Control Design in Simulink

Specify time-domain and frequency-domain requirements, tune controller parameters such as PID gains

Simulink^® Design Optimization™ software provides several ways to specify design requirements. You can use the Check blocks to specify typical control design requirements such as reference tracking and satisfying signal bounds. You can then optimize the controller parameters in your model to meet these design requirements using the Response Optimizer app or at the command line.

Apps

Response Optimizer

Optimize model response to satisfy design requirements, test model robustness

Blocks

Check Against Reference	Check that model signal tracks reference signal during simulation
Check Custom Bounds	Check that model signal satisfies bounds during simulation
Check Step Response Characteristics	Check that model signal satisfies step response bounds during simulation

Functions

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Configure Cost Function

Create Simulation Scenario

`sdo.SimulationTest`	Simulation scenario description
`setup`	Configure simulation scenario and model for optimization and evaluation (Since R2024a)
`restore`	Restore simulation scenario and model to their previous state (Since R2024a)

Specify Time-Domain Requirements

`sdo.requirements.SignalBound`	Piecewise-linear amplitude bound
`sdo.requirements.SignalTracking`	Reference signal to track
`sdo.requirements.StepResponseEnvelope`	Step response bound on signal
`sdo.requirements.PhasePlaneEllipse`	Impose elliptic bound on phase plane trajectory of two signals
`sdo.requirements.PhasePlaneRegion`	Impose region bound on phase plane trajectory of two signals

Specify Variable Requirements

`sdo.requirements.FunctionMatching`	Impose function matching constraint on variable
`sdo.requirements.MonotonicVariable`	Impose monotonic constraint on variable
`sdo.requirements.RelationalConstraint`	Impose relational constraint on pair of variables
`sdo.requirements.SmoothnessConstraint`	Impose bounds on gradient magnitude of variable

Specify Frequency-Domain Requirements

`sdo.requirements.BodeMagnitude`	Bode magnitude bound
`sdo.requirements.ClosedLoopPeakGain`	Closed loop peak gain bound
`sdo.requirements.GainPhaseMargin`	Gain and phase margin bounds
`sdo.requirements.OpenLoopGainPhase`	Nichols response bound
`sdo.requirements.PZDampingRatio`	Damping ratio bound
`sdo.requirements.PZNaturalFrequency`	Natural frequency bound
`sdo.requirements.PZSettlingTime`	Settling time bound
`sdo.requirements.SingularValue`	Singular value bound

Configure Cost Function Optimization

`sdo.optimize`	Solve design optimization problem
`sdo.OptimizeOptions`	Optimization option set for `sdo.optimize` function
`sdo.getParameterFromModel`	Get design variables for optimization
`sdo.setValueInModel`	Set design variable value in model
`sdo.getValueFromModel`	Get design variable value from model
`sdo.getModelDependencies`	List of model file and path dependencies
`evalRequirement`	Evaluate design requirement

Check Blocks

`getbounds`	Get bounds specified in Check block
`sdo.setCheckBlockEnabled`	Enable or disable all check blocks in model

Topics

Optimization Basics

How the Optimization Algorithm Formulates Minimization Problems
When you optimize parameters of a Simulink model to meet design requirements, Simulink Design Optimization software automatically converts the requirements into a constrained optimization problem and then solves the problem using optimization techniques.
Design Optimization to Meet Step Response Requirements (GUI)
Optimize controller parameters to meet step response requirements using Response Optimizer.
Design Optimization to Track Reference Signal (GUI)
Optimize parameters without adding Signal Constraint blocks to the model.
Design Optimization to Meet Frequency-Domain Requirements (GUI)
This example shows how to tune model parameters to meet frequency-domain requirements using the Response Optimizer app.
Design Optimization to Meet Frequency-Domain Requirements (Code)
This example shows how to tune model parameters to meet frequency-domain requirements, using the sdo.optimize command.
Design Optimization Using Frequency-Domain Check Blocks (GUI)
Optimize model parameters to meet frequency-domain design requirements using the Response Optimizer.
Design Optimization to Meet Time-Domain and Frequency-Domain Requirements (GUI)
Interactively tune a controller to satisfy time-domain and frequency-domain design requirements using the Response Optimizer app.
Design Optimization to Meet Step Response Requirements (Code)
Optimize controller parameters at the command line.
Write a Cost Function
Write a cost function for parameter estimation, response optimization, or sensitivity analysis. The cost function evaluates your design requirements using design variable values.

