, returned as a state-space model.

When applied to multiloop control systems, tuning goals that involve an open-loop response can be sensitive to the scaling of the loop transfer functions to which they apply. This sensitivity can lead to poor optimization results. systune automatically corrects scaling issues and returns the optimal diagonal scaling matrix D as a state-space model in info.LoopScaling.

The loop channels associated with each diagonal entry of D are listed in info.LoopScaling.InputName. The scaled loop transfer is D\L*D, where L is the open-loop transfer measured at the locations info.LoopScaling.InputName.

Tuning goals affected by such loop scaling include:

• TuningGoal.LoopShape

• TuningGoal.MinLoopGain and TuningGoal.MaxLoopGain

• TuningGoal.Sensitivity

• TuningGoal.Rejection

• TuningGoal.Margins

info also contains the following fields, whose entries are meaningful when you use systune for robust tuning of control systems with uncertainty.

FieldValue
wcPert

Worst combinations of uncertain parameters, returned as a structure array. Each structure contains one set of uncertain parameter values. The perturbations with the worst performance are listed first.

wcf

Worst soft-goal value, returned as a scalar. This value is the largest soft goal value (f) over the uncertainty range when using the tuned controller.

wcg

Worst hard-goal value, returned as a scalar. This value is the largest hard goal value (g) over the uncertainty range when using the tuned controller.

wcDecay

Smallest closed-loop decay rate over the uncertainty range when using the tuned controller, returned as a scalar. A positive value indicates robust stability. For more information about stabilized dynamics and decay rates, see the MinDecay option of systuneOptions.

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### Tuned Blocks

Tuned blocks, used by the slTuner interface, identify blocks in a Simulink model whose parameters are to be tuned to satisfy tuning goals. You can tune most Simulink blocks that represent linear elements such as gains, transfer functions, or state-space models. (For the complete list of blocks that support tuning, see How Tuned Simulink Blocks Are Parameterized). You can also tune more complex blocks such as SubSystem or S-Function blocks by specifying an equivalent tunable linear model.

Use tuning commands such as systune to tune the parameters of tuned blocks.

You must specify tuned blocks (for example, C1 and C2) when you create an slTuner interface.

You can modify the list of tuned blocks using addBlock and removeBlock.

To interact with the tuned blocks use:

### Analysis Points

Analysis points, used by the slLinearizer and slTuner interfaces, identify locations within a model that are relevant for linear analysis and control system tuning. You use analysis points as inputs to the linearization commands, such as getIOTransfer, getLoopTransfer, getSensitivity, and getCompSensitivity. As inputs to the linearization commands, analysis points can specify any open-loop or closed-loop transfer function in a model. You can also use analysis points to specify design requirements when tuning control systems using commands such as systune.

Location refers to a specific block output port within a model or to a bus element in such an output port. For convenience, you can use the name of the signal that originates from this port to refer to an analysis point.

You can add analysis points to an slLinearizer or slTuner interface, s, when you create the interface. For example:

Alternatively, you can use the addPoint command.

To view all the analysis points of s, type s at the command prompt to display the interface contents. For each analysis point of s, the display includes the block name and port number and the name of the signal that originates at this point. You can also programmatically obtain a list of all the analysis points using getPoints.

For more information about how you can use analysis points, see Mark Signals of Interest for Control System Analysis and Design and Mark Signals of Interest for Batch Linearization.

## Algorithms

x is the vector of tunable parameters in the control system to tune. systune converts each soft and hard tuning requirement SoftReqs(i) and HardReqs(j) into normalized values fi(x) and gj(x), respectively. systune then solves the constrained minimization problem:

Minimize $\underset{i}{\mathrm{max}}{f}_{i}\left(x\right)$ subject to $\underset{j}{\mathrm{max}}{g}_{j}\left(x\right)<1$, for ${x}_{\mathrm{min}}.

xmin and xmax are the minimum and maximum values of the free parameters of the control system.

When you use both soft and hard tuning goals, the software approaches this optimization problem by solving a sequence of unconstrained subproblems of the form:

$\underset{x}{\mathrm{min}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\mathrm{max}\left(\alpha f\left(x\right),g\left(x\right)\right).$

The software adjusts the multiplier α so that the solution of the subproblems converges to the solution of the original constrained optimization problem.

systune returns the slTuner interface with parameters tuned to the values that best solve the minimization problem. systune also returns the best achieved values of fi(x) and gj(x), as fSoft and gHard respectively.

For information about the functions fi(x) and gj(x) for each type of constraint, see the reference pages for each TuningGoal requirement object.

systune uses the nonsmooth optimization algorithms described in [1],[2],[3],[4]

systune computes the H norm using the algorithm of [5] and structure-preserving eigensolvers from the SLICOT library. For information about the SLICOT library, see http://slicot.org.

## Alternative Functionality

Tune interactively using Control System Tuner.

## References

[1] P. Apkarian and D. Noll, "Nonsmooth H-infinity Synthesis," IEEE Transactions on Automatic Control, Vol. 51, Number 1, 2006, pp. 71–86.

[2] Apkarian, P. and D. Noll, "Nonsmooth Optimization for Multiband Frequency-Domain Control Design," Automatica, 43 (2007), pp. 724–731.

[3] Apkarian, P., P. Gahinet, and C. Buhr, "Multi-model, multi-objective tuning of fixed-structure controllers," Proceedings ECC (2014), pp. 856–861.

[4] Apkarian, P., M.-N. Dao, and D. Noll, "Parametric Robust Structured Control Design," IEEE Transactions on Automatic Control, 2015.

[5] Bruinsma, N.A., and M. Steinbuch. "A Fast Algorithm to Compute the H Norm of a Transfer Function Matrix." Systems & Control Letters, 14, no.4 (April 1990): 287–93.

## Extended Capabilities

| | | | | | | | (Robust Control Toolbox)

### Topics

Introduced in R2014a