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Control Systems
  • Functions
    • AffineStateSpaceModel
    • BodePlot
    • ControllabilityMatrix
    • DescriptorStateSpace
    • DiscreteLQRegulatorGains
    • DiscreteLyapunovSolve
    • DiscreteRiccatiSolve
    • InputOutputResponse
    • InputOutputResponseData
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    • JordanModelDecomposition
    • KalmanEstimator
    • LQEstimatorGains
    • LyapunovSolve
    • MicrocontrollerCodeData
    • MicrocontrollerEmbedCode
    • NonlinearStateSpaceModel
    • NyquistPlot
    • ObservabilityMatrix
    • OutputResponse
    • PIDTune
    • RiccatiSolve
    • RootLocusPlot
    • StateFeedbackGains
    • StateResponse
    • StateSpaceModel
    • SystemsModelDelay
    • SystemsModelDelete
    • SystemsModelExtract
    • SystemsModelFeedbackConnect
    • SystemsModelSeriesConnect
    • ToContinuousTimeModel
    • ToDiscreteTimeModel
    • TransferFunctionModel
  • Related Guides
    • System Modeling
    • Matrices & Linear Algebra
    • Signal Processing
    • Time Series Processes
    • Functions
      • AffineStateSpaceModel
      • BodePlot
      • ControllabilityMatrix
      • DescriptorStateSpace
      • DiscreteLQRegulatorGains
      • DiscreteLyapunovSolve
      • DiscreteRiccatiSolve
      • InputOutputResponse
      • InputOutputResponseData
      • InternallyBalancedDecomposition
      • JordanModelDecomposition
      • KalmanEstimator
      • LQEstimatorGains
      • LyapunovSolve
      • MicrocontrollerCodeData
      • MicrocontrollerEmbedCode
      • NonlinearStateSpaceModel
      • NyquistPlot
      • ObservabilityMatrix
      • OutputResponse
      • PIDTune
      • RiccatiSolve
      • RootLocusPlot
      • StateFeedbackGains
      • StateResponse
      • StateSpaceModel
      • SystemsModelDelay
      • SystemsModelDelete
      • SystemsModelExtract
      • SystemsModelFeedbackConnect
      • SystemsModelSeriesConnect
      • ToContinuousTimeModel
      • ToDiscreteTimeModel
      • TransferFunctionModel
    • Related Guides
      • System Modeling
      • Matrices & Linear Algebra
      • Signal Processing
      • Time Series Processes
GUIDE
  • Functions
    • AffineStateSpaceModel
    • BodePlot
    • ControllabilityMatrix
    • DescriptorStateSpace
    • DiscreteLQRegulatorGains
    • DiscreteLyapunovSolve
    • DiscreteRiccatiSolve
    • InputOutputResponse
    • InputOutputResponseData
    • InternallyBalancedDecomposition
    • JordanModelDecomposition
    • KalmanEstimator
    • LQEstimatorGains
    • LyapunovSolve
    • MicrocontrollerCodeData
    • MicrocontrollerEmbedCode
    • NonlinearStateSpaceModel
    • NyquistPlot
    • ObservabilityMatrix
    • OutputResponse
    • PIDTune
    • RiccatiSolve
    • RootLocusPlot
    • StateFeedbackGains
    • StateResponse
    • StateSpaceModel
    • SystemsModelDelay
    • SystemsModelDelete
    • SystemsModelExtract
    • SystemsModelFeedbackConnect
    • SystemsModelSeriesConnect
    • ToContinuousTimeModel
    • ToDiscreteTimeModel
    • TransferFunctionModel
  • Related Guides
    • System Modeling
    • Matrices & Linear Algebra
    • Signal Processing
    • Time Series Processes
    • Functions
      • AffineStateSpaceModel
      • BodePlot
      • ControllabilityMatrix
      • DescriptorStateSpace
      • DiscreteLQRegulatorGains
      • DiscreteLyapunovSolve
      • DiscreteRiccatiSolve
      • InputOutputResponse
      • InputOutputResponseData
      • InternallyBalancedDecomposition
      • JordanModelDecomposition
      • KalmanEstimator
      • LQEstimatorGains
      • LyapunovSolve
      • MicrocontrollerCodeData
      • MicrocontrollerEmbedCode
      • NonlinearStateSpaceModel
      • NyquistPlot
      • ObservabilityMatrix
      • OutputResponse
      • PIDTune
      • RiccatiSolve
      • RootLocusPlot
      • StateFeedbackGains
      • StateResponse
      • StateSpaceModel
      • SystemsModelDelay
      • SystemsModelDelete
      • SystemsModelExtract
      • SystemsModelFeedbackConnect
      • SystemsModelSeriesConnect
      • ToContinuousTimeModel
      • ToDiscreteTimeModel
      • TransferFunctionModel
    • Related Guides
      • System Modeling
      • Matrices & Linear Algebra
      • Signal Processing
      • Time Series Processes

Control Systems

Topic Overview

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

InputOutputResponse — complete simulation response

InputOutputResponseData — simulation data object

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

Deploy to Microcontrollers »

MicrocontrollerEmbedCode  ▪  MicrocontrollerCodeData

Related Guides

    ▪
  • System Modeling
  • ▪
  • Matrices & Linear Algebra
  • ▪
  • Signal Processing
  • ▪
  • Time Series Processes

Related Links

  • Wolfram Core Areas: Controls
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