Robust sliding mode control of multivariable time-delay systems

• Autorzy: Jafarov E.M.
• Języki publikacji: EN

Abstrakty

EN

In this paper, robust stabilization of multivariable single state-delayed systems with mismatching parameter uncertainties and matching/mismatching external disturbances is considered. To achieve this goal two types of robust sliding mode controller design techniques are advanced. The first one is an integral sliding mode controller design modification to Shyu and Yan type controller design. By using the Lyapunov-Razumikhin-Hale method the mismatching sliding conditions are parametrically obtained and formulated in terms of matrix norm inequalities. In the second contribution, a new combined sliding mode controller design technique for the stabilization of multivariable single state-delayed systems with mismatching parameter perturbations are advanced by using Lyapunov-Krasovskii V-functional method. The sliding, global stability and β-stability conditions are parametrically obtained and formulated in terms of matrix inequalities. Numerical examples with simulation results show the effectiveness of design procedures.

Słowa kluczowe

EN

control equipment; stabilization; perturbation techniques; matrix algebra; computer simulation; linear systems

• Wydawca: Oficyna Wydawnicza Politechniki Wrocławskiej
• Czasopismo: Systems Science
• Rocznik: 2003
• Tom: Vol. 29, nr 3
• Strony: 17--36
• Opis fizyczny: Bibliogr. 27 poz.,

Twórcy

autor

Jafarov E.M.

• Dept. of Aeronautical Engineering, Istanbul Technical University, 80626 Maslak, Istanbul, Turkey

Bibliografia

• [1] Blakelock J. H., Automatic Control of Aircraft and Missiles, John Wiley, New York, 1991.
• [2] Cause A. J., Kramer F. S., A variable structure approach to robust control of VTOL aircraft, International Journal of Guidance, Control and Dynamics, Vol. 7, No. 5, 1984, 620-626.
• [3] Cheres E. Gutman S., Palmor Z. J., Stabilization of uncertain dynamic systems including state delay, IEEE Transactions on Automatic Control, Vol. 34, 1989, 1199-1203.
• [4] Dorling С. M., Zinober A. S. I., Robust hyperplane design in multivariable structure control sys¬tems, International Journal of Control, Vol. 48, No. 5, 1988, 2043-2054.
• [5] Drazenovic В., The invariance conditions in variable structure systems, Automatica, Vol. 5, 1969, 287-295.
• [6] Edwards Ch., Spurgeon S. K., Sliding Mode Control, Theory and Applications, Taylor and Fran¬cis, London, 1998.
• [7] El-Ghezawi О. M. E., Zinober A. S. I., Billing S. A., Analysis and design of variable structure system using a geometric approach, International Journal of Control, 38, 1983, 657-671.
• [8] Emelyanov S. V., Variable Structure Control Systems, Nauka, Moscow, 1967, (in Russian).
• [9] Garofalo F., Glielmo L. (eds), Robust Control via Variable Structure and Lyapunov Techniques, Springer-Verlag, London, 1996.
• [10] Ha Q. P., Rye D. C., Durrant-Whyte H. F„ Robust sliding mode control with application, Inter¬national Journal of Control, Vol. 72, No. 12, 1999, 1087-1096.
• [11] Hale J., Theory of Functional Equations, Springer-Verlag, New York, 1977.
• [12] Jafarov E. M., State feedback sliding mode control for SISO systems with time-delay. Proceedings of IFAC 8th Symposium on Large Scale Systems: Theory and Applications, University of Patras, Rio, Greece 195-200; 1980, Study of the stability of VSS with time-delay. Novel Approaches in the Theory of VSS. Emelyanov, S.V. (ed.), Proceedings of VNIISI AN SSSR, 4, Moscow, 1998, 24-28, (in Russian).
• [13] Koshkoueu A. J., Zinober A. S. U., Sliding mode time-delay systems. Proceedings of the IEEE International Workshop on Variable Structure Systems, VSS'96, Tokyo, IEEE, 1996, 97-101.
• [14] Krasovskii N. N„ Some Problems of Stability of Motion (Moscow, Phusmatgiz, in Russian); 1963, Stability of Motion: Application of Lyapunov's Second Method to Differential Systems and Equa¬tions with Time-Delay (Stanford: SU Press), 1959.
• [15] Li X., Decarlo R. A., Memoryless sliding mode control of uncertain time-delay systems, Proceedings of 2001 American Control Conference, Crystal Gateway Marriot, Arlington, Virginia, June 25- 27, 2001.
• [16] Luo N., De La Sen M., State feedback sliding mode control of a class of uncertain time-delay sys. terns. Proceedings of IEE-D: Control Theory and Applications, Vol. 140, No. 4, 1993, 261-274.
• [17] Luo N.. De La Sen M., Rodellar J., Robust stabilization of a class of uncertain time-delay systems in sliding mode. International Journal Robust and Nonlinear Control, Vol. 7. 1997, 59-74.
• [18] Lyapunov A. M., The general problem of the stability of motion. International Journal of Control Vol. 55, 1992, 531-773.
• [19] Mahmoud M. S., Al-Muthairi N.. Design of robust controllers for time-delay systems, IEEE Transactions on Automatic Control, Vol. 39, 1994, 995-999.
• [20] Nazaroff G. J., Stability and stabilization of linear differential delay systems, IEEE Transactions on Automatic Control, Vol. 18, 1973, 317-318.
• [21] Razumikhin B. S„ On the stability of system with a delay, Prikladnaya Mathemalica i Mekhanica, 20, iss 4, 1956, 500-512, (in Russian).
• [22] Ryan E. P., A variable structure approach to feedback regulation of uncertain dynamical systems, International Journal of Control, Vol. 38, No. 6, 1983, 1121-1134.
• [23] Shyu К. K., Yan J. J., Robust stability of uncertain time-delay system and its stabilization by variable structure control, International Journal of Control, Vol. 57, 1993, 237-246.
• [24] Spurgeon S. K., Choice of discontinuous control component for robust sliding mode performance, International Journal of Control, Vol. 53, 1991, 163-179.
• [25] Thowsen A., Stabilization of a class of linear time-delay systems. International Journal of System Science, Vol. 12, 1981, 1485-1492.
• [26] Utkin V. I., Variable structure system with sliding modes, IEEE Transactions on Automatic Control, Vol. 22, 1977,212-222.
• [27] Young K. D., Utkin V. I., Ozguner U„ A control engineer's guide to sliding mode control, IEEE Transactions on Automatic Control, Vol. 7, No. 3, 1999, 328-342