Stability considerations in controller designs developed using the LF transformation

• Autorzy: Szász G. , Flowers G. T.
• Konferencja: International Conference on Numerical Mathematics and Computational Mechanics : NMCM'98 (8 th ; August 1998 ; Miskolc ; Hungary)
• Języki publikacji: EN

Abstrakty

EN

Controlling time periodic systems is a significant engineering challenge. One innovative approach that seems to be especially promising involves application of the Lyapunov Floquet (LF) transformation to eliminate time periodic terms from the system state matrices. Traditional control design techniques are then applied and the resulting gains transformed back to the original domain. Typically, the controller design process involves the use of an auxiliary control matrix and (assuming that the actual control matrix is time-varying and non-invertable) a pseudo inverse (which introduces approximations into the procedure). The degree to which the desired control results are achieved depends very strongly upon the impact of these approximations on the actual system dynamics. The research effort described below is concerned with investigating the performance of this LF control strategy and the existence of situations in which application of the procedure may produce undesirable behaviors.

Słowa kluczowe

EN

Lapunov-Floquet transformation; matrix

PL

przekształcenie Lapunowa-Floquet'a; macierz

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Computer Assisted Mechanics and Engineering Sciences
• Rocznik: 1999
• Tom: Vol. 6, No. 3-4
• Strony: 495--503
• Opis fizyczny: Bibliogr. 9 poz., rys., wykr.

Twórcy

autor

Szász G.

• Department of Mechanical Engineering, Auburn University, Auburn, AL, USA

autor

Flowers G. T.

• Department of Mechanical Engineering, Auburn University, Auburn, AL, USA

Bibliografia

• [1] W.L. Brogan. Modern Control Theory. Prentice Hall, Englewood Cliffs, 1991.
• [2] R.A. Calico, W.E. Wiesel. Control of time-periodic systems. Journal of Guidance, 7(6): 671-676, 1984.
• [3] A.J. Calise, M.E. Wasikowski, D.P. Schrage. Optimal output feedback for linear time periodic systems. Journal of Guidance Control and Dynamics, 15(2): 16-423, 1992.
• [4] P. Joseph, R. Pandiyan, S.C. Sinha. Optimal control of mechanical systems subjected to periodic loading via Chebysev polynomials. Optimal Control Applications and Methods, 14: 75-90, 1993.
• [5] T. Kailath. Linear Systems. Prentice Hall, Englewood Cliffs, 1980.
• [6] V. Lovass-Nagy, R.J. Miller, D.L. Powers. An introduction to the application of the simplest matrix generalized inverse in system science. IEEE Transactions on Circuits and Systems, CAS-25: 766-771, 1978.
• [7] A.H. Nayfeh. Problems in Perturbation. John Wiley and Sons, New York, 1985.
• [8] S.C. Sinha, P. Joseph. Control of general dynamic systems with periodically varying parameters via Lyapunov Floquet transformation. Transactions of the ASME, 116: 650-658, 1994.
• [9] V.A. Yakubovich, V.M. Starzhinski. Linear Differential Equations with Periodic Coefficients, Part I and Part II. John Wiley and Sons, New York, 1975.