Feedback control strategies for a cerium-catalyzed Belousov–Zhabotinsky chemical reaction system

A number of control schemes including nonlinear feedback, dislocated feedback, and speed feedback have been proposed and assessed for a bromate-malonic acid-cerium Belousov–Zhabotinsky batch reaction process. The tuning parameters of the Oregonator model were firstly adjusted based on a UV-vis spectrophotometric analysis in the experimental part of the research. The adjusted Oregonator model successfully reproduced the innate induction time and periodicity of the BZ-batch system. Subsequently, the controllers were implemented and numerical simulations were carried out by employing the multi-stage Adomian decomposition method. The nominal analysis method was used to study the linear stability of each design. All the controlled systems were found to be linearly stable for certain continuous regions of controller gain. The performance of the proposed control laws was assessed and the dislocated feedback control strategy was shown to be able to drive the system states toward desired setpoints quickly. Furthermore, the validity of the dislocated feedback control design was doubly ensured by the sliding mode control theory. It was found that those feedback schemes which manipulate cerium ion concentration can be practically realized by means of electrochemical oxidation or oxygen aeration. Our results were confirmed by the Simulink software package and the block diagram representations are included in the paper.

[1]  R. Rach,et al.  An improved algorithm for calculation of the natural gas compressibility factor via the Hall‐Yarborough equation of state , 2014 .

[2]  John L. Hudson,et al.  The Belousov—Zhabotinskii reaction in a continuous flow reactor , 1976 .

[3]  Duu-Jong Lee,et al.  Effects of macromixing on the Oregonator model of the Belousov-Zhabotinsky reaction in a stirred reactor , 1994 .

[4]  G. Adomian.  A review of the decomposition method and some recent results for nonlinear equations , 1990 .

[5]  Hooman Fatoorehchi,et al.  Improving the differential transform method: A novel technique to obtain the differential transforms of nonlinearities by the Adomian polynomials , 2013 .

[6]  Richard J. Field,et al.  Simple models of deterministic chaos in the Belousov-Zhabotinskii reaction , 1991 .

[7]  Mohd. Salmi Md. Noorani,et al.  Further accuracy tests on Adomian decomposition method for chaotic systems , 2008 .

[8]  A. T. Winfree,et al.  The prehistory of the Belousov-Zhabotinsky oscillator , 1984 .

[9]  Congxu Zhu,et al.  Feedback control strategies for the Liu chaotic system , 2008 .

[10]  Jun-Sheng Duan.  Recurrence triangle for Adomian polynomials , 2010, Appl. Math. Comput..

[11]  D. Simakov,et al.  Effect of noise correlation on noise-induced oscillation frequency in the photosensitive Belousov-Zhabotinsky reaction in a continuous stirred tank reactor. , 2013, The journal of physical chemistry. A.

[12]  Christopher Edwards,et al.  Sliding mode control : theory and applications , 1998 .

[13]  George Adomian,et al.  The decomposition method applied to stiff systems , 1988 .

[14]  S. Spurgeon,et al.  Output feedback stabilization of SISO nonlinear systems via dynamic sliding modes , 1998 .

[15]  D. Barragán,et al.  Understanding the induction period of the Belousov-Zhabotinsky reaction , 2005 .

[16]  M. Koch,et al.  Effect of Oxygen on the Belousov-Zhabotinsky Reaction at Low Cerium Concentrations , 1999 .

[17]  R. M. Noyes,et al.  Oscillations in chemical systems. II. Thorough analysis of temporal oscillation in the bromate-cerium-malonic acid system , 1972 .

[18]  R. Rach,et al.  An accurate explicit form of the Hankinson–Thomas–Phillips correlation for prediction of the natural gas compressibility factor , 2014 .

[19]  Balaram Kundu,et al.  An analytical method for determination of the performance of a fin assembly under dehumidifying conditions: A comparative study , 2009 .

[20]  Dynamical behaviour of the Belousov–Zhabotinsky reaction in a fed-batch reactor , 2004 .

[21]  J. L. Hudson,et al.  Chaos in the Belousov-Zhabotinskii reaction , 1981 .

[22]  H. Fatoorehchi,et al.  A more realistic approach toward the differential equation governing the glass transition phenomenon , 2013 .

[23]  R. M. Noyes,et al.  Oscillations in chemical systems. IV. Limit cycle behavior in a model of a real chemical reaction , 1974 .

[24]  Abraham J. Arenas,et al.  Piecewise finite series solutions of seasonal diseases models using multistage Adomian method , 2009 .

[25]  Hooman Fatoorehchi,et al.  Approximating the minimum reflux ratio of multicomponent distillation columns based on the Adomian decomposition method , 2014 .

[26]  Lan Chen,et al.  Experimental study of chaos synchronization in the Belousov–Zhabotinsky chemical system , 2004 .

[27]  Effects of positive electrical feedback in the oscillating Belousov–Zhabotinsky reaction: Experiments and simulations , 2006 .

[28]  Randolph Rach,et al.  A new definition of the Adomian polynomials , 2008, Kybernetes.

[29]  R. J. Field,et al.  Simulation of the effect of stirring rate on bistability in the bromate-cerium(III)-bromide CSTR reaction , 1992 .

[30]  V. Jayalakshmi,et al.  Influence of working electrodes in Belousov–Zhabotinsky oscillatory system , 1997 .

[31]  Chunde Yang,et al.  Speed feedback control of chaotic system , 2004 .

[32]  Z. A. Schelly,et al.  Explodator: A new skeleton mechanism for the halate driven chemical oscillators , 1984 .

[33]  Abdul M. Siddiqui,et al.  Use of Adomian decomposition method in the study of parallel plate flow of a third grade fluid , 2010 .

[34]  Sang J. Chung,et al.  Mediated electrochemical oxidation process: Electro-oxidation of cerium(III) to cerium(IV) in nitric acid medium and a study on phenol degradation by cerium(IV) oxidant , 2007 .

[35]  Lucas Jódar,et al.  Piecewise finite series solution of nonlinear initial value differential problem , 2009, Appl. Math. Comput..

[36]  Jamal M. Nazzal,et al.  Chaos control using sliding-mode theory , 2007 .

[37]  Jun-Sheng Duan,et al.  An efficient algorithm for the multivariable Adomian polynomials , 2010, Appl. Math. Comput..

[38]  Rebirth of a dead Belousov-Zhabotinsky oscillator. , 2011, The journal of physical chemistry. A.

[39]  Luis Casasús,et al.  The decomposition method for stiff systems of ordinary differential equations , 2005, Appl. Math. Comput..

[40]  Tamás Turányi,et al.  Mechanistic details of the oscillatory Belousov-Zhabotinskii reaction , 1990 .

[41]  A. Rèpaci,et al.  Nonlinear dynamical systems: On the accuracy of adomian's decomposition method , 1990 .

[42]  Jun-Sheng Duan,et al.  Convenient analytic recurrence algorithms for the Adomian polynomials , 2011, Appl. Math. Comput..

[43]  Congxu Zhu,et al.  Feedback control methods for stabilizing unstable equilibrium points in a new chaotic system , 2009 .

[44]  Randolph Rach,et al.  A convenient computational form for the Adomian polynomials , 1984 .

[45]  R. Blittersdorf,et al.  Continuous control of chemical chaos by time delayed feedback , 1993 .

[46]  R. Rach,et al.  An Efficient Numerical Scheme to Solve a Quintic Equation of State for Supercritical Fluids , 2015 .

[47]  E. S. Ismail,et al.  Accuracy of the Adomian decomposition method applied to the Lorenz system , 2006 .