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:

In[1]:=
Click for copyable input
Out[1]=

Scope  (6)

Options  (6)

Applications  (1)

Properties & Relations  (2)

See Also

ToDiscreteTimeModel  LaplaceTransform  MatrixLog

Introduced in 2010
(8.0)