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Control System Toolbox Functions

Alphabetical List By Category

Dynamic System Models

Linear System Representation

Basic Models

tfCreate transfer function model, convert to transfer function model
zpkCreate zero-pole-gain model; convert to zero-pole-gain model
ssCreate state-space model, convert to state-space model
frdCreate frequency-response data model, convert to frequency-response data model
filtSpecify discrete transfer functions in DSP format
dssCreate descriptor state-space models
pidCreate PID controller in parallel form, convert to parallel-form PID controller
pidstd Create a PID controller in standard form, convert to standard-form PID controller
pid2Create 2-DOF PID controller in parallel form, convert to parallel-form 2-DOF PID controller
pidstd2 Create 2-DOF PID controller in standard form, convert to standard-form 2-DOF PID controller
rssGenerate random continuous test model
drssGenerate random discrete test model

Tunable Models

tunableGainTunable static gain block
tunablePIDTunable PID controller
tunablePID2Tunable two-degree-of-freedom PID controller
tunableSSTunable fixed-order state-space model
tunableTFTunable transfer function with fixed number of poles and zeros
realpReal tunable parameter
AnalysisPointPoints of interest for linear analysis
genssGeneralized state-space model
genfrdGeneralized frequency response data (FRD) model
genmatGeneralized matrix with tunable parameters
getLoopTransferOpen-loop transfer function of control system
getIOTransferClosed-loop transfer function from generalized model of control system
getSensitivitySensitivity function from generalized model of control system
getCompSensitivityComplementary sensitivity function from generalized model of control system
getPointsGet list of analysis points in generalized model of control system
replaceBlockReplace or update Control Design Blocks in Generalized LTI model
sampleBlockSample Control Design blocks in generalized model
rsampleBlockRandomly sample Control Design blocks in generalized model
getValueCurrent value of Generalized Model
setValueModify current value of Control Design Block
getBlockValueCurrent value of Control Design Block in Generalized Model
setBlockValueModify value of Control Design Block in Generalized Model
showBlockValueDisplay current value of Control Design Blocks in Generalized Model
showTunableDisplay current value of tunable Control Design Blocks in Generalized Model
nblocksNumber of blocks in Generalized matrix or Generalized LTI model
getLFTModelDecompose generalized LTI model

Models with Time Delays

padePadé approximation of model with time delays
absorbDelayReplace time delays by poles at z = 0 or phase shift
thiranGenerate fractional delay filter based on Thiran approximation
hasdelayTrue for linear model with time delays
hasInternalDelayDetermine if model has internal delays
totaldelayTotal combined I/O delays for LTI model
delayssCreate state-space models with delayed inputs, outputs, and states
setDelayModelConstruct state-space model with internal delays
getDelayModelState-space representation of internal delays

Model Attributes

getAccess model property values
setSet or modify model properties
tfdataAccess transfer function data
zpkdataAccess zero-pole-gain data
ssdataAccess state-space model data
frdataAccess data for frequency response data (FRD) object
piddataAccess coefficients of parallel-form PID controller
pidstddataAccess coefficients of standard-form PID controller
piddata2Access coefficients of parallel-form 2-DOF PID controller
pidstddata2Access coefficients of standard-form 2-DOF PID controller
dssdataExtract descriptor state-space data
chgFreqUnitChange frequency units of frequency-response data model
chgTimeUnitChange time units of dynamic system
isctDetermine if dynamic system model is in continuous time
isdtDetermine if dynamic system model is in discrete time
isemptyDetermine whether dynamic system model is empty
isfiniteDetermine if model has finite coefficients
isParametricDetermine if model has tunable parameters
isproperDetermine if dynamic system model is proper
isrealDetermine if model has real-valued coefficients
issisoDetermine if dynamic system model is single-input/single-output (SISO)
isstableDetermine whether system is stable
isstaticDetermine if model is static or dynamic
orderQuery model order
ndimsQuery number of dimensions of dynamic system model or model array
sizeQuery output/input/array dimensions of input–output model and number of frequencies of FRD model

Model Arrays

stackBuild model array by stacking models or model arrays along array dimensions
nmodelsNumber of models in model array
permuteRearrange array dimensions in model arrays
reshapeChange shape of model array
repsysReplicate and tile models
voidModelMark missing or irrelevant models in model array
sampleBlockSample Control Design blocks in generalized model
rsampleBlockRandomly sample Control Design blocks in generalized model

Model Interconnection

feedbackFeedback connection of two models
connectBlock diagram interconnections of dynamic systems
sumblkSumming junction for name-based interconnections
seriesSeries connection of two models
parallelParallel connection of two models
appendGroup models by appending their inputs and outputs
blkdiagBlock-diagonal concatenation of models
imp2expConvert implicit linear relationship to explicit input-output relation
invInvert models
lftGeneralized feedback interconnection of two models (Redheffer star product)
connectOptionsOptions for the connect command

