Output-Error Model Definitions (System Identification Toolkit)

LabVIEW System Identification Toolkit

Output-Error Model Definitions (System Identification Toolkit)

When A(z), C(z), and D(z) equal 1, the general-linear polynomial model reduces to the output-error model. This model describes the system dynamics separately from the stochastic dynamics. The output-error model does not use any parameters for simulating the disturbance characteristics.

Use the SI Estimate OE Model VI to estimate output-error models. The identification method of the output-error model is the prediction error method, which is the same as that of the ARMAX model. If the disturbance e(k) is white noise, all minima are global. However, a local minimum can exist if the disturbance is not white noise.

The following equation shows the form of the output-error model.

where y(k) is the system outputs
u(k) is the system inputs
n is the system delay
e(k) is the system disturbance

B(z) and F(z) are polynomials with respect to the backward shift operator z –1 and defined by the following equations.

The following figure depicts the signal flow of an output-error model.

where u is the system inputs
e is the system disturbance
y is the system outputs


The following are the time domain equations for the output-error SISO model.

where kf is the F order
kb is the B order
n is the system delay
e(k) is the system disturbance

Refer to the Estimate Polynomial Models VI in the labview\examples\System Identification\Getting Started\Parametric Estimation.llb for an example that demonstrates how to estimate Output-Error models for an unknown system.

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