Practical adaptive sliding-mode control approach for precise tracking of robot manipulators

Abstract

We present a practical adaptive sliding-mode control approach, namely, the strong and stable adaptive sliding-mode control (SS-ASMC), in this paper. There is a significant effort towards addressing the technical challenges associated with the switching gains with two adaptive laws, which are called parent and child adaptive laws. A parent adaptive law helps achieve strong switching gains through fast adaptation rate when sliding variable moves away from the sliding manifold. A child adaptive law updates the parameter of the parent adaptive law, which helps to achieve the switching gains with fast and stable adaptation rate in the vicinity of the sliding manifold. Such switching gains with two adaptive laws provide remarkably precise tracking performance while enhancing the robustness. Besides, to yield desirable closed-loop poles and simplicity of control approach structure, the proposed SS-ASMC approach employs a combination of time-delayed estimation and pole-placement method, which makes it unnecessary to have a rather complete system dynamics. It is shown by the bounded-input-bounded-output stability through the Lyapunov approach, and thus the tracking errors are also proved to be uniformly ultimately bounded. The effectiveness of the proposed SS-ASMC approach is illustrated in simulations with robot manipulators, which is compared with that of the existing control approaches.