Julia for MATLAB Users/Index/Toolboxes/Control System Toolbox

Maps functionality from the MATLAB Control System Toolbox to equivalent(s) in Julia.

Related Julia packages:

• ControlSystems.jl

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Dynamic System Models

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
• voidModel Mark missing or irrelevant models in model array
• 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, or magnitude and phase data
• 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 and Estimation

State-Space Control Design

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

State Estimation

• kalman Kalman filter design, Kalman estimator
• kalmd Design discrete Kalman estimator for continuous plant
• estim Form state estimator given estimator gain
• extendedKalmanFilter Create extended Kalman filter object for online state estimation
• unscentedKalmanFilter Create unscented Kalman filter object for online state estimation
• particleFilter Particle filter object for online state estimation
• correct Correct state and state estimation error covariance using extended or unscented Kalman filter, or particle filter and measurements
• predict Predict state and state estimation error covariance at next time step using extended or unscented Kalman filter, or particle filter
• initialize Initialize the state of the particle filter
• clone Copy online state estimation object

Multiloop, Multiobjective Tuning

Programmatic Tuning

Setup for Tuning Simulink Models

• slTuner Interface for control system tuning of Simulink models
• slTunerOptions Set slTuner interface options
• 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
• 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
• 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
• writeBlockValue Update block values in Simulink model
• writeLookupTableData Update portion of tuned lookup table
• 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
• showTunable Show value of parameterizations of tunable blocks of slTuner interface

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
• viewGoal View tuning goals; validate design against tuning goals
• evalGoal Evaluate tuning goals 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
• viewGoal View tuning goals; validate design against tuning goals
• evalGoal Evaluate tuning goals 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
• codegen Generate MATLAB code for tunable gain surfaces
• 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
• voidModel Mark missing or irrelevant models in model array
• varyingGoal Variable tuning goal for gain-scheduled controllers
• getGoal Evaluate variable tuning goal at specified design point

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