OutputResponse

OutputResponse[sys,u,{t,tmin,tmax}]
gives the numeric output response of systems model sys to the input u for .

OutputResponse[sys,{u[0],u[1],}]
gives the output response of the discrete-time system sys to the input sequence .

OutputResponse[sys,u,t]
gives the symbolic output response of system sys to the input u as a function of time t.

OutputResponse[sys,{u1,,um},]
gives the output response for multiple inputs .

DetailsDetails

  • OutputResponse is also known as impulse response, step response, and ramp response.
  • OutputResponse solves the underlying differential or difference equations for the given input.
  • The systems model sys can be a TransferFunctionModel, a StateSpaceModel, a continuous-time AffineStateSpaceModel, or a continuous-time NonlinearStateSpaceModel.
  • A linear TransferFunctionModel or StateSpaceModel sys can also be a descriptor and delay system.
  • The initial values for the differential and difference equations are taken to be zero for a TransferFunctionModel. For the state-space models, they are taken to be the state operating values of sys unless specified.
  • OutputResponse[{sys,{x10,x20,,xn0}},] can be used to specify the initial state for a state-space model sys.
  • For descriptor state-space systems, the initial states need to be consistent.
  • For delay state-space systems, the initial states include history and can be given as for t0. »

ExamplesExamplesopen allclose all

Basic Examples  (4)Basic Examples  (4)

The step response of a second-order system:

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The output response of a transfer-function model to a sinusoidal input:

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Visualize the response:

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The response of a state-space model from nonzero initial conditions:

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The response of a discrete-time system to a sampled sinusoid:

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Introduced in 2010
(8.0)
| Updated in 2014
(10.0)