Model Transformation

Model Type Conversion

tfCreate transfer function model, convert to transfer function model
zpkCreate zero-pole-gain model; convert to zero-pole-gain model
ssCreate state-space model, convert to state-space model
frdCreate frequency-response data model, convert to frequency-response data model
pidCreate PID controller in parallel form, convert to parallel-form PID controller
pidstd Create a PID controller in standard form, convert to standard-form PID controller
pid2Create 2-DOF PID controller in parallel form, convert to parallel-form 2-DOF PID controller
pidstd2 Create 2-DOF PID controller in standard form, convert to standard-form 2-DOF PID controller
make1DOFConvert 2-DOF PID controller to 1-DOF controller
make2DOFConvert 1-DOF PID controller to 2-DOF controller
getComponentsExtract SISO control components from a 2-DOF PID controller

Continuous-Discrete Conversion

c2dConvert model from continuous to discrete time
d2cConvert model from discrete to continuous time
d2dResample discrete-time model
upsampleUpsample discrete-time models
c2dOptionsCreate option set for continuous- to discrete-time conversions
d2cOptionsCreate option set for discrete- to continuous-time conversions
d2dOptionsCreate option set for discrete-time resampling

State-Coordinate Transformation

balrealGramian-based input/output balancing of state-space realizations
canonState-space canonical realization
prescaleOptimal scaling of state-space models
ss2ssState coordinate transformation for state-space model
xperm Reorder states in state-space models

Modal Decomposition

modsepRegion-based modal decomposition
stabsepStable-unstable decomposition
stabsepOptionsOptions for stable-unstable decomposition
freqsepSlow-fast decomposition
freqsepOptionsOptions for slow-fast decomposition
spectralfactSpectral factorization of linear systems

Model Reduction

balredModel order reduction
balredOptionsCreate option set for model order reduction
balrealGramian-based input/output balancing of state-space realizations
minrealMinimal realization or pole-zero cancelation
sminrealStructural pole/zero cancellations
modredEliminate states from state-space models
freqsepSlow-fast decomposition
freqsepOptionsOptions for slow-fast decomposition
hsvdHankel singular values of dynamic system
hsvplotPlot Hankel singular values and return plot handle
hsvdOptionsCreate option set for computing Hankel singular values and input/output balancing

Linear Analysis

Time and Frequency Domain Analysis

stepStep response plot of dynamic system; step response data
stepinfoRise time, settling time, and other step-response characteristics
impulseImpulse response plot of dynamic system; impulse response data
initialInitial condition response of state-space model
lsimSimulate time response of dynamic system to arbitrary inputs
lsiminfoCompute linear response characteristics
gensigGenerate test input signals for lsim
covarOutput and state covariance of system driven by white noise
stepDataOptionsOptions set for step
bodeBode plot of frequency response, or magnitude and phase data
bodemagBode magnitude response of LTI models
nyquistNyquist plot of frequency response
nicholsNichols chart of frequency response
ngridSuperimpose Nichols chart on Nichols plot
sigmaSingular values plot of dynamic system
freqrespFrequency response over grid
evalfrEvaluate frequency response at given frequency
dcgainLow-frequency (DC) gain of LTI system
bandwidthFrequency response bandwidth
getPeakGainPeak gain of dynamic system frequency response
getGainCrossoverCrossover frequencies for specified gain
fnormPointwise peak gain of FRD model
normNorm of linear model
db2magConvert decibels (dB) to magnitude
mag2dbConvert magnitude to decibels (dB)

Stability Analysis

poleCompute poles of dynamic system
zeroZeros and gain of SISO dynamic system
dampNatural frequency and damping ratio
dsortSort discrete-time poles by magnitude
esortSort continuous-time poles by real part
tzeroInvariant zeros of linear system
pzplotPole-zero map of dynamic system model with plot customization options
iopzplotPlot pole-zero map for I/O pairs and return plot handle
allmarginGain margin, phase margin, delay margin and crossover frequencies
marginGain margin, phase margin, and crossover frequencies

Sensitivity Analysis

sampleBlockSample Control Design blocks in generalized model
rsampleBlockRandomly sample Control Design blocks in generalized model

Passivity and Sector Bounds

isPassiveCheck passivity of linear systems
getPassiveIndexCompute passivity index of linear system
passiveplotCompute or plot passivity index as function of frequency
getSectorIndexCompute conic-sector index of linear system
getSectorCrossoverCrossover frequencies for sector bound
sectorplotCompute or plot sector index as function of frequency

