InputOutputResponse

InputOutputResponse[sys,u,tspec]

gives the response of the input-output model sys with input signals u and temporal specification tspec.

InputOutputResponse[sys,,"prop"]

gives the value of property "prop".

Details and Options

  • InputOutputResponse is also known as simulation.
  • InputOutputResponse is typically used to simulate a complete system such as a plant and controller together to accurately analyze system behavior, verify performance and measure controller effort.
  • The results are computed by solving the underlying equations of sys. Generally, they are ordinary differential or difference equations or their combination for mixed continuous- and discrete-time systems.
  • For mixed continuous- and discrete-time systems, the result is continuous-time but typically piecewise in value.
  • For systems represented as a SystemsConnectionsModel, all the internal signals can also be computed.
  • The input-output model sys can have the following forms:
  • TransferFunctionModel[]transfer-function model
    StateSpaceModel[]state-space model
    AffineStateSpaceModel[]affine state-space model
    NonlinearStateSpaceModel[]nonlinear state-space model
    DiscreteInputOutputModel[]discrete input-output model
    SamplerModel[]sampler model
    HolderModel[]holder model
    SystemsConnectionsModel[]connections model
  • InputOutputResponse[{sys,ics},] can be used to specify initial conditions ics.
  • The input signal u can have the following forms:
  • {u1[t],,up[t]}continuous-time signals ui[t] as functions of time t
    {{u11,,u1k},,{up1,,upk}}discrete-time signal sequences {ui1,,uik}
    {,ui[t],,{uj1,,ujk},}a combination of continuous- and discrete-time signals
  • The temporal specification tspec can have the following forms:
  • tcompute the symbolic solution as a function of
    {t,0,tmax}compute the numeric or symbolic solution for
  • The property "prop" can have the following forms:
  • "Data"the InputOutputResponseData object
    "OutputResponse"output response as a list
    "OutputResponseAssociation"the output response as an association
    "PropertyAssociation"property names and values as an association
    "PropertyDataset"property names and values as a Dataset
    "StateResponse"state response as a list
    "StateResponseAssociation"
  • state response as an association
  • "SubsystemOutputResponse"output response of subsystems as a list
    "SubsystemOutputResponseAssociation"output response of subsystems as an association
    {p1,p2,}values of properties pi
  • InputOutputResponse accepts a Method option that can take the following values:
  • "DSolve"DSolve
    "Integrate"Integrate
    "Iterate"iterate to get the solution
    "NDSolve"NDSolve
    "RecurrenceTable"RecurrenceTable
    "RSolve"RSolve
    "Sum"Sum
  • With Method{m,opt1val1,}, method m is used with option opti set to value vali.

Examples

open allclose all

Basic Examples  (4)

The unit step response of a second-order transfer-function model:

The impulse response of a mass-spring-damper system:

The response of a 2-input, 1-output connections model:

Plot the output response:

Compute the result as a data object:

Obtain the output response:

The output response of all subsystems:

All available properties:

Scope  (31)

Basic Uses  (9)

Simulate the response of a system to a unit-step input:

Compute a symbolic solution:

Compute the response of a state-space model:

Compute the state response:

Specify initial conditions:

The response starts from the specified values:

The response of a multiple-input system:

If fewer signals are specified, default values that are usually 0 are chosen for the remaining inputs:

For discrete-time systems, the input signal is a discrete sequence:

An input sequence can be generated from a time specification:

The input sequence is generated taking the sampling period of the system into consideration:

Specifying the input sequence directly gives the same result:

They are indeed the same:

Models  (11)

The response of a transfer-function model to a sinusoid:

Simulate it numerically:

They are the same:

The response of a state-space model to a unit-step input:

The response of a delay model to a sinusoid:

The response of the system with no delays:

Compare the two responses:

The response of a descriptor model to a unit-step input:

The response of an affine state-space model:

A nonlinear state-space model:

A discrete input-output model:

A sampler model:

A holder model:

A systems connections model:

Obtain the responses of the subsystems of a sampled data system:

Plot them:

Properties  (11)

Compute a single property:

Compute a list of properties:

Compute the data object first:

Obtain properties from the data object:

List computable properties:

Obtain all properties as an association:

Obtain all properties as a dataset:

The state response:

The state response as an association:

Obtain the state response of the fourth subsystem:

The output response:

The output response as an association:

The output response of the subsystems:

The output response of the subsystems as an association:

The outputs of the fifth subsystem:

Properties & Relations  (2)

Superposition principle for linear systems:

The additive property states that the response to a sum of inputs is the same as the sum of the responses to individual inputs:

The homogeneity property states that the response to an input multiplied by a scalar is the same as the response multiplied by the same scalar:

The sinusoidal responses of linear systems can be seen in a Bode plot:

The response of the system to an input signal of frequency :

After the transients are gone, the response is essentially identical to the input signal:

The gain is 1 and the phase lead is 0:

The response of the system to an input signal of frequency :

After the transients are gone, the response is another pure sinusoid:

Compute a time instance when the response peaks:

The gain:

Compute a time instance when the input signal peaks:

The phase lead in radians:

Points on the Bode magnitude plot for the two input sinusoids:

Points on the Bode phase plot for the two input sinusoids:

The Bode plot:

Wolfram Research (2023), InputOutputResponse, Wolfram Language function, https://reference.wolfram.com/language/ref/InputOutputResponse.html.

Text

Wolfram Research (2023), InputOutputResponse, Wolfram Language function, https://reference.wolfram.com/language/ref/InputOutputResponse.html.

CMS

Wolfram Language. 2023. "InputOutputResponse." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/InputOutputResponse.html.

APA

Wolfram Language. (2023). InputOutputResponse. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/InputOutputResponse.html

BibTeX

@misc{reference.wolfram_2024_inputoutputresponse, author="Wolfram Research", title="{InputOutputResponse}", year="2023", howpublished="\url{https://reference.wolfram.com/language/ref/InputOutputResponse.html}", note=[Accessed: 21-April-2024 ]}

BibLaTeX

@online{reference.wolfram_2024_inputoutputresponse, organization={Wolfram Research}, title={InputOutputResponse}, year={2023}, url={https://reference.wolfram.com/language/ref/InputOutputResponse.html}, note=[Accessed: 21-April-2024 ]}