Design Requirements

Supported Design Requirements
Time-domain and frequency-domain requirements.
Specify Time-Domain Design Requirements in the App
Specify time-domain requirements such as lower and upper amplitude bounds, step response bounds, reference signals, elliptical bounds, and custom bounds.
Specify Variable Requirements in the App
Specify monotonic, smoothness, and relational constraints on variables in your model.
Specify Frequency-Domain Design Requirements in the App
Specify frequency-domain requirements, such as gain and phase margin bounds, closed-loop peak response bounds, step-response bounds, and custom bounds.

Speed Up Optimization

Skip Model Simulation Based on Parameter Constraint Violation (GUI)
This example shows how to optimize a design and specify parameter-only constraints that prevent the model from being evaluated in an invalid solution space.
Speed Up Response Optimization Using Parallel Computing
Scenarios when you can speed up optimization using parallel computing, and how the speedup happens.
Use Parallel Computing for Response Optimization
Use parallel computing for response optimization in the app, or at the command line.
Use Fast Restart Mode During Response Optimization
This topic shows how to speed up response optimization using Simulink fast restart.
Use Accelerator Mode During Simulations
Simulink Design Optimization software supports Normal and Accelerator simulation modes.

Response Optimizer Tasks

Specify Design Variables for Optimization
Specify continuous and discrete variables to tune in the Response Optimizer app, including initial values and allowed ranges or values.
Specify Signals to Log
Specify signals to log in the Response Optimizer.
Create Linearization I/O Sets
Create linearization input/output sets in the Response Optimizer or Sensitivity Analyzer.
Compare Requirements and Design Variables Using Spider Plot
This example shows how to use a spider plot to compare requirement evaluations before and after optimizing the response.

Code Generation

Generate MATLAB Code for Design Optimization Problems (GUI)
This example shows how to automatically generate a MATLAB® function to solve a design optimization problem.

Troubleshooting

Optimization Does Not Make Progress

What to do if the optimization stalls or no changes are seen in parameters values.

Optimization Convergence

What to do if the optimization does not satisfy design requirements or takes a long time to converge near a solution, or if the system response becomes unstable.

Optimization Speed and Parallel Computing

What to do if no speedup is seen with parallel computing, if the results are different, or if the optimization stalls.

Undesirable Parameter Values

What to do if optimization gives undesirable parameter values or violates bounds on values.

Reverting to Initial Parameter Values

How to quit optimizing and revert to original values.

Featured Examples

Enforcing Time and Frequency Requirements on a Single-Loop Controller Design

Use Simulink® Design Optimization™ to tune a compensator in a Simulink model. You will add performance requirements to further refine and optimize an initial compensator design performed with Simulink Control Design™ (see Single Loop Feedback/Prefilter Compensator Design (Simulink Control Design)).

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Airframe Controller Tuning

Design two feedback loops in a cascaded control system to track reference signals. The design uses the body rate (q) as an inner feedback loop and the acceleration (az) as an outer feedback signal. This example is based on the Simulink® Control Design™ example Cascaded Multiloop Feedback Design (Simulink Control Design).

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DC Motor Controller Tuning

Design a PI control system to control the speed of a DC motor. It is based on the Control System Toolbox™ DC Motor Control example.

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Hydraulic Piston Regulator Tuning

Tune a lead-lag regulator for a simplified hydraulic piston. The piston model is given by:

Open Live Script