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Add model simulation blocks to your Simulink^{®} model from
the System
Identification Toolbox™ block library when you want to:

Represent the dynamics of a physical component in a Simulink model using a data-based nonlinear model.

Replace a complex Simulink subsystem with a simpler data-based nonlinear model.

You use the model simulation blocks to import the models you
identified using System
Identification Toolbox software from the MATLAB^{®} workspace
into the Simulink environment. For a list of System
Identification Toolbox simulation
blocks, see Summary of Simulation Blocks.

The following table summarizes the blocks you use to import models from the MATLAB environment into a Simulink model for simulation. Importing a model corresponds to entering the model variable name in the block parameter dialog box.

Block | Description |
---|---|

Idmodel | Simulate a linear identified model in Simulink software.
The model can be a process (`idproc` ), linear polynomial
(`idpoly` ), state-space (`idss` ),
grey-box (`idgrey` ) and transfer-function (`idtf` )
model. |

Nonlinear ARX Model | Simulate `idnlarx` model in Simulink. |

Hammerstein-Wiener Model | Simulate `idnlhw` model in Simulink. |

Nonlinear Grey-Box Model | Simulate nonlinear ODE (`idnlgrey` model
object) in Simulink. |

After you import the model into Simulink software, use the block parameter dialog box to specify the initial conditions for simulating that block. (See Specifying Initial Conditions for Simulation.) For information about configuring each block, see the corresponding reference pages.

For accurate simulation of a linear or a nonlinear model, you can use default initial conditions or specify the initial conditions for simulation using the block parameters dialog box.

Specify the initial states for simulation in the **Initial
states (state space only: idss, idgrey)** field of the Function
Block Parameters: Idmodel dialog box:

For

`idss`

and`idgrey`

models, initial states must be a vector of length equal to the order of the model.For models other than

`idss`

and`idgrey`

, initial conditions are zero.In some situations, you may want to match the simulated response of the model to a certain input/output data set:

Convert the identified model into state-space form (

`idss`

model), and use the state-space model in the block.Compute the initial state values that produce the best fit between the model output and the measured output signal using

`findstates`

.Specify the same input signal for simulation that you used as the validation data in the app or in the

`compare`

plot.For example:

% Convert to state-space model mss = idss(m); % Estimate initial states from data X0 = findstates(mss,z);

`z`

is the data set you used for validating the model`m`

. Use the model`mss`

and initial states`X0`

in the Idmodel block to perform the simulation.

The states of a nonlinear ARX model correspond to the dynamic
elements of the nonlinear ARX model structure, which are the model
regressors. *Regressors* can be the delayed input/output
variables (standard regressors) or user-defined transformations of
delayed input/output variables (custom regressors). For more information
about the states of a nonlinear ARX model, see the `idnlarx`

reference page.

For simulating nonlinear ARX models, you can specify the initial conditions as input/output values, or as a vector. For more information about specifying initial conditions for simulation, see the IDNLARX Model reference page.

The states of a Hammerstein-Wiener model correspond to the states
of the embedded linear (`idpoly`

or `idss`

)
model. For more information about the states of a Hammerstein-Wiener
model, see the `idnlhw`

reference
page.

The default initial state for simulating a Hammerstein-Wiener model is 0. For more information about specifying initial conditions for simulation, see the IDNLHW Model reference page.

This example shows how to set the initial states for simulating a model such that the simulation provides a best fit to measured input-output data.

To simulate the model using input `u2`

, use `x0(:,2)`

as
the initial states. `x0(:,2)`

is computed to maximize
the fit between the measured output, `y2`

, and the
response of `M`

.

To compute initial states that maximizes the fit to the corresponding
output `y2`

, and simulate the model using the second
experiment:

Extract the initial states that correspond to the second experiment for simulation.

X0est = x0(:,2);

Open the System Identification Toolbox library by typing the following command at the MATLAB prompt.

slident

Open a new Simulink model window. Then, drag and drop an

`Idmodel`

block from the library into the model window.Open the Function Block Parameters dialog box by double-clicking the

`Idmodel`

block. Specify the following block parameters:In the

**Model variable**field, type`M`

to specify the estimated model.In the

**Initial state**field, type`X0est`

to specify the estimated initial states. Click**OK**.

Drag and drop an

`Iddata Source`

block into the model window. Then, configure the model, as shown in the following figure.Simulate the model for 2 seconds, and compare the simulated output

`ysim`

with the measured output`ymeasured`

using the Scope block.

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