Optimal Control of Nonlinear Multivariable Systems

Document Type: Research Article

Authors

Department of Chemical and Petroleum Engineering, Sharif University of Technology, Tehran, I.R. IRAN

Abstract

This paper concerns a study on the optimal control for nonlinear systems. An appropriate alternative in order to alleviate the nonlinearity of a system is the exact linearization approach. In this fashion, the nonlinear system has been linearized using input-output feedback linearization (IOFL). Then, by utilizing the well developed optimal control theory of linear systems, the compensated nonlinear system has been controlled. Thus, the structure of the objective function will be converted into a quadratic form which is qualitativly comparable with usual cost functions, and from operating viewpoint is more favorable. To qualify such a procedure, it has been applied to two minimum and nonminimum-phase chemical processes, and its performance is verified through computer simulations.

Keywords


[1] Robinson , D., Chen, R., McAvoy, T., and Schnelle, P. D., An Optimal Control Based Approach to Designing Plant-wide Control System Architecture, Journal of Process Control, p. 223 (2001). 

[2] Prata, A., Oldenburg, J., Kroll, A. and Marquardt, W., Integrated Scheduling and Dynamic Optimization of Grade Transitions for a Continuous Polymerization Reactor, Comp. Chem. Eng.,31(2007).

[3] Hunt, R.L., Su, R. and Meyer, G., Design for Multi-Input Nonlinear Systems, Differential Geometric Control Theory, Birkhauser, Boston, p. 268 (1983).

[4] Ha, I.J. and Gilbert, E.G., A Complete Characterization of Decoupling Control Laws for General Class of Nonlinear Systems, IEEE Trans. Autom. Contr., AC-31, 823(1986).

[5] Kravaris, C. and Soroush, M., Synthesis of Multivariable Nonlinear Controllers by Input/Output Linearization, AICHE Journal, p. 249 (1990).

[6] Daoutidis, P., Soroush,  M. and   Kravaris, C., Feedforward/Feedback Control of Multivariable Nonlinear Processes, AICHE Journal, p. 1471 (1990).

[7] Guardabassi, G.O. and Savaressi, S.M., Approximate Linearization via feedback- an Overview, Automatica, 37, p. 1 (2001).

[8] Kravaris, C., Daoutidis, P. and Wright, R. A., Output Feedback Control of Non-Minimum-Phase Nonlinear Processes, Chemical Engineering Science, 49,
p. 2107 (1994).

[9] Niemeic, M. P. and Kravaris, C., Nonlinear Model-State Feedback Control for Non-Minimum-Pphase Processes, Automatica, 39, p. 1295 (2003).

[10] Kravaris, C., Niemiec, M.P. and Kazantzis, N., Singular PDEs and the Assignment of Zero Dynamics in Nonlinear Systems, Systems and Control Letters, 51, p. 67 (2004).

[11] Doyle, F. J., Allgower, F., Oliveria, S., Gilles E. and Morari, M., On Nonlinear Systems with Poorly Behaved Zero Dynamics, Proceedings of the American Control Conference, p. 2571 (1992).

[12] McLain,  R.B.,  Kurtz,  M.J.,  Henson, M.A.,  and Doyle, F.J., Habituating Control for Non-Square Nonlinear Processes, Industrial and Engineering Chemistry Research, 34, p. 4067 (1996).

[13] Kolavennu, S., Palanki, S. and Cockburn, J.C., Nonlinear Control of Nonsquare Multivariable Systems, Chemical Engineering Science, 56, p. 2103 (2001).

[14] Soroush, M. and Kravaris, C., Nonlinear Control of a Polymerization CSTR with Singular Characteristic Matrix, AICHE Journal, 40, p. 980 (1994).

[15] Bryson, A. E. and Ho, Y. C., Applied Optimal Control, Hemisphere(1975).

[16] Agrawal, S. K. and Fabien, B.C., “Optimization of Dynamic Systems”, Kluwer Academic Publishers(1999).

[17] Isidori, A., “Nonlinear Control Systems”, 2nd Ed., Berlin: Springer, (1989).

[18] Engell, S. and Klatt, K.U., Nonlinear Control of a Non-Minimum-Phase CSTR, Proceedings of the ACC, San Francisco, CA, USA, 2341(1993).