Control Systems

The Wolfram Language provides an extensive suite of built-in functionality to carry out analysis, design, and simulation of continuous- and discrete-time control systems using both classical and modern techniques. Building on the Wolfram Language's proven symbolic architecture, state-space and transfer function models can be represented in symbolic as well as numeric form, yielding closed-form symbolic solutions where traditional tools only provide numerical answers. All built-in numerical solvers use the Wolfram Language's hybrid symbolic-numeric approach and highly efficient numerical algorithms.

Basic Modeling »

TransferFunctionModel a transfer-function model

StateSpaceModel a state-space model

ToContinuousTimeModel  ▪  ToDiscreteTimeModel  ▪  ...

Models with Time Delays »

SystemsModelDelay  ▪  TransferFunctionModel  ▪  StateSpaceModel  ▪  ...

Models with Algebraic Constraints »

DescriptorStateSpace  ▪  StateSpaceModel  ▪  ...

Nonlinear Models »

AffineStateSpaceModel  ▪  NonlinearStateSpaceModel  ▪  ...

Model Connections and Manipulations »

SystemsModelSeriesConnect connects two models in series

SystemsModelExtract extracts a subsystem

SystemsModelFeedbackConnect  ▪  SystemsModelDelete  ▪  ...

Model Simulations

StateResponse  ▪  OutputResponse

Classical Analysis and Design »

RootLocusPlot  ▪  BodePlot  ▪  NyquistPlot  ▪  PIDTune  ▪  ...

Analysis of State-Space Models »

ControllabilityMatrix  ▪  ObservabilityMatrix  ▪  JordanModelDecomposition  ▪  InternallyBalancedDecomposition  ▪  ...

Design using State-Space Models »

StateFeedbackGains  ▪  LQEstimatorGains  ▪  DiscreteLQRegulatorGains  ▪  KalmanEstimator  ▪  ...

Matrix Equation Solvers

RiccatiSolve  ▪  DiscreteRiccatiSolve  ▪  LyapunovSolve  ▪  DiscreteLyapunovSolve