Application of nonlinear dynamic analysis to the identification and control of nonlinear systems—III. n-Dimensional systems

Abstract In two previous publications, the authors have shown that normal form theory, a method used extensively in dynamic analysis, can be applied in the structure identification of nonlinear systems. In particular, normal form theory bridges the gap between structure of a nonlinear, low order polynomial dynamical system and the behavior it is able to predict or represent. This is important because knowing a system's dynamic behavior automatically leads to a simple nonlinear normal form model that can be used for (nonlinear) control. Previously, only two-dimensional normal form models were derived. For this paper, simple, n -dimensional, low order polynomial dynamical models will be derived that can represent a nonlinear system with multiple steady states or a limit cycle in the operating region of interest. Using as a plant the nonisothermal Continuous Stirred Tank Reactor with consecutive reactions ( A → B → C ), it is shown that identification and control of this three-dimensional system using the aforementioned normal form models is feasible.

[1]  Yaman Arkun,et al.  Control of nonlinear systems using polynomial ARMA models , 1993 .

[2]  Ronald K. Pearson,et al.  Low Order Empirical Modeling for Nonlinear Systems , 1994 .

[3]  Kee Hoh Byeon,et al.  Analysis of the multiple hope bifurcation phenomena in a CSTR with two consecutive reactions—the singlularity theory approach , 1989 .

[4]  C. Kravaris,et al.  Synthesis of multivariable nonlinear controllers by input/output linearization , 1990 .

[5]  Martin Pottman,et al.  Identification of non-linear processes using reciprocal multiquadric functions , 1992 .

[6]  Stanley H. Johnson,et al.  Use of Hammerstein Models in Identification of Nonlinear Systems , 1991 .

[7]  P. Holmes,et al.  Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields , 1983, Applied Mathematical Sciences.

[8]  Arvind Varma,et al.  Dynamics of consecutive reactions in a CSTR—a case study , 1987 .

[9]  C. Kahlert,et al.  Chaos in a Continuous Stirred Tank Reactor with Two Consecutive First-Order Reactions, One Exo-, One Endothermic , 1981 .

[10]  Ali Cinar,et al.  Approximate Dynamic Models for Chemical Processes: A Comparative Study of Neural Networks and Nonlinear Time Series Modeling Techniques , 1992 .

[11]  S. Wiggins.  Introduction to Applied Nonlinear Dynamical Systems and Chaos , 1989 .

[12]  Bilinear Identification of Nonlinear Processes , 1994 .

[13]  Dan Luss,et al.  Exact steady-state multiplicity criteria for two consecutive or parallel reactions in lumped-parameter systems , 1982 .

[14]  R. Aris,et al.  More on the dynamics of a stirred tank with consecutive reactions , 1983 .

[15]  W. Harmon Ray,et al.  Application of nonlinear dynamic analysis in the identification and control of nonlinear systems—II. More complex dynamics , 1998 .