Functions in Robust Control Toolbox

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  • Uncertain System Representation

    Uncertain Models

    ureal Create uncertain real parameter
    umat Create uncertain matrix
    ucomplex Create uncertain complex parameter
    ucomplexm Create uncertain complex matrix
    ultidyn Create uncertain linear time-invariant object
    uss Specify uncertain state-space models or convert LTI model to uncertain state-space model
    ufrd Uncertain frequency response data model
    randatom Generate random uncertain atom objects
    randumat Generate random uncertain umat objects
    randuss Generate stable, random uss objects
    actual2normalized Transform actual values to normalized values
    normalized2actual Convert value for atom in normalized coordinates to corresponding actual value
    simplify Simplify representation of uncertain object
    isuncertain Check whether argument is uncertain class type
    lftdata Decompose uncertain objects into fixed normalized and fixed uncertain parts
    ltiarray2uss Compute uncertain system bounding given LTI ss array
    ucover Fit an uncertain model to set of LTI responses

    Uncertain Models in Simulink

    ulinearize Linearize Simulink model with Uncertain State Space block

    Uncertain System Analysis

    Nominal Performance Analysis

    loopmargin Stability margin analysis of LTI and Simulink feedback loops
    dmplot Interpret disk gain and phase margins
    cpmargin Coprime stability margin of plant-controller feedback loop
    gapmetric Compute upper bounds on Vinnicombe gap and nugap distances between two systems
    loopsens Sensitivity functions of plant-controller feedback loop
    ncfmargin Calculate normalized coprime stability margin of plant-controller feedback loop
    sdhinfnorm Compute L2 norm of continuous-time system in feedback with discrete-time system
    sdlsim Time response of sampled-data feedback system

    Worst-Case Analysis

    robustperf Robust performance margin of uncertain multivariable system
    robuststab Calculate robust stability margins of uncertain multivariable system
    wcgain Calculate bounds on worst-case gain of uncertain system
    wcgainplot Graphical worst-case gain analysis
    wcnorm Worst-case norm of uncertain matrix
    wcsens Calculate worst-case sensitivity and complementary sensitivity functions of plant-controller feedback loop
    wcmargin Worst-case disk stability margins of uncertain feedback loops
    mussv Compute bounds on structured singular value (µ)
    mussvextract Extract muinfo structure returned by mussv
    popov Perform Popov robust stability test
    robustperfOptions Option set for robustperf
    robuststabOptions Option set for robuststab
    wcgainOptions Option set for wcgain, wcgainplot, wcnorm, or wcsens
    wcmarginOptions Option set for wcmargin

    Monte Carlo Analysis

    usample Generate random samples of uncertain variables
    uss/usample Generate random samples of uncertain object
    usubs Substitute given values for uncertain elements of uncertain objects
    gridureal Grid ureal parameters uniformly over their range
    complexify Replace ureal atoms by summations of ureal and ucomplex (or ultidyn) atoms

    Uncertainty Analysis with Simulink Models

    ufind Find uncertain variables in Simulink model
    ulinearize Linearize Simulink model with Uncertain State Space block
    usample Generate random samples of uncertain variables
    loopmargin Stability margin analysis of LTI and Simulink feedback loops

    Control System Tuning

    Tuning with Control System Tuner

    Model Setup

    controlSystemTuner Open Control System Tuner

    Programmatic Control System 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
    ltiblock.gain Tunable static gain block
    ltiblock.tf Tunable transfer function with fixed number of poles and zeros
    ltiblock.pid Tunable PID controller
    ltiblock.pid2 Tunable two-degree-of-freedom PID controller
    ltiblock.ss 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.Poles Constraint on control system dynamics
    TuningGoal.ControllerPoles Constraint on controller dynamics for control system tuning

    Parameter Tuning

    systune Tune control system parameters in Simulink using slTuner interface
    systuneOptions Set options for systune
    systune Tune fixed-structure control systems
    systuneOptions Set options for systune

    Validation of Tuned Simulink Models

    getIOTransfer Transfer function for specified I/O set using slLinearizer or slTuner interface
    getLoopTransfer Open-loop transfer function at specified point using slLinearizer or slTuner interface
    getSensitivity Sensitivity function at specified point using slLinearizer or slTuner interface
    getCompSensitivity Complementary sensitivity function at specified point using slLinearizer or slTuner interface
    writeBlockValue Update block values in Simulink model
    viewSpec View tuning requirements; validate design against requirements
    evalSpec Evaluate tuning requirements for tuned control system

    Validation of Tuned MATLAB Models

    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-Scheduled Controllers

    gainsurf Create tunable gain surface for gain scheduling
    gainsurfdata Get values of gain surface coefficients
    view (genmat) Visualize gain surface as a function of scheduling variables
    systune Tune fixed-structure control systems
    looptune Tune fixed-structure feedback loops

