ToContinuousTimeModel

ToContinuousTimeModel[lsys]

gives the continuous-time approximation of the discrete-time systems models lsys.

ToContinuousTimeModel[tfm,s]

specifies the transform variable s.

Details and Options

  • ToContinuousTimeModel is also known as inverse sampling.
  • The systems model lsys can be a TransferFunctionModel or StateSpaceModel.
  • ToContinuousTimeModel accepts a Method option that can be used to specify the approximation method.
  • Possible settings for the Method option include:
  • "ForwardRectangularRule"Euler forward method
    "BackwardRectangularRule"Euler backward method
    "BilinearTransform"Tustin bilinear approximation
    "ZeroPoleMapping"exact matching of zeros and poles
    "ZeroOrderHold"piecewise constant approximation
    "FirstOrderHold"piecewise linear (triangular) approximation
  • The default setting Method->Automatic implements the bilinear transformation.
  • The setting Method->"ZeroPoleMapping" does not support time delays.
  • A bilinear transform with critical frequency ω radians per time unit can be specified by setting Method->{"BilinearTransform","CriticalFrequency"->ω}.
  • The "FirstOrderHold" method gives the non-causal first-order hold equivalent.
  • When approximating TransferFunctionModel objects, "StateSpaceConversion" can be specified as a suboption.
  • The setting Method->{m,"StateSpaceConversion"->True} computes the approximation using the state-space representation and converts the result to the transfer-function representation.
  • The setting "StateSpaceConversion"->False computes using the transfer-function object.
  • The setting "StateSpaceConversion"->Automatic computes the approximation using the transfer-function representation, except for the "ZeroOrderHold" method.

Examples

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Basic Examples  (1)

A continuous-time approximation of a discrete-time system:

Scope  (6)

Convert a discrete-time transfer-function model to a continuous-time model:

Convert a discrete-time state-space model to a continuous-time model:

Convert a multiple-input, multiple-output system to a continuous-time system:

Convert a symbolic system:

Convert a time-delay StateSpaceModel:

Convert a singular descriptor StateSpaceModel:

Options  (6)

Method  (6)

By default, the approximation is based on the bilinear transformation:

Specify the approximation method:

Compare various approximation methods:

An approximation that preserves the transmission at a specified frequency:

The backward Euler method adds states if the state and descriptor matrices are both singular:

The bilinear method adds states if the sum of the state and descriptor matrices is singular:

Applications  (1)

Various continuous-time approximations to a fourth-order Chebyshev II bandstop filter:

Bode plots:

Properties & Relations  (2)

ToDiscreteTimeModel is essentially the inverse of ToContinuousTimeModel:

ToContinuousTimeModel may add states to systems with neutral time delays:

Wolfram Research (2010), ToContinuousTimeModel, Wolfram Language function, https://reference.wolfram.com/language/ref/ToContinuousTimeModel.html.

Text

Wolfram Research (2010), ToContinuousTimeModel, Wolfram Language function, https://reference.wolfram.com/language/ref/ToContinuousTimeModel.html.

BibTeX

@misc{reference.wolfram_2021_tocontinuoustimemodel, author="Wolfram Research", title="{ToContinuousTimeModel}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/ToContinuousTimeModel.html}", note=[Accessed: 27-September-2021 ]}

BibLaTeX

@online{reference.wolfram_2021_tocontinuoustimemodel, organization={Wolfram Research}, title={ToContinuousTimeModel}, year={2010}, url={https://reference.wolfram.com/language/ref/ToContinuousTimeModel.html}, note=[Accessed: 27-September-2021 ]}

CMS

Wolfram Language. 2010. "ToContinuousTimeModel." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/ToContinuousTimeModel.html.

APA

Wolfram Language. (2010). ToContinuousTimeModel. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ToContinuousTimeModel.html