Output-Error Model Definitions

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) represents the system outputs
• u(k) represents 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 represents the system inputs
• y represents the system outputs
• e is the system disturbance
• ω is the auxiliary variable

SISO

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

$w\left(k\right)+f_{1}w\left(k-1\right)+...+f_{k_f}w\left(k-k_f\right)=b_{o}u\left(k-n\right)+b_{1}u\left(k-n-1\right)+...+b_{k_b-1}u\left(k-n-k_b+1\right)$

$y\left(k\right)=w\left(k\right)+e\left(k\right)$

where

• k_f is the F order
• k_b is the B order
• n is the system delay
• e(k) is the system disturbance
• w is the auxiliary variable