looptune

Tune MIMO feedback loops in Simulink using slTuner interface

Syntax

[st,gam,info] = looptune(st0,controls,measurements,wc)

[st,gam,info] = looptune(st0,controls,measurements,wc,req1,...,reqN)

[st,gam,info] = looptune(___,opt)

Description

[st,gam,info] = looptune(st0,controls,measurements,wc) tunes the free parameters of the control system of the Simulink^® model associated with the slTuner interface, st0, to achieve the following goals:

• Bandwidth — Gain crossover for each loop falls in the frequency interval wc

• Performance — Integral action at frequencies below wc

• Robustness — Adequate stability margins and gain roll-off at frequencies above wc

controls and measurements specify the controller output signals and measurement signals that are subject to the goals, respectively. st is the updated slTuner interface, gam indicates the measure of success in satisfying the goals, and info gives details regarding the optimization run.

Tuning is performed at the sample time specified by the Ts property of st0. For tuning algorithm details, see Algorithms.

[st,gam,info] = looptune(st0,controls,measurements,wc,req1,...,reqN) tunes the feedback loop to meet additional goals specified in one or more tuning goal objects, req. Omit wc to drop the default loop shaping goal associated with wc. Note that the stability margin goals remain in force.

[st,gam,info] = looptune(___,opt) specifies further options, including target gain and phase margins, number of runs, and computation options for the tuning algorithm. Use looptuneOptions to create opt.

If you specify multiple runs using the RandomStarts property of opt, looptune performs only as many runs required to achieve the target objective value of 1. Note that all tuning goals should be normalized so that a maximum value of 1 means that all design goals are met.

Examples

Tune Controller to Achieve Specified Bandwidth

Tune the PID Controller in the rct_engine_speed model to achieve the specified bandwidth.

Open the Simulink model.

mdl = 'rct_engine_speed';
open_system(mdl);

Create an slTuner interface for the model.

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

Add the PID Controller output, u, as an analysis point to st0.

addPoint(st0,'u');

Based on first-order characteristics, the crossover frequency should exceed 1 rad/s for the closed-loop response to settle in less than 5 seconds. So, tune the PID loop using 1 rad/s as the target 0 dB crossover frequency.

wc = 1;
st = looptune(st0,'u','Speed',wc);

Final: Peak gain = 0.979, Iterations = 4
Achieved target gain value TargetGain=1.

In the call to looptune, 'u' specifies the control signal, and 'Speed' specifies the measured signal.

Compare the tuned and initial response.

stepplot(getIOTransfer(st0,'Ref','Speed'),getIOTransfer(st,'Ref','Speed'));
legend('Initial','Speed');

View the tuned block value.

showTunable(st)

Block 1: rct_engine_speed/PID Controller =
 
             1            s    
  Kp + Ki * --- + Kd * --------
             s          Tf*s+1 

  with Kp = 0.000619, Ki = 0.00303, Kd = 0.000168, Tf = 0.01
 
Name: PID_Controller
Continuous-time PIDF controller in parallel form.

To write the tuned values back to the Simulink model, use writeBlockValue.

Input Arguments

st0 — Interface for tuning control systems modeled in Simulink

slTuner interface

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

controls — Controller output

character vector | cell array of character vectors

Controller output name, specified as one of the following:

• Character vector — Name of an analysis point of st0.

  You can specify the full name or any portion of the name that uniquely identifies the analysis point among the other analysis points of st0.

  For example, 'u'.

• Cell array of character vectors — Multiple analysis point names.

  For example, {'u','y'}.

measurements — Measurement

character vector | cell array of character vectors

Measurement signal name, specified as one of the following:

• Character vector — Name of an analysis point of st0.

  You can specify the full name or any portion of the name that uniquely identifies the analysis point among the other analysis points of st0.

  For example, 'u'.

• Cell array of character vector — Multiple analysis point names.

  For example, {'u','y'}.

wc — Target crossover region

[wcmin,wcmax] | positive scalar

Target crossover region, specified as one of the following:

• [wcmin,wcmax] — looptune attempts to tune all loops in the control system so that the open-loop gain crosses 0 dB within the target crossover region.

• Positive scalar — Specifies the target crossover region as [wc/10^0.1,wc*10^0.1] or wc +/- 0.1 decades.

Specify wc in the working time units, that is, the time units of the model.

req1,...,reqN — Design goals

TuningGoal objects

Design goals, specified as one or more TuningGoal objects.

For a complete list of the design goals you can specify, see Tuning Goals.

opt — Tuning algorithm options

options set created using looptuneOptions

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

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

• Specification of target gain and phase margin

Output Arguments

st — Tuned interface

slTuner interface

Tuned interface, returned as an slTuner interface.

gam — Parameter indicating degree of success at meeting all tuning constraints

scalar

Parameter indicating degree of success at meeting all tuning constraints, returned as a scalar.

A value of gam <= 1 indicates that all goals are satisfied. A value of gam >> 1 indicates failure to meet at least one requirement. Use loopview to visualize the tuned result and identify the unsatisfied requirement.

For best results, use the RandomStart option in looptuneOptions to obtain several minimization runs. Setting RandomStart to an integer N > 0 causes looptune to run the optimization N additional times, beginning from parameter values it chooses randomly. You can examine gam for each run to help identify an optimization result that meets your design goals.

info — Detailed information about each optimization run

structure

Detailed information about each optimization run, returned as a structure with the following fields:

Di,Do — Optimal input and output scalings

state-space models

Optimal input and output scalings, return as state-space models.

The scaled plant is given by Do\G*Di.

Specs — Design goals used for tuning

vector of TuningGoal requirement objects

Design goals used for tuning, returned as a vector of TuningGoal requirement objects.

Runs — Detailed information about each optimization run

structure

Detailed information about each optimization run, returned as a structure. For details, see Algorithms.

The contents of Runs are the info output of the call to systune performed by looptune. For information about the fields of Runs, see the info output argument description on the systune reference page.

More About

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.

st = slTuner('scdcascade',{'C1','C2'})

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

To interact with the tuned blocks use:

• getBlockParam, getBlockValue, and getTunedValue to access the tuned block parameterizations and their current values.

• setBlockParam, setBlockValue, and setTunedValue to modify the tuned block parameterizations and their values.

• writeBlockValue to update the blocks in a Simulink model with the current values of the tuned block parameterizations.

Algorithms

looptune automatically converts target bandwidth, performance goals, and additional design goals into weighting functions that express the goals as an H_∞ optimization problem. looptune then uses systune to optimize tunable parameters to minimize the H_∞ norm.

For information about the optimization algorithms, see [1].

looptune computes the H_∞ norm using the algorithm of [2] and structure-preserving eigensolvers from the SLICOT library. For more information about the SLICOT library, see http://slicot.org.

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] 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

Automatic Parallel Support

Accelerate code by automatically running computation in parallel using Parallel Computing Toolbox™.

To run in parallel, set 'UseParallel' to true using looptuneOptions.