    Robust Controller Synthesis

    H-Infinity Synthesis

    hinfstruct H∞ tuning of fixed-structure controllers
    hinfstructOptions Set options for hinfstruct
    hinfsyn Compute H∞ optimal controller for LTI plant
    h2syn H2 control synthesis for LTI plant
    sdhinfsyn Compute H∞ controller for sampled-data system
    h2hinfsyn Mixed H2/H∞ synthesis with pole placement constraints
    hinfnorm H∞ norm of dynamic system
    augw State-space or transfer function plant augmentation for use in weighted mixed-sensitivity H∞ and H2 loopshaping design
    mkfilter Generate Bessel, Butterworth, Chebyshev, or RC filter
    makeweight First-order weighting function with specified DC gain, crossover frequency, and high-frequency gain

    Loop-Shaping Synthesis

    loopsyn H∞ optimal controller synthesis for LTI plant
    mixsyn H∞ mixed-sensitivity synthesis method for robust control loopshaping design
    ncfsyn Loop shaping design using Glover-McFarlane method

    Mu Synthesis

    dksyn Robust controller design using µ-synthesis
    dksynOptions Set options for dksyn
    cmsclsyn Approximately solve constant-matrix, upper bound µ-synthesis problem
    drawmag Mouse-based tool for sketching and fitting
    fitfrd Fit frequency response data with state-space model
    fitmagfrd Fit frequency response magnitude data with minimum-phase state-space model using log-Chebychev magnitude design
    genphase Fit single-input/single-output magnitude data with real, rational, minimum-phase transfer function

    Model Simplification

    balancmr Balanced model truncation via square root method
    bstmr Balanced stochastic model truncation (BST) via Schur method
    dcgainmr Reduced order model
    hankelmr Hankel minimum degree approximation (MDA) without balancing
    hankelsv Compute Hankel singular values for stable/unstable or continuous/discrete system
    modreal Modal form realization and projection
    ncfmr Balanced model truncation for normalized coprime factors
    reduce Simplified access to Hankel singular value based model reduction functions
    schurmr Balanced model truncation via Schur method
    slowfast Slow and fast modes decomposition

    Linear Matrix Inequalities

    LMI Solvers

    getlmis Internal description of LMI system
    lmiedit Specify or display systems of LMIs as MATLAB expressions
    lmiterm Specify term content of LMIs
    lmivar Specify matrix variables in LMI problem
    newlmi Attach identifying tag to LMIs
    setlmis Initialize description of LMI system
    dellmi Remove LMI from system of LMIs
    delmvar Remove one matrix variable from LMI problem
    setmvar Instantiate matrix variable and evaluate all LMI terms involving this matrix variable
    dec2mat Given values of decision variables, derive corresponding values of matrix variables
    decinfo Describe how entries of matrix variable X relate to decision variables
    decnbr Total number of decision variables in system of LMIs
    lmiinfo Information about variables and term content of LMIs
    lminbr Return number of LMIs in LMI system
    mat2dec Extract vector of decision variables from matrix variable values
    matnbr Number of matrix variables in system of LMIs
    defcx Help specify cTx objectives for mincx solver
    feasp Compute solution to given system of LMIs
    gevp Generalized eigenvalue minimization under LMI constraints
    mincx Minimize linear objective under LMI constraints
    evallmi Given particular instance of decision variables, evaluate all variable terms in system of LMIs
    showlmi Return left and right sides of LMI after evaluation of all variable terms

    Parameter-Dependent Systems

    aff2pol Convert affine parameter-dependent models to polytopic models
    decay Quadratic decay rate of polytopic or affine P-systems
    ispsys True for parameter-dependent systems
    pdlstab Assess robust stability of polytopic or parameter-dependent system
    pdsimul Time response of parameter-dependent system along given parameter trajectory
    polydec Compute polytopic coordinates with respect to box corners
    psinfo Inquire about polytopic or parameter-dependent systems created with psys
    psys Specify polytopic or parameter-dependent linear systems
    pvec Specify range and rate of variation of uncertain or time-varying parameters
    pvinfo Describe parameter vector specified with pvec
    quadperf Compute quadratic H∞ performance of polytopic or parameter-dependent system
    quadstab Quadratic stability of polytopic or affine parameter-dependent systems

    LMI Controller Synthesis

    hinfgs Synthesis of gain-scheduled H∞ controllers
    hinfsyn Compute H∞ optimal controller for LTI plant
    h2hinfsyn Mixed H2/H∞ synthesis with pole placement constraints
    msfsyn Multi-model/multi-objective state-feedback synthesis
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