Stability Analysis of Nonlinear Parametric and Coulomb Control Systems

Abstract

Stability analysis of nonlinear control systems using Lypunov's direct method is reported in this paper. A general nonlinear controlled system and two different types of controllers are examined for stability analysis. The first category is the parametric controller. Importance of parametric controllers is illustrated through examples of various engineering systems. A general control algorithm is derived, and stability of the closed-loop system is examined. Stability under small external disturbances is also examined. The second category of controllers examined in this paper is the Coulomb-type controllers. Stability analysis is performed using Lypunov's direct method. Stability under a general forcing excitation is examined for linear systems with Coulomb controllers.

Keywords

Key Words: Lypunov's method parametric systems coulomb dampers nonlinear control

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References

Billah, K. Yr. , 1989, "A study of vortex-induced vibration," Ph.D. dissertation , Princeton University, Princeton, NJ.

Cartmell, M. , 1990, Introduction to Linear, Parametric and Nonlinear Vibrations , Chapman and Hall, New York .

Constantinou, M.C. and Tadjbakhsh, I.G. , 1984, "Response of a sliding structure to filtered random excitation," Journal of Structural Mechanics 12(3), 401-418.

Crandall, S.H. , Lee, S.S. , and Williams Jr., J.H. , 1974, "Accumulated slip of a friction-controlled mass excited by earthquake motions," ASME, Applied Mechanics Division, December, 1094-1098.

Fujino, Y. , Warnitchai, P. , and Pacheo, B.M. , 1993, "Active stiffness control of cable vibration," Journal of Applied Mechanics 60 , 948-953.

Hagedom, P. , 1981, Nonlinear Oscillations, Oxford University Press, Oxford, U.K.

Hahn, W. , 1963, Theory and Applications of Lypunovs Direct Method , Prentice Hall, Englewood Cliffs, NJ .

Jones, N.P. and Shenton III, H.W. , 1990, "Generalized slide-rock response of rigid blocks during earthquakes," Volume 3, in Proceedings of the Fourth US National Conference on Earthquake Engineering, Vol. 3, Palm Springs, CA.

Lin, Y.K. , Dimentberg, M.F. , Zhang, R. , Cai, G.Q. , and HoLung, J.A. , 1994,"Sliding motion of anchored rigid block under random base excitation," Probabilistic Engineering Mechanics 9, 33-38.

10.

Minorsky, N. , 1962, Nonlinear Oscillations, D. V. Nostrand, Princeton, NJ.

11.

Mohler, R.R. , 1973, Bilinear Control Processes, Academic Press, New York.

12.

Mohler, R.R. , 1991, Nonlinear Systems - I, Prentice Hall, Englewood Cliffs, NJ.

13.

Nayfeh, A.H. and Mook, D.J. , 1979, Nonlinear Oscillations, John Wiley, New York.

14.

Slotine, J.-J.E. and Li, W. , 1991, Applied Nonlinear Control, Academic Press, New York.

15.

Soong, T.T. and Skinner, G.T. , 1981, "Experimental study of active structural control," Journal of Engineering Mechanics 107 , 1057-1068.

16.

Westermo, B. and Udwadia, F. , 1983, "Periodic response of a sliding isolator system to harmonic excitation," Earthquake Engineering and Structural Dynamics 11, 135-146.