Sliding Mode Control with Chattering Reduction

In variable structure control algorithms, sliding mode plays a key role in desensitizing the closed loop system with respect to parameter variations, in rejecting unknown disturbances, and in reducing the systems dynamics to a prescribed lower dimension manifold on which desirable dynamic behavior of the plant is attained. In its original theoretical developement, sliding mode corresponds to a special class of system trajectories which is produced by a certain control action that is discontinuous on a switching manifold [1]. However, in the presence of switching nonidealities, such as delays and time lags, the discontinuity in the control variables may excite umodeled fast dynamics in the plant, thus producing unacceptable system dynamic behavior which is commonly referred to as chattering phenomenon. Presently, two approaches have been proposed to reduce chattering. The first one is the use of continuous approximation in the boundary layer [2, 3, 4]. This approach replaces the switching function in the discontinuous control by a continuous approximation in the vicinity of the switching manifold. However, although chattering can be removed, the robustness of sliding mode is comprimised. The second approach utilizes a localization of high frequency phenomenon [5]- it introduces a discontinous control loop which is closed through an asymptotic observer of the plant. Since the model imperfections of the observer are supposedly smaller than that in the plant, and the control is discontinuous only with respect to the observer, chattering is localized to a high frequency loop which bypasses the plant.