Nonlinear Control Systems
Nonlinear models naturally occur in most areas of engineering (mechanical, electrical, chemical, …) and are traditionally dealt with by linear approximations. However, by using the nonlinear model, better controllers can be designed that take into account the nonlinear behavior. The Wolfram Language provides full support for affine and general nonlinear models. For affine models, you can automatically find a transformation that makes the system linear, allowing for the full suite of linear analysis and design functionality to be used. For general nonlinear models, automatic approximation schemes allow one to reduce to linear or affine systems or directly design a full information regulator.
Modeling & Simulation
AffineStateSpaceModel — affine model and
NonlinearStateSpaceModel — nonlinear model and
SystemsModelSeriesConnect ▪ SystemsModelFeedbackConnect ▪ ...
OutputResponse ▪ StateResponse ▪ ...
Design by Approximate Linearization
StateSpaceModel — Taylor linearize a model to a StateSpaceModel
CarlemanLinearize — Carleman bilinearize a model to an AffineStateSpaceModel
StateFeedbackGains ▪ EstimatorRegulator ▪ ...
Design by Exact Linearization
FeedbackLinearize — linearization through nonlinear feedback and state transformation
StateTransformationLinearize — linearization through state transformation
StateSpaceTransform — change of variables for state space models
StateFeedbackGains ▪ EstimatorRegulator ▪ LinearizingTransformationData ▪ ...
Nonlinear Design
FullInformationOutputRegulator — regulate output with full information state feedback
AsymptoticOutputTracker — tracker with state feedback
Nonlinear Analysis
SystemsModelVectorRelativeOrders — vector relative orders for affine models
ControllableModelQ ▪ ObservableModelQ ▪ ControllableDecomposition ▪ ObservableDecomposition ▪ MinimalStateSpaceModel ▪ SystemsModelLinearity
Deploy to Microcontrollers »
ToDiscreteTimeModel — gives the discrete-time approximation of a model
MicrocontrollerEmbedCode — deploys code to microcontrollers