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Control System Toolbox Functions

Alphabetical List By Category

Dynamic System Models

Linear System Representation

Basic Models

tf Create transfer function model, convert to transfer function model
zpk Create zero-pole-gain model; convert to zero-pole-gain model
ss Create state-space model, convert to state-space model
frd Create frequency-response data model, convert to frequency-response data model
filt Specify discrete transfer functions in DSP format
dss Create descriptor state-space models
pid Create 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
pid2 Create 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
rss Generate random continuous test model
drss Generate random discrete test model

Tunable Models

tunableGain Tunable static gain block
tunablePID Tunable PID controller
tunablePID2 Tunable two-degree-of-freedom PID controller
tunableSS Tunable fixed-order state-space model
tunableTF Tunable transfer function with fixed number of poles and zeros
realp Real tunable parameter
AnalysisPoint Points of interest for linear analysis
genss Generalized state-space model
genfrd Generalized frequency response data (FRD) model
genmat Generalized matrix with tunable parameters
getLoopTransfer Open-loop transfer function of control system
getIOTransfer Closed-loop transfer function from generalized model of control system
getSensitivity Sensitivity function from generalized model of control system
getCompSensitivity Complementary sensitivity function from generalized model of control system
getPoints Get list of analysis points in generalized model of control system
replaceBlock Replace or update Control Design Blocks in Generalized LTI model
sampleBlock Sample Control Design blocks in generalized model
rsampleBlock Randomly sample Control Design blocks in generalized model
getValue Current value of Generalized Model
setValue Modify current value of Control Design Block
getBlockValue Current value of Control Design Block in Generalized Model
setBlockValue Modify value of Control Design Block in Generalized Model
showBlockValue Display current value of Control Design Blocks in Generalized Model
showTunable Display current value of tunable Control Design Blocks in Generalized Model
nblocks Number of blocks in Generalized matrix or Generalized LTI model
getLFTModel Decompose generalized LTI model

Models with Time Delays

pade Padé approximation of model with time delays
absorbDelay Replace time delays by poles at z = 0 or phase shift
thiran Generate fractional delay filter based on Thiran approximation
hasdelay True for linear model with time delays
hasInternalDelay Determine if model has internal delays
totaldelay Total combined I/O delays for LTI model
delayss Create state-space models with delayed inputs, outputs, and states
setDelayModel Construct state-space model with internal delays
getDelayModel State-space representation of internal delays

Model Attributes

get Access model property values
set Set or modify model properties
tfdata Access transfer function data
zpkdata Access zero-pole-gain data
ssdata Access state-space model data
frdata Access data for frequency response data (FRD) object
piddata Access coefficients of parallel-form PID controller
pidstddata Access coefficients of standard-form PID controller
piddata2 Access coefficients of parallel-form 2-DOF PID controller
pidstddata2 Access coefficients of standard-form 2-DOF PID controller
dssdata Extract descriptor state-space data
chgFreqUnit Change frequency units of frequency-response data model
chgTimeUnit Change time units of dynamic system
isct Determine if dynamic system model is in continuous time
isdt Determine if dynamic system model is in discrete time
isempty Determine whether dynamic system model is empty
isfinite Determine if model has finite coefficients
isParametric Determine if model has tunable parameters
isproper Determine if dynamic system model is proper
isreal Determine if model has real-valued coefficients
issiso Determine if dynamic system model is single-input/single-output (SISO)
isstable Determine whether system is stable
isstatic Determine if model is static or dynamic
order Query model order
ndims Query number of dimensions of dynamic system model or model array
size Query output/input/array dimensions of input–output model and number of frequencies of FRD model

Model Arrays

stack Build model array by stacking models or model arrays along array dimensions
nmodels Number of models in model array
permute Rearrange array dimensions in model arrays
reshape Change shape of model array
repsys Replicate and tile models
sampleBlock Sample Control Design blocks in generalized model
rsampleBlock Randomly sample Control Design blocks in generalized model

Model Interconnection

feedback Feedback connection of two models
connect Block diagram interconnections of dynamic systems
sumblk Summing junction for name-based interconnections
series Series connection of two models
parallel Parallel connection of two models
append Group models by appending their inputs and outputs
blkdiag Block-diagonal concatenation of models
imp2exp Convert implicit linear relationship to explicit input-output relation
inv Invert models
lft Generalized feedback interconnection of two models (Redheffer star product)
connectOptions Options for the connect command

Model Transformation

Model Type Conversion

tf Create transfer function model, convert to transfer function model
zpk Create zero-pole-gain model; convert to zero-pole-gain model
ss Create state-space model, convert to state-space model
frd Create frequency-response data model, convert to frequency-response data model
pid Create 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
pid2 Create 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
make1DOF Convert 2-DOF PID controller to 1-DOF controller
make2DOF Convert 1-DOF PID controller to 2-DOF controller
getComponents Extract SISO control components from a 2-DOF PID controller

Continuous-Discrete Conversion

c2d Convert model from continuous to discrete time
d2c Convert model from discrete to continuous time
d2d Resample discrete-time model
upsample Upsample discrete-time models
c2dOptions Create option set for continuous- to discrete-time conversions
d2cOptions Create option set for discrete- to continuous-time conversions
d2dOptions Create option set for discrete-time resampling

State-Coordinate Transformation

balreal Gramian-based input/output balancing of state-space realizations
canon State-space canonical realization
prescale Optimal scaling of state-space models
ss2ss State coordinate transformation for state-space model
xperm Reorder states in state-space models

Modal Decomposition

modsep Region-based modal decomposition
stabsep Stable-unstable decomposition
stabsepOptions Options for stable-unstable decomposition
freqsep Slow-fast decomposition
freqsepOptions Options for slow-fast decomposition
spectralfact Spectral factorization of linear systems

Model Reduction

balred Model order reduction
balredOptions Create option set for model order reduction
balreal Gramian-based input/output balancing of state-space realizations
minreal Minimal realization or pole-zero cancelation
sminreal Structural pole/zero cancellations
modred Eliminate states from state-space models
freqsep Slow-fast decomposition
freqsepOptions Options for slow-fast decomposition
hsvd Hankel singular values of dynamic system
hsvplot Plot Hankel singular values and return plot handle
hsvdOptions Create option set for computing Hankel singular values and input/output balancing

Linear Analysis

Time and Frequency Domain Analysis

step Step response plot of dynamic system; step response data
stepinfo Rise time, settling time, and other step response characteristics
impulse Impulse response plot of dynamic system; impulse response data
initial Initial condition response of state-space model
lsim Simulate time response of dynamic system to arbitrary inputs
lsiminfo Compute linear response characteristics
gensig Generate test input signals for lsim
covar Output and state covariance of system driven by white noise
stepDataOptions Options set for step
bode Bode plot of frequency response, magnitude and phase of frequency response
bodemag Bode magnitude response of LTI models
nyquist Nyquist plot of frequency response
nichols Nichols chart of frequency response
ngrid Superimpose Nichols chart on Nichols plot
sigma Singular values plot of dynamic system
freqresp Frequency response over grid
evalfr Evaluate frequency response at given frequency
dcgain Low-frequency (DC) gain of LTI system
bandwidth Frequency response bandwidth
getPeakGain Peak gain of dynamic system frequency response
getGainCrossover Crossover frequencies for specified gain
fnorm Pointwise peak gain of FRD model
norm Norm of linear model
db2mag Convert decibels (dB) to magnitude
mag2db Convert magnitude to decibels (dB)

Stability Analysis

pole Compute poles of dynamic system
zero Zeros and gain of SISO dynamic system
damp Natural frequency and damping ratio
dsort Sort discrete-time poles by magnitude
esort Sort continuous-time poles by real part
tzero Invariant zeros of linear system
pzplot Pole-zero map of dynamic system model with plot customization options
iopzplot Plot pole-zero map for I/O pairs and return plot handle
allmargin Gain margin, phase margin, delay margin and crossover frequencies
margin Gain margin, phase margin, and crossover frequencies

Sensitivity Analysis

sampleBlock Sample Control Design blocks in generalized model
rsampleBlock Randomly sample Control Design blocks in generalized model

Passivity and Sector Bounds

isPassive Check passivity of linear systems
getPassiveIndex Compute passivity index of linear system
passiveplot Compute or plot passivity index as function of frequency
getSectorIndex Compute conic-sector index of linear system
getSectorCrossover Crossover frequencies for sector bound
sectorplot Compute or plot sector index as function of frequency

Plot Customization

impulseplot Plot impulse response and return plot handle
initialplot Plot initial condition response and return plot handle
lsimplot Simulate response of dynamic system to arbitrary inputs and return plot handle
stepplot Plot step response and return plot handle
bodeplot Plot Bode frequency response with additional plot customization options
nicholsplot Plot Nichols frequency responses and return plot handle
nyquistplot Nyquist plot with additional plot customization options
sigmaplot Plot singular values of frequency response and return plot handle
bodeoptions Create list of Bode plot options
hsvoptions Plot options for hsvplot
nicholsoptions Create list of Nichols plot options
nyquistoptions List of Nyquist plot options
pzoptions Create list of pole/zero plot options
sigmaoptions Create list of singular-value plot options
timeoptions Create list of time plot options
setoptions Set plot options for response plot
getoptions Return @PlotOptions handle or plot options property
ctrlpref Set Control System Toolbox preferences
updateSystem Update dynamic system data in a response plot

Control System Design and Tuning

PID Controller Tuning

pidTuner Open PID Tuner for PID tuning
pidtune PID tuning algorithm for linear plant model
pidtuneOptions Define options for pidtune command

Classical Control Design

rlocus Root locus plot of dynamic system
rlocusplot Plot root locus and return plot handle
sisoinit Configure Control System Designer at startup

State-Space Control Design

Linear-Quadratic-Gaussian Control

lqr Linear-Quadratic Regulator (LQR) design
lqry Form linear-quadratic (LQ) state-feedback regulator with output weighting
lqi Linear-Quadratic-Integral control
dlqr Linear-quadratic (LQ) state-feedback regulator for discrete-time state-space system
lqrd Design discrete linear-quadratic (LQ) regulator for continuous plant
kalman Kalman filter design, Kalman estimator
kalmd Design discrete Kalman estimator for continuous plant
extendedKalmanFilter Create extended Kalman filter object for online state estimation
unscentedKalmanFilter Create unscented Kalman filter object for online state estimation
correct Correct state and state estimation error covariance using extended or unscented Kalman filter and measurements
predict Predict state and state estimation error covariance at next time step using extended or unscented Kalman filter
clone Copy online state estimation object
lqg Linear-Quadratic-Gaussian (LQG) design
lqgreg Form linear-quadratic-Gaussian (LQG) regulator
lqgtrack Form Linear-Quadratic-Gaussian (LQG) servo controller
augstate Append state vector to output vector
norm Norm of linear model

Pole Placement

estim Form state estimator given estimator gain
place Pole placement design
reg Form regulator given state-feedback and estimator gains

Multiloop, Multiobjective Tuning

Programmatic Tuning

Setup for Tuning Simulink Models
slTuner Interface for control system tuning of Simulink models
addBlock Add block to list of tuned blocks for slTuner interface
addOpening Add signal to list of openings for slLinearizer or slTuner interface
addPoint Add signal to list of analysis points for slLinearizer or slTuner interface
setBlockParam Set parameterization of tuned block in slTuner interface
setBlockRateConversion Set rate conversion settings for tuned block in slTuner interface
setBlockValue Set value of tuned block parameterization in slTuner interface
getBlockParam Get parameterization of tuned block in slTuner interface
getBlockRateConversion Get rate conversion settings for tuned block in slTuner interface
getBlockValue Get current value of tuned block parameterization in slTuner interface
getOpenings Get list of openings for slLinearizer or slTuner interface
getPoints Get list of analysis points for slLinearizer or slTuner interface
refresh Resynchronize slLinearizer or slTuner interface with current model state
removeAllOpenings Remove all openings from list of permanent openings in slLinearizer or slTuner interface
removeAllPoints Remove all points from list of analysis points in slLinearizer or slTuner interface
removeBlock Remove block from list of tuned blocks in slTuner interface
removeOpening Remove opening from list of permanent loop openings in slLinearizer or slTuner interface
removePoint Remove point from list of analysis points in slLinearizer or slTuner interface
showTunable Show value of parameterizations of tunable blocks of slTuner interface
writeBlockValue Update block values in Simulink model
Setup for Tuning MATLAB Models
tf Create transfer function model, convert to transfer function model
zpk Create zero-pole-gain model; convert to zero-pole-gain model
ss Create state-space model, convert to state-space model
tunableGain Tunable static gain block
tunableTF Tunable transfer function with fixed number of poles and zeros
tunablePID Tunable PID controller
tunablePID2 Tunable two-degree-of-freedom PID controller
tunableSS Tunable fixed-order state-space model
realp Real tunable parameter
AnalysisPoint Points of interest for linear analysis
connect Block diagram interconnections of dynamic systems
feedback Feedback connection of two models
Tuning Goals
TuningGoal.StepTracking Step response requirement for control system tuning
TuningGoal.StepRejection Step disturbance rejection requirement for control system tuning
TuningGoal.Transient Transient matching requirement for control system tuning
TuningGoal.LQG Linear-Quadratic-Gaussian (LQG) goal for control system tuning
TuningGoal.Gain Gain constraint for control system tuning
TuningGoal.Variance Noise amplification constraint for control system tuning
TuningGoal.Tracking Tracking requirement for control system tuning
TuningGoal.Overshoot Overshoot constraint for control system tuning
TuningGoal.Rejection Disturbance rejection requirement for control system tuning
TuningGoal.Sensitivity Sensitivity 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.MinLoopGain Minimum loop gain constraint for control system tuning
TuningGoal.MaxLoopGain Maximum 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.Passivity Passivity constraint for control system tuning
TuningGoal.ConicSector Sector bound for control system tuning
TuningGoal.WeightedPassivity Frequency-weighted passivity constraint
TuningGoal.Poles Constraint on control system dynamics
TuningGoal.ControllerPoles Constraint on controller dynamics for control system tuning
Tuning, Analysis, and Validation
systune (slTuner) Tune control system parameters in Simulink using slTuner interface
systuneOptions Set 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
writeBlockValue Update block values in Simulink model
systune Tune fixed-structure control systems modeled in MATLAB
systuneOptions Set options for systune
getIOTransfer Closed-loop transfer function from generalized model of control system
getLoopTransfer Open-loop transfer function of control system
getSensitivity Sensitivity function from generalized model of control system
getCompSensitivity Complementary sensitivity function from generalized model of control system
viewSpec View tuning requirements; validate design against requirements
evalSpec Evaluate tuning requirements for tuned control system

Loop-Shaping Design

slTuner Interface for control system tuning of Simulink models
looptune Tune MIMO feedback loops in Simulink using slTuner interface
looptuneOptions Set options for looptune
loopview Graphically analyze results of control system tuning using slTuner interface
looptuneSetup Construct tuning setup for looptune to tuning setup for systune using slTuner interface
looptune Tune fixed-structure feedback loops
looptuneOptions Set options for looptune
loopview Graphically analyze MIMO feedback loops
looptuneSetup Convert tuning setup for looptune to tuning setup for systune
viewSpec View tuning requirements; validate design against requirements
evalSpec Evaluate tuning requirements for tuned control system

Gain Scheduling

tunableSurface Create tunable gain surface for gain scheduling
polyBasis Polynomial basis functions for tunable gain surface
fourierBasis Fourier basis functions for tunable gain surface
ndBasis Basis functions for tunable gain surface
viewSurf Visualize gain surface as a function of scheduling variables
evalSurf Evaluate gain surfaces at specific design points
getData Get current values of tunable-surface coefficients
setData Set values of tunable-surface coefficients
systune Tune fixed-structure control systems modeled in MATLAB
slTuner Interface for control system tuning of Simulink models
systune (slTuner) Tune control system parameters in Simulink using slTuner interface

Matrix Computations

lyap Continuous Lyapunov equation solution
lyapchol Square-root solver for continuous-time Lyapunov equation
dlyap Solve discrete-time Lyapunov equations
dlyapchol Square-root solver for discrete-time Lyapunov equations
care Continuous-time algebraic Riccati equation solution
dare Solve discrete-time algebraic Riccati equations (DAREs)
gcare Generalized solver for continuous-time algebraic Riccati equation
gdare Generalized solver for discrete-time algebraic Riccati equation
ctrb Controllability matrix
obsv Observability matrix
ctrbf Compute controllability staircase form
obsvf Compute observability staircase form
gram Controllability and observability Gramians
gramOptions Options for the gram command
bdschur Block-diagonal Schur factorization
norm Norm of linear model
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