Nonlinear System (2)

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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:

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

Type: 

Form: 

Model order: 

3

Time domain: 

Linearity: 

Autonomity: 

Publication details: 

TitleIdentification and Control of Bilinear Systems
Publication TypeConference Paper
Year of Publication1992
AuthorsBartee, James F., and Georgakis Christos
Conference NameAmerican Control Conference, 1992
Date Published06/1992
PublisherIEEE
Conference LocationChicago, Illinois
ISBN Number0-7803-0210-9
KeywordsAlgorithm design and analysis, Chemical processes, Continuous-stirred tank reactor, control system synthesis, Control systems, Control theory, linear systems, nonlinear control systems, nonlinear systems, process control
AbstractThe research presented in this paper combines the problem of identifiction and control of nonlinear processes. This is done by approximating the process with a bilinear model and designing model-based control structures (Reference System Controllers) based on the bilinear approximation. The identification of the bilinear model and the construction of the controller are described below. An example of the identification and control of an exothermic CSTR is also presented.
URLhttp://ieeexplore.ieee.org/xpl/articleDetails.jsp?tp=&arnumber=4792606&queryText%3DIdentification+and+Control+of+Bilinear+Systems

Nonlinear System (2)

Model description: 

Consider the nonlinear system

$$\begin{align*} y_{1}(k+1)&={{2.5y_{1}(k)y_{1}(k-1)}\over{1+y_{1}(k)^{2}+y_{2}(k-1)^{2}+y_{1}(k-2)^{2}}} \\ &+0.09u_{1}(k)u_{1}(k-1)+1.2u_{1}(k)+1.6u_{1}(k-2) \\ &+0.5u_{2}(k)+0.7\sin (0.5(y_{1}(k)+y_{1}(k-1))) \\ &\times\cos (0.5(y_{1}(k)+y_{1}(k-1))) \\ y_{2}(k+1)&=\displaystyle{{5y_{2}(k)y_{2}(k-1)}\over{1+y_{2}(k)^{2}+y_{1}(k-1)^{2}+y_{2}(k-2)^{2}}} \\ &+u_{2}(k)+1.1u_{2}(k-1)+1.4u_{2}(k-2) \\ &+0.5u_{1}(k). \end{align*}$$

The initial values are: $y_1(1)=y_1(3)=0$, $y_1(2)=1$, $y_2(1)=y_1(3)=0$, $y_2(2)=1$, $u(1)=u(2)=[0,0]^{\mathrm T}$

Type: 

Form: 

Model order: 

3

Time domain: 

Linearity: 

Autonomity: 

Publication details: 

TitleData-Driven Model-Free Adaptive Control for a Class of MIMO Nonlinear Discrete-Time Systems
Publication TypeJournal Article
Year of Publication2011
AuthorsHou, Zhongsheng, and Jin ShangTai
JournalIEEE Transactions on Neural Networks
Volume22
Issue12
Start Page2173
Pagination2173-2188
Date Published11/2011
ISSN1045-9227
ISBN Number12409274
Keywordsadaptive control, control system synthesis, convergence, discrete time systems, linearisation techniques, MIMO systems, nonlinear control systems, stability, tracking
AbstractIn this paper, a data-driven model-free adaptive control (MFAC) approach is proposed based on a new dynamic linearization technique (DLT) with a novel concept called pseudo-partial derivative for a class of general multiple-input and multiple-output nonlinear discrete-time systems. The DLT includes compact form dynamic linearization, partial form dynamic linearization, and full form dynamic linearization. The main feature of the approach is that the controller design depends only on the measured input/output data of the controlled plant. Analysis and extensive simulations have shown that MFAC guarantees the bounded-input bounded-output stability and the tracking error convergence.
DOI10.1109/TNN.2011.2176141