Discrete bilinear plant

Third-order nonlinear discrete-time system #2

Model description: 

Image below shows the block diagram of a discrete-time system.

$$\begin{align*} H_1(z) &=\dfrac{0.2z^{-1}}{z^{-1}-0.21z^{-2}} \\ H_2(z) &=\dfrac{0.1z^{-1}}{1-1.1z^{-1}+0.3z^{-2}} \\ H_3(z) &=\dfrac{0.3z^{-1}}{1-0.4z^{-1}} \end{align*}$$

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Model order: 

3

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Linearity: 

Publication details: 

TitleNonlinear system identification using genetic algorithms with application to feedforward control design
Publication TypeConference Paper
AuthorsLuh, Guan-Chun, and Rizzoni G.

Third-order nonlinear discrete-time system #1

Model description: 

The block diagram of a third-order nonlinear discrete time system adopted by Fakhouri for identification evaluation is shown below.

$$\begin{align*} H_1(z) &=\dfrac{0.1z^{-1}}{1-0.5z^{-1}} \\ H_2(z) &=\dfrac{0.1z^{-1}}{1-1.3z^{-1}+0.42z^{-2}} \\ H_3(z) &=\dfrac{1.0z^{-1}}{1-0.7z^{-1}} \end{align*}$$

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Model order: 

3

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Publication details: 

TitleNonlinear system identification using genetic algorithms with application to feedforward control design
Publication TypeConference Paper
AuthorsLuh, Guan-Chun, and Rizzoni G.

Continuous stirred-tank reactor system

Model description: 

The following CSTR system developed by Liu(1967). The reaction is exothermic first-order, $A \rightarrow B$, and is given by the following mass and energy balances. One should notice that the energy balance includes cooling water jacket dynamics. The following model was identified using regression techniques on the energy balance equations:

$$\begin{align*} y(k) &= 1.3187y(k-1) - 0.2214y(k-2) - 0.1474y(k-3) \\ &- 8.6337u(k-1) + 2.9234u(k-2) + 1.2493u(k-3) \\ &- 0.0858y(k-1)u(k-1) + 0.0050y(k-2)u(k-1) \\ &+ 0.0602y(k-2)u(k-2) + 0.0035y(k-3)u(k-1) \\ &- 0.0281y(k-3)u(k-2) + 0.0107y(k-3)u(k-3). \end{align*}$$

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Model order: 

3

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Publication details: 

TitleIdentification and Control of Bilinear Systems
Publication TypeConference Paper
AuthorsBartee, James F., and Georgakis Christos

Generic nonlinear system 2

Model description: 

$$\begin{align*} x_1(k+1) &= 0.9x_1(k)\sin{[x_2(k)]} + \left(2 + 1.5 \dfrac{x_1(k)u_1(k)}{1+x_1^2(k)u_1^2(k)}\right)u_1(k) + \left(x_1(k) + \dfrac{2x_1(k)}{1+x_1^2(k)}\right)u_1(k)\\ x_2(k+1) &= x_3(k)(1+\sin{[4x_3(k)]}+ \dfrac{x_3(k)}{1+x_3^2(k)}\\ x_3(k+1) &= (3 + \sin{[2x_1(k)]})u_2(k)\\ y_1(k)&=x_1(k)\\ y_2(k)&=x_2(k) \end{align*}$$

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Form: 

Model order: 

3

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Linearity: 

Publication details: 

TitleAdaptive control of nonlinear multivariable systems using neural networks
Publication TypeConference Paper
AuthorsNarendra, K.S., and Mukhopadhyay S.

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