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# OutputResponse

 OutputResponsegives the output response of a TransferFunctionModel or StateSpaceModel object sys to the input u as a function of time t. OutputResponse gives the response from to . OutputResponse gives the response of the discrete-time system sys to the input sequence du. OutputResponsegives the response of a StateSpaceModel object ss with initial conditions .
• The state-space model ss can be given as StateSpaceModel, where a, b, c, and d represent the state, input, output, and transmission matrices in either a continuous-time or a discrete-time system:
 continuous-time system discrete-time system
• Transfer-function models are converted to state-space models before computing the output response.
• The output response:
 continuous-time system discrete-time system
• By default, the initial conditions and are assumed to be zero.
The output response of a transfer-function model to a sinusoidal input:
Visualize the response:
A response of a second-order system to a unit step input:
The response of a second-order system to a unit step input changes from pure oscillation for damping to an overdamped one for :
The response of a system from nonzero initial conditions:
The response of a discrete-time system to a sampled sinusoid:
The response of a two-output system to a delayed step input:
The response of a two-input discrete-time system to a ramp and decaying exponential signal:
The output response of a discrete-time system to a time-dependent input:
The response for :
The output response of a transfer-function model to a sinusoidal input:
 Out[1]=
Visualize the response:
 Out[2]=

A response of a second-order system to a unit step input:
 Out[1]=

The response of a second-order system to a unit step input changes from pure oscillation for damping to an overdamped one for :
 Out[1]=

The response of a system from nonzero initial conditions:
 Out[1]=
 Out[2]=

The response of a discrete-time system to a sampled sinusoid:
 Out[1]=
 Out[2]=

The response of a two-output system to a delayed step input:
 Out[1]=
 Out[2]=

The response of a two-input discrete-time system to a ramp and decaying exponential signal:
 Out[1]=

The output response of a discrete-time system to a time-dependent input:
 Out[1]=
The response for :
 Out[2]=
 Scope   (13)
The output response of a continuous-time system to a step input:
The response for various damping ratios:
The response of a state-space model:
The initial values of the states are assumed to be zero:
The output response for nonzero initial conditions:
Plot the response:
The output response for a system with two inputs:
If the number of input signals is less than the number of inputs of the system, the remaining input signals are assumed to be zero:
If a scalar input signal is specified for a multi-input system, the signal is applied to each input channel in turn:
If the time interval is specified, the result is computed numerically:
The symbolic result:
The results are equivalent:
The response of a generic continuous-time system:
The response to a sine wave:
The output response of a single-input system to a sampled sinusoid:
Plot of the sampled output with a zero-order hold:
The response of a two-input system:
The response of a first-order discrete-time system:
The response to a unit step sequence:
 Applications   (4)
Determine the steady-state output value of a stable first-order system in response to a unit step input:
The time constant:
Visualize it:
The steady-state output value of a stable second-order system to a unit step input:
The percent overshoot:
The peak time:
The rise time:
Plot the response:
Visualize the response of an unstable system, and its response after feedback stabilization:
The zero-input response of a system:
The natural response is determined by the poles of the system:
The poles:
For state-space models, OutputResponse and StateResponse give the same result if the output matrix is identity and the transmission matrix is zero:
For discrete-time systems excited with continuous-time inputs, more sample points are selected as the sampling period decreases:
The impulse response of a system:
OutputResponse assumes that the input is zero for :
Thus the solution obtained using InverseLaplaceTransform is different for :
A continuous-time system cannot be simulated with sampled inputs:
Discretize the system:
Computations with machine numbers can be unstable:
Rationalize the system:
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