A new adaptive sliding mode control scheme

This paper presents a new adaptive sliding mode control (ASMC) scheme using time-delay estimation (TDE) technique and then applies it to robot manipulators. The proposed ASMC employs a new adaptive law to achieve good tracking performance with small chattering effect. The new adaptive law considers an arbitrarily small vicinity of the sliding manifold, where the derivatives of its adaptive gains are inversely proportional to the sliding variables. Such an adaptive law provides remarkably fast adaptation and chattering reduction near the sliding manifold. To yield the desirable closed-loop poles and simplify a complicated system model through feedback compensation, the proposed ASMC scheme works together with a pole placement control and a TDE module. It is shown