Multi-loop decentralized PID control based on covariance control criteria: An LMI approach

ISA Transactions

Volumn 43, Issue 1, 2004, Pages 49-59

  Huang, Xin ^a   Huang, Biao ^a  

^a UNIVERSITY OF ALBERTA   (Canada)

Author keywords

Covariance control; LMI; PID; Semidefinite programming

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; COMPUTATIONAL METHODS; COMPUTER SIMULATION; MATRIX ALGEBRA; PROBLEM SOLVING; STATE SPACE METHODS; STATISTICAL METHODS; STOCHASTIC CONTROL SYSTEMS; VECTORS;

COVARIANCE CONTROL; LINEAR MATRIX INEQUALITY (LMI); PROPORTIONAL-INTEGRAL-DERIVATIVES (PID); SEMIDEFINITE PROGRAMMING;

DECENTRALIZED CONTROL;

EID: 0742304413     PISSN: 00190578     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0019-0578(07)60019-6     Document Type: Article

References (27)

1. Ziegler, J. G. and Nichols, N. B., Optimum settings for automatic controllers. Trans. ASME 62, 759-768 (1942).
2. Cohen, G. H. and Coon, G. A., Theoretical considerations of retarded control. Trans. ASME 75, 827-834 (1953).
3. Åström, K. J. and Hagglund, T., PID Controller, 2nd ed. Instrument of Society of America, Research Triangle Park, NC, 1995.
4. Morari, M. and Zafiriou, E., Robust Process Control. Prentice-Hall, Englewood Cliffs, NJ, 1989.
5. Rivera, D. E., Morari, M., and Skogestad, S., Internal model control - PID control design. Ind. Eng. Chem. Process Des. Dev. 25, 252-265 (1986).
6. Bao, J., Forbes, J. F., and McLellan, P. J., Robust multi-loop PID controller design - A successive semi-definite programming approach. Ind. Eng. Chem. Res. 38, 3407-3419 (1999).
7. Feng, Z., Wang, Q. G., and Lee, T. H., On the design of multivariable PID controllers via LMI approach. Automatica 38, 517-526 (2002).
8. Ge, M., Chiu, M., and Wang, Q. G., Robust PID controller design via LMI approach. J. Process Control 12, 3-13 (2002).
9. Shunta, J. P., Achieving World Class Manufacturing through Process Control. Prentice-Hall PTR, Englewood Cliffs, NJ, 1995.
10. Kowk, K. E., Ping, M. C., and Li, P., A model based augmented PID algorithm. J. Process Control 10, 9-18 (2000).
11. Miller, R. M., Kwok, K. E., Shah, S. L., and Wood, R. K., Development of a stochastic predictive PID controller. Proceedings of American Control Conf., 1995, pp. 4204-4208.
12. Miura, N., Imaeda, M., Hashimoto, K., Wood, R. K., Hattori, H., and Onishi, M., Auto-tuning PID controller based on generalized minimum variance control for a PVC reactor. J. Chem. Eng. Jpn. 31, 626-632 (1998).
13. Sato, T., Inoue, A., and Hirashima, Y., Self-tuning two-degree-of freedom PID controller reducing the effect of disturbance. Am. Control. Conf., 2002, pp. 3997-4002.
14. Yamamoto, T., Inoue, A., and Shah, S. L., Generalized minimum variance self-tuning pole-assignment controller with a PID structure. Proc. IEEE Int. Conf. on Control Appl., Hawaii, 1999, pp. 125-130.
15. Gahinet, P., Nemirovski, A., Laub, A., and Chilali, M., LMI Control Toolbox. The Mathworks, Natick, MA, 1995.
16. Åström, K. J., Introduction to Stochastic Control Theory. Academic Press, New York, 1970.
17. Kalman, R. E., Contribution to the theory of optimal control. Bol. Soc. Mat. Mex. 5, 102-119 (1960).
18. MacGregor, J. F., Optimal discrete stochastic control theory for process application. Can. J. Chem. Eng. 51, 468-478 (1973).
19. Mäkilä, P. M., Westerlund, T., and Toivonen, H. T., Constrained linear quadratic Guassian control with process applications. Automatica 20, 15-29 (1984).
20. Skelton, R. and Iwasaki, T., Liapunov and covariance controller. Int. J. Control 57, 519-536 (1993).
21. Skelton, R., Iwasaki, T., and Grigoriadis, K., A Unified Algebraic Approach to Linear Control Design. Taylor & Francis, London, 1998.
22. Huang, X., Zhang L. Q., and Huang, B., LQG Control with the Generalized Covariance Constraints for Discrete-Time Systems. CSCHE, Vancouver, 2002.
23. Boyd, S., El Ghaoui, L., Feron, E., and Balakrishnan, V., Linear Matrix Inequalities in Systems and Control Theory. SIAM, Philadelphia, PA, 1994.
24. El Ghaoui, L., Oustry, F., and AitRami, M., A cone complementarity linearization algorithm for static output feedback and related problem. IEEE Trans. Autom. Control 42, 1171-1176 (1997).
25. Qin, J., Control performance monitoring - A review and assessment. Comput. Chem. Eng. 23, 178-186 (1998).
26. Ogunnaike, B. A. and Harmon Ray, W., Process Dynamics, Modeling and Control. Oxford University Press, New York, 1994.
27. Inoue, A., Yanou, A., Sato, T., and Hirashima Y., An extension of generalized minimum variance control for multi-input multi-output system using coprime factorization approach. Am. Control. Conf., 2000, pp. 4184-4188.