Documentation

Robust Control Toolbox Functions

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-Chebyshev 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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