# OutputResponse

OutputResponse[sys,u,{t,tmin,tmax}]

gives the numeric output response of systems model sys to the input u for tminttmax.

OutputResponse[sys,{u[0],u[1],}]

gives the output response of the discrete-time system sys to the input sequence u[i].

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 ui.

# Details

• 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 xi0[t] for t0. »

# Examples

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## 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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