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Simulate nonlinear ARX model in Simulink software


System Identification Toolbox


The IDNLARX Model block simulates a nonlinear ARX (idnlarx) model for time-domain input and output data.


Input signal to the model.

For multi-input models, specify the input as an Nu-element vector, where Nu is the number of inputs. For example, you can use a Vector Concatenate block to concatenate scalar signals into a vector signal.

    Note:   Do not use a Bus Creator or Mux block to produce the vector signal.


Simulated output from the model.



Name of idnlarx variable in the MATLAB® workspace.

Initial conditions

Specifies the initial states as one of the following:

  • Input and output values: Specify the input and output levels, as follows:

    • Input level

      If known, enter a vector of length equal to the number of model inputs. If you enter a scalar, it is the signal value for all inputs.

    • Output level

      If known, enter a vector of length equal to the number of model's outputs. If you enter a scalar, it is the signal value for all outputs.

  • State values: When selected, you must specify a vector of length equal to the number of states in the model in the Vector of state values field.

    If you do not know the initial states, you can estimate these states, as follows:

    • To simulate around a given input level when you do not know the corresponding output level, you can estimate the equilibrium state values using the findop command.

      For example, to simulate a model M about a steady-state point where the input is 1 and the output is unknown, you can enter X0, such that:

      X0 = findop(M,'steady',1,NaN)
    • To estimate the initial states that provide a best fit between measured data and the simulated response of the model for the same input, use the findstates command.

      For example, to compute initial states such that the response of the model M matches the output data in the data set z, you can enter X0, such that:

      X0 = findstates(M,z,[],'sim')
    • To continue a simulation from a previous run, use the simulated input-output values from the previous simulation to compute the initial states X0 for the current simulation.

      For example, suppose that firstSimData is a variable that stores the input and output values from a previous simulation. For a model M, you can enter X0, such that:

      X0 = data2state(M,firstSimData)


Simulate Nonlinear ARX Model in Simulink®

Load the sample data.

load twotankdata

Create a data object from sample data.

z = iddata(y,u,0.2,'Tstart',0,'Name','Two tank system');
z1 = z(1:1000);

Estimate a nonlinear ARX model.

mw1 = nlarx(z1,[5 1 3],wavenet('NumberOfUnits',8));

Open a preconfigured Simulink model.

model = fullfile(matlabroot,'examples','ident','ex_idnlarx_block');

The model uses the Iddata Source, Nonlinear ARX Model, and Scope blocks. The following block parameters have been preconfigured to specify the estimation data, estimated model, and input and output levels:

1. Block parameters of Iddata Source block:

  • IDDATA Object - z1

2. Block parameters of Nonlinear ARX Model block:

  • Model - mw1

  • Initial conditions - Input and output values (default)

  • Input level - 10

  • Output level - 0.1

Run the simulation.

Click the Scope block to view the difference between measured output and model output.

To reduce the difference between the measured and simulated responses, estimate an initial state vector for the model from the estimation data, z1.

x0 = findstates(mw1,z1,[],'simulation');

Set the Initial Conditions block parameter value of the Nonlinear ARX Model block to State Values.

Specify initial states as x0.

Run the simulation, and view the difference between measured output and model output.


See Also

Related Commands

Topics in the System Identification Toolbox User's Guide

Introduced in R2008a

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