Plot Customization

impulseplotPlot impulse response and return plot handle
initialplotPlot initial condition response and return plot handle
lsimplotSimulate response of dynamic system to arbitrary inputs and return plot handle
stepplotPlot step response and return plot handle
bodeplotPlot Bode frequency response with additional plot customization options
nicholsplotPlot Nichols frequency responses and return plot handle
nyquistplotNyquist plot with additional plot customization options
sigmaplotPlot singular values of frequency response and return plot handle
bodeoptionsCreate list of Bode plot options
hsvoptionsPlot options for hsvplot
nicholsoptionsCreate list of Nichols plot options
nyquistoptionsList of Nyquist plot options
pzoptionsCreate list of pole/zero plot options
sigmaoptionsCreate list of singular-value plot options
timeoptionsCreate list of time plot options
setoptionsSet plot options for response plot
getoptionsReturn @PlotOptions handle or plot options property
ctrlprefSet Control System Toolbox preferences
updateSystemUpdate dynamic system data in a response plot

Control System Design and Tuning

PID Controller Tuning

pidTunerOpen PID Tuner for PID tuning
pidtunePID tuning algorithm for linear plant model
pidtuneOptionsDefine options for pidtune command

Classical Control Design

rlocus Root locus plot of dynamic system
rlocusplotPlot root locus and return plot handle
sisoinitConfigure Control System Designer at startup

State-Space Control Design and Estimation

State-Space Control Design

lqrLinear-Quadratic Regulator (LQR) design
lqryForm linear-quadratic (LQ) state-feedback regulator with output weighting
lqiLinear-Quadratic-Integral control
dlqrLinear-quadratic (LQ) state-feedback regulator for discrete-time state-space system
lqrdDesign discrete linear-quadratic (LQ) regulator for continuous plant
lqgLinear-Quadratic-Gaussian (LQG) design
lqgregForm linear-quadratic-Gaussian (LQG) regulator
lqgtrackForm Linear-Quadratic-Gaussian (LQG) servo controller
augstateAppend state vector to output vector
normNorm of linear model
estimForm state estimator given estimator gain
placePole placement design
regForm regulator given state-feedback and estimator gains

State Estimation

kalmanKalman filter design, Kalman estimator
kalmdDesign discrete Kalman estimator for continuous plant
estimForm state estimator given estimator gain
extendedKalmanFilterCreate extended Kalman filter object for online state estimation
unscentedKalmanFilterCreate unscented Kalman filter object for online state estimation
particleFilterParticle filter object for online state estimation
correctCorrect state and state estimation error covariance using extended or unscented Kalman filter, or particle filter and measurements
predictPredict state and state estimation error covariance at next time step using extended or unscented Kalman filter, or particle filter
initializeInitialize the state of the particle filter
cloneCopy online state estimation object

Multiloop, Multiobjective Tuning

Programmatic Tuning

Setup for Tuning Simulink Models
slTunerInterface for control system tuning of Simulink models
slTunerOptionsSet slTuner interface options
addBlockAdd block to list of tuned blocks for slTuner interface
addOpeningAdd signal to list of openings for slLinearizer or slTuner interface
addPointAdd signal to list of analysis points for slLinearizer or slTuner interface
refreshResynchronize slLinearizer or slTuner interface with current model state
removeAllOpeningsRemove all openings from list of permanent openings in slLinearizer or slTuner interface
removeAllPointsRemove all points from list of analysis points in slLinearizer or slTuner interface
removeBlockRemove block from list of tuned blocks in slTuner interface
removeOpeningRemove opening from list of permanent loop openings in slLinearizer or slTuner interface
removePointRemove point from list of analysis points in slLinearizer or slTuner interface
setBlockParamSet parameterization of tuned block in slTuner interface
setBlockRateConversionSet rate conversion settings for tuned block in slTuner interface
setBlockValueSet value of tuned block parameterization in slTuner interface
writeBlockValueUpdate block values in Simulink model
writeLookupTableDataUpdate portion of tuned lookup table
getBlockParamGet parameterization of tuned block in slTuner interface
getBlockRateConversionGet rate conversion settings for tuned block in slTuner interface
getBlockValueGet current value of tuned block parameterization in slTuner interface
getOpeningsGet list of openings for slLinearizer or slTuner interface
getPointsGet list of analysis points for slLinearizer or slTuner interface
showTunableShow value of parameterizations of tunable blocks of slTuner interface
Setup for Tuning MATLAB Models
tfCreate transfer function model, convert to transfer function model
zpkCreate zero-pole-gain model; convert to zero-pole-gain model
ssCreate state-space model, convert to state-space model
tunableGainTunable static gain block
tunableTFTunable transfer function with fixed number of poles and zeros
tunablePIDTunable PID controller
tunablePID2Tunable two-degree-of-freedom PID controller
tunableSSTunable fixed-order state-space model
realpReal tunable parameter
AnalysisPointPoints of interest for linear analysis
connectBlock diagram interconnections of dynamic systems
feedbackFeedback connection of two models
Tuning Goals
TuningGoal.StepTrackingStep response requirement for control system tuning
TuningGoal.StepRejectionStep disturbance rejection requirement for control system tuning
TuningGoal.TransientTransient matching requirement for control system tuning
TuningGoal.LQGLinear-Quadratic-Gaussian (LQG) goal for control system tuning
TuningGoal.Gain Gain constraint for control system tuning
TuningGoal.VarianceNoise amplification constraint for control system tuning
TuningGoal.Tracking Tracking requirement for control system tuning
TuningGoal.OvershootOvershoot constraint for control system tuning
TuningGoal.Rejection Disturbance rejection requirement for control system tuning
TuningGoal.SensitivitySensitivity requirement for control system tuning
TuningGoal.WeightedGain Frequency-weighted gain constraint for control system tuning
TuningGoal.WeightedVariance Frequency-weighted H2 norm constraint for control system tuning
TuningGoal.MinLoopGainMinimum loop gain constraint for control system tuning
TuningGoal.MaxLoopGainMaximum loop gain constraint for control system tuning
TuningGoal.LoopShape Target loop shape for control system tuning
TuningGoal.Margins Stability margin requirement for control system tuning
TuningGoal.PassivityPassivity constraint for control system tuning
TuningGoal.ConicSectorSector bound for control system tuning
TuningGoal.WeightedPassivityFrequency-weighted passivity constraint
TuningGoal.PolesConstraint on control system dynamics
TuningGoal.ControllerPolesConstraint on controller dynamics for control system tuning
Tuning, Analysis, and Validation
systune (slTuner)Tune control system parameters in Simulink using slTuner interface
systuneOptionsSet options for systune
getIOTransfer (slTuner)Transfer function for specified I/O set using slLinearizer or slTuner interface
getLoopTransfer (slTuner)Open-loop transfer function at specified point using slLinearizer or slTuner interface
getSensitivity (slTuner)Sensitivity function at specified point using slLinearizer or slTuner interface
getCompSensitivity (slTuner)Complementary sensitivity function at specified point using slLinearizer or slTuner interface
writeBlockValueUpdate block values in Simulink model
systuneTune fixed-structure control systems modeled in MATLAB
systuneOptionsSet options for systune
getIOTransferClosed-loop transfer function from generalized model of control system
getLoopTransferOpen-loop transfer function of control system
getSensitivitySensitivity function from generalized model of control system
getCompSensitivityComplementary sensitivity function from generalized model of control system
viewGoalView tuning goals; validate design against tuning goals
evalGoalEvaluate tuning goals for tuned control system

Loop-Shaping Design

slTunerInterface for control system tuning of Simulink models
looptuneTune MIMO feedback loops in Simulink using slTuner interface
looptuneOptionsSet options for looptune
loopviewGraphically analyze results of control system tuning using slTuner interface
looptuneSetupConstruct tuning setup for looptune to tuning setup for systune using slTuner interface
looptuneTune fixed-structure feedback loops
looptuneOptionsSet options for looptune
loopview Graphically analyze MIMO feedback loops
looptuneSetupConvert tuning setup for looptune to tuning setup for systune
viewGoalView tuning goals; validate design against tuning goals
evalGoalEvaluate tuning goals for tuned control system

Gain Scheduling

tunableSurfaceCreate tunable gain surface for gain scheduling
polyBasisPolynomial basis functions for tunable gain surface
fourierBasisFourier basis functions for tunable gain surface
ndBasisBasis functions for tunable gain surface
viewSurfVisualize gain surface as a function of scheduling variables
evalSurfEvaluate gain surfaces at specific design points
getDataGet current values of tunable-surface coefficients
setDataSet values of tunable-surface coefficients
codegenGenerate MATLAB code for tunable gain surfaces
systuneTune fixed-structure control systems modeled in MATLAB
slTunerInterface for control system tuning of Simulink models
systune (slTuner)Tune control system parameters in Simulink using slTuner interface
voidModelMark missing or irrelevant models in model array
varyingGoalVariable tuning goal for gain-scheduled controllers
getGoalEvaluate variable tuning goal at specified design point

Matrix Computations

lyapContinuous Lyapunov equation solution
lyapcholSquare-root solver for continuous-time Lyapunov equation
dlyapSolve discrete-time Lyapunov equations
dlyapcholSquare-root solver for discrete-time Lyapunov equations
careContinuous-time algebraic Riccati equation solution
dareSolve discrete-time algebraic Riccati equations (DAREs)
gcareGeneralized solver for continuous-time algebraic Riccati equation
gdareGeneralized solver for discrete-time algebraic Riccati equation
ctrbControllability matrix
obsvObservability matrix
ctrbfCompute controllability staircase form
obsvfCompute observability staircase form
gramControllability and observability Gramians
gramOptionsOptions for the gram command
bdschurBlock-diagonal Schur factorization
normNorm of linear model