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On the effect of chattering in the sliding mode control systems.

Bartoszewicz A.

Systems Science

2000

Vol. 26, nr 1

29-42

Variable structure control systems with the ideal sliding motion are perfectly robust with respect to matched disturbance and parameter uncertainty. However, this mode of operation is not achieved in practice. Thus, in this paper the non-ideal sliding motion actually taking place in variable structure systems is investigated. The phenomenon of chattering, i.e., high frequency oscillations which inevitably occur in the systems with ideal relays, is analysed. It is shown that the oscillations are caused by fast usually neglected dynamics of the system, for instance, unmodelled delay or inertia. The describing function method is used to predict the amplitude and the frequency of the oscillations. Furthermore, a simple method is given to determine how the ideal relay input-output characteristics should be modified to eliminate the chattering without introducing excessive control errors. Simulation results confirming the theoretical analysis presented.