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:



Dynamic System ModelsEdit

Linear System RepresentationEdit

Basic ModelsEdit

  • 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 ModelsEdit

  • 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 DelaysEdit

  • 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 AttributesEdit

  • 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 ArraysEdit

  • 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 InterconnectionEdit

  • 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 TransformationEdit

Model Type ConversionEdit

  • 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 ConversionEdit

  • 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 TransformationEdit

  • 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 DecompositionEdit

Model ReductionEdit

  • 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 AnalysisEdit

Time and Frequency Domain AnalysisEdit

  • 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 AnalysisEdit

  • 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 AnalysisEdit

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

Passivity and Sector BoundsEdit

Plot CustomizationEdit

  • 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 TuningEdit

PID Controller TuningEdit

Classical Control DesignEdit

  • 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 EstimationEdit

State-Space Control DesignEdit

  • 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 EstimationEdit

  • 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 TuningEdit

Programmatic TuningEdit

Setup for Tuning Simulink ModelsEdit

  • 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 ModelsEdit

  • 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 GoalsEdit

  • 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 ValidationEdit

  • 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 DesignEdit

  • 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 SchedulingEdit

  • 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 ComputationsEdit

  • 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