A Stabilization Approach of a CSTR with Two Arbitrarily Switching Modes Using a Common Control Lyapunov Function

Abdessamad Abdelhedi(1*), Lassaâd Sbita(2)

(1) National Engineering School of Gabes, Research Unit of Photovoltaic, Wind and Geothermal Systems, University of Gabes, Gabes, Tunisia
(2) National Engineering School of Gabes, Research Unit of Photovoltaic, Wind and Geothermal Systems, University of Gabes, Gabes, Tunisia
(*) Corresponding author


DOI's assignment:
the author of the article can submit here a request for assignment of a DOI number to this resource!
Cost of the service: euros 10,00 (for a DOI)

Abstract


This paper presents a study of stabilization for a class of the nonlinear switched systems. This study, indeed, is based on stabilization by using control Lyapunov functions. Firstly, a necessary and sufficient condition of stabilization is clarified. This condition hinges on the existence of a common control Lyapunov functions in the switching subsystems. The common controlled Lyapunov function is explicitly built by using controlled Lyapunov functions associated with the sub-systems. Secondly, a stabilization controller is designed for the nonlinear switching system by using the common Lyapunov function theory. Lastly, to illustrate this study, the example of a continuous stirred tank reactor (CSTR) with two modes is deemed to show the applicability of the suggested approach.
Copyright © 2013 Praise Worthy Prize - All rights reserved.

Keywords


Switched Systems; Stabilization; Control Lyapunov Functions; CSTR

Full Text:

PDF


References


G.K. Fourlas, K.J. Kyriakopoulos, and C.D. Vournas, Hybrid systems modeling for power systems, IEEE Circuits and Systems Magazine, Vol. 4 (Issue 3):16-23, octobre 2004.

M.B. Yazdi, and M.R. Jahed-Motlagh , Stabilization of a CSTR with two arbitrarily switching modes using modal state feedback linearization, Chemical Engineering Journal , Vol. 155(Issue 3):838-843, December 2009.

P.I. Barton, and Ch. Kun Lee, Modeling, simulation, sensitivity analysis, and optimization of hybrid systems, ACM Transactions on Modeling and Computer Simulation - TOMACS, Vol. 12(Issue 4):256-289, 2002.

Z.H. Guan, D.J. Hill, and X. Shen, On Hybrid Impulsive and Switching Systems and Application to Nonlinear Control, IEEE Transactions on automatic control, Vol. 50(Issue 7):1058-1062, July 2005

Z. Jia, L. Wang, X. Guo, Design of switching sequences for controllability realization of switched linear systems, Automatica, Vol. 43(Issue 4):662-668, 2007.

M.B Yazdi, M.R. Jahed-Motlagh, S.A. Attia, and J. Raisch, Modal exact linearization of a class of second-order switched nonlinear systems, Nonlinear Analysis: Real World Applications Vol. 11(Issue 4):2243-2252, 2010

J. Lygeros, D.N. Godbole, and S. Sastry, Verified hybrid controllers for automated vehicles, IEEE Transactions on Automatic Control, Vol. 43(Issue 4):522-539, 1998

J. Zhao, and D.J. Hill, On stability, L2-gain and H∞ control for switched systems, Automatica (Journal of IFAC), Vol. 44(Issue 5):1220-1232, May 2008

Abderrezak, H., Hafsaoui, A., Bouazza, S.E., Hybrid model for insulation active component control in an isolated neutral electrical network, (2008) International Review of Electrical Engineering (IREE), 3 (3), pp. 484-490.

J. Tan, N. Xi, and Y. Wang, A singularity-free motion control algorithm for robot manipulators-A hybrid system approach, Automatica, Vol. 40(Issue 7):1239-1245, July 2004

K. Artiouchine, P. Baptiste, and J. Mattioli, On modeling a dynamic hybrid system with constraints: Computing aircraft landing trajectories, INFORMS Journal on Computing, Vol. 20(Issue 2):222-233, 2008.

Z. Sun, A note on marginal stability of switched systems, IEEE Transactions on Automatic Control, Vol. 53(Issue 2):625-631, 2008

D. Liberzon, Swithcing in Systems and Control. Systems and Control, Foundation and Applications. (Birkhäuser, 2003, pp 17-39)

X. Xu, and P. Antsaklis, Stabilization of second-order LTI switched system, International Journal of Control , Vol. 73(Issue 14):1261-1279, September 2000.

L. Ozkan, and M.V. Kothare, Stability analysis of a multi-model predictive control algorithm with application to control of chemical reactors, Journal of Process Control, Vol. 16(Issue 2):81-90, 2006.

R.A. Decarlo, M.S. Branicky, S. Pettersson, and B, Lennartson, Perspective and results on the stability and stabilizability of hybrid systems, Proceding of the. IEEE, Vol. 88(Issue 7):1069–1082, Jul 2000.

M.B. Yazdi, M.R. Jahed-Motlagh, S.A. Attia, J. Raisch, Switched Feedback Equivalence of a Class of Planar Switched, Nonlinear Systems, Joint 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference, pp 4264-4269, Shanghai, China, December 2009.

J. Ben Salah, C. Valentin, H. Jerbi, and C.Z. Xu, Geometric synthesis of a hybrid limit cycle for the stabilizing control of a class of nonlinear switched dynamical systems, Systems & Control Letters, Vol. 60(Issue 12):967-976, december 2011.

M. Branicky, Multiple Lyapunov functions and other analysis tools for switched and hybrid systems, IEEE Transactions on Automatic Control, Vol. 43(Issue 4):475-482, April 1998.

Jafarboland, M., Nekoubin, A., Finite-element analysis of permanent magnets structure and switching angle effects on the efficiency of two-phase brushless DC motor, (2010) International Review of Electrical Engineering (IREE), 5 (5), pp. 2013-2021.

R. Shorten, F. Wirth, O. Mason, K. Wulff, and C. King, Stability Criteria for Switched and Hybrid Systems, SIAM Review, Vol. 49(Issue 4):545-592, 2007.

M. Branicky, Multiple Lyapunov functions and other analysis tools for switched and hybrid systems, IEEE Transactions on Automatic Control, Vol. 43(Issue 4):475-482, 1998.

S. Mitra, N. Lynch, D. Liberzon, Verifying average dwell time by solving optimization problems, in: J. Hespanha,A.Tiwari(Eds.), Hybrid Systems:Computation and Control (Springer-Verlag , 2006, pp. 476-490).

H. Sun, J. Zhao, Control Lyapunov functions for switched control systems. Proccedings of the Amrican Control Conference, Vo1. 3, pp. 1890–1891, Arlington, USA, June 2001.

R. Bourdais, E. Moulay, W. Perruquettia, Stabilization of nonlinear switched systems using control Lyapunov functions, Proceedings of the International Conference on Hybrid Systems and Applications, Vol. 1(Issue 4):482–490, LA, USA, December 2007.

J.L. Mancilla-Aguilar et R.A. García. A converse Lyapunov theorem for nonlinear switched systems. Systems & Control Letters, Vol. 41(Issue 1):67–71, 2000.

N.H. EI-Farra, P. Mhaskar, P.D. Christofides, Output feedback control of switched nonlinear systems using multiple lyapunov functions, System and Control Letters Vol. 54(Issue 12):1163-1182, December 2005

J. Daafouz, P. Riedinger, and C. Iung, Stability analysis and control synthesis for switched systems: A switched Lyapunov function approach, IEEE Transactions on Automatic Control, Vol. 47(Issue 11):1883–1887, 2002.

M. Heymann, Feng Lin, G. Meyer, S Resmerita, Analysis of Zeno behaviors in a class of hybrid systems, IEEE Transactions on Automatic Control, Vol. 50(Issue 3):376-83, March 2005.

R.Chibani, E.M. Berkouk and M.S.Boucherit, Lyapunov control of three-level PWM rectifiers to equilibrate input DC voltages of five-level NPC-VSI, (2007) International Review of Electrical Engineering (IREE), 2 (1), pp. 36-49.

J. L. Mancilla-Aguilar, R. Garcia, E. Sontag, and Y. Wang, On the representation of switched systems with inputs by perturbed control systems, Nonlinear Analysis-theory Methods & Applications, Vol. 60(Issue 6):1111-1150, 2005.

E. Mickael. Continuous selections. Annals of Mathematics, Vol. 63(Issue 2):361–382, march 1956.

Y. Lin and E.D. Sontag, A universal formula for stabilization with bounded controls. Systems & Control Letters, Vol. 16(Issue 6):393–397, 1991.


Refbacks

  • There are currently no refbacks.



Please send any question about this web site to info@praiseworthyprize.com
Copyright © 2005-2021 Praise Worthy Prize