Performance limitations in the robust servomechanism problem for discrete-time LTI systems

IEEE Transactions on Automatic Control

Volumn 48, Issue 8, 2003, Pages 1299-1311

  Ben Jemaa, Lamia ^a   Davison, Edward J ^a  

^a UNIVERSITY OF TORONTO   (Canada)

Author keywords

Cheap control problem; Nonminimum phase; Optimal control; Performance limitations; Sampled systems; Servomechanism problem

Indexed keywords

COMPUTATIONAL COMPLEXITY; DISCRETE TIME CONTROL SYSTEMS; ERROR COMPENSATION; LINEAR CONTROL SYSTEMS; OPTIMAL CONTROL SYSTEMS; POLES AND ZEROS; RICCATI EQUATIONS; ROBUSTNESS (CONTROL SYSTEMS); SAMPLED DATA CONTROL SYSTEMS; SERVOMECHANISMS;

ALGEBRAIC RICCATI EQUATION; CHEAP CONTROL PROBLEM; NONMINIMUM PHASE; PERFORMANCE LIMITATIONS;

FEEDBACK CONTROL;

EID: 0042883910     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2003.815010     Document Type: Article

References (24)

1. E. J. Davison and B. M. Scherzinger, "Perfect control of the robust servomechanism problem," IEEE Trans. Automat. Contr., vol. AC-32, pp. 689-702, Aug. 1987.
2. L. Qiu and E. J. Davison, "Performance limitations of nonminimum phase systems in the servomechanism problem," Automatica, vol. 29, no. 2, pp. 337-349, 1993.
3. L. Qiu and J. Chen, "Time domain performance limitations of feedback control," in Mathematical Theory of Networks and Systems, A. Beghi, L. Finesso, and G. Picci, Eds. Padova Italy: II Poligrafo, 1998, pp. 369-372.
4. J. Chen, L. Qiu, and O. Toker, "Limitations on maximal tracking accuracy," IEEE Trans. Automat. Contr., vol. 45, pp. 326-331, Feb. 2000.
5. A. R. Woodyatt, J. S. Freudenberg, M. M. Seron, and R. H. Middleton, "Cheap control tracking performance for non-right-invertible systems," University of Newcastle, Newcastle, NSW, Australia, Tech. Rep. EE9818, 1998.
6. O. Toker, J. Chen, and L. Qiu, "Limitations on optimal tracking performance of discrete time systems," in Proc. Ameri. Control Conf., Albuquerque, NM, June 1997, pp. 3887-3892.
7. L. Ben Jemaa and E. J. Davison, "The perfect robust servomechanism problem for sampled LTI systems," in Proc. 4th IEEE Med. Symp. New Direction Control Automation, Maleme, Crete, June 10-14, 1996, pp. 298-303.
8. H. Kwakernaak and R. Sivan, Linear Optimal Control Systems. New York: Willy, 1972.
9. B. Priel and U. Shaked, "'Cheap' optimal control of discrete single input single output systems," Int. J. Syst., vol. 38, no. 6, pp. 1087-1113, June 1983.
10. U. Shaked, "A transfer function approach to the linear discrete stationary filtering and the steady-state discrete optimal control problems," Int. J. Control, vol. 29, no. 2, pp. 279-291, Jan. 1979.
11. L. Ben Jemaa and E. J. Davison, "Performance limitations in the robust servomechanism problem for sampled LTI systems," in Proc. 14th World IFAC Congr., vol. C. Beijing, China, July 1999, pp. 37-42.
12. E. J. Davison and S. H. Wang, "Properties and calculation of transmission zeros of linear multivariable systems," Automatica, vol. 10, pp. 643-658, 1974.
13. Z. Zhang and J. Freudenberg, "Discrete-time loop transfer recovery for systems with nonminimum phase zeros and time delays," Automatica, vol. 29, no. 2, pp. 351-363, Mar. 1993.
14. K. Zhou, J. C. Doyle, and K. Glover, Robust and Optimal Control. Upper Saddle River, NJ: Prentice-Hall, 1995.
15. E. J. Davison, "The robust control of a servomechanism problem for linear time-invariant multivariable systems," IEEE Trans. Automat. Contr., vol. AC-21, pp. 25-34, Jan. 1976.
16. A. Goldenberg and E. J. Davison, "The feedforward and robust control of a general servomechanism problem with time lag," in Proc. 8th Annu. Princeton Conf. Information Science Systems, 1974, pp. 80-84.
17. E. J. Davison and S. H. Wang, "Properties of LTI multivariable systems subject to arbitrary output and state feedback," IEEE Trans. Automat. Contr., vol. AC-18, pp. 24-32, Jan. 1973.
18. D. F. Delchamps, State Space and Input-Output Linear Systems. New York: Springer-Verlag, 1988.
19. K. J. Astrom, P. Hagander, and J. Sternby, "Zeros of sampled systems," Automatica, vol. 20, pp. 31-38, Jan. 1984.
20. T. Hagiwara, R. Yuasa, and M. Araki, "Stability and the limiting zeros of sampled-data systems with zero and first order holds," Int. J. Control, vol. 58, no. 6, pp. 1325-1346, 1993.
21. T. Hagiwara, "Analytical study on the intrinsic zeros of sampled-data systems," IEEE Trans. Automat. Contr., vol. 41, pp. 261-263, Feb. 1996.
22. J. R. MacLean, "Modeling and Control of a Flexible Beam," M.A.Sc. Thesis, Univ. Toronto, Toronto, ON, Canada, 1990.
23. H. H. Rosenbrock, Computer-Aided Control System Design. New York: Academic, 1974.
24. A. M. Krall, Stability Techniques for Continuous Linear Systems. New York: Gordon and Breach, 1967.