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
open allclose allBasic 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:
See Also
Related Guides
History
Text
Wolfram Research (2010), ToContinuousTimeModel, Wolfram Language function, https://reference.wolfram.com/language/ref/ToContinuousTimeModel.html.
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
BibTeX
@misc{reference.wolfram_2025_tocontinuoustimemodel, author="Wolfram Research", title="{ToContinuousTimeModel}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/ToContinuousTimeModel.html}", note=[Accessed: 27-April-2025 ]}
BibLaTeX
@online{reference.wolfram_2025_tocontinuoustimemodel, organization={Wolfram Research}, title={ToContinuousTimeModel}, year={2010}, url={https://reference.wolfram.com/language/ref/ToContinuousTimeModel.html}, note=[Accessed: 27-April-2025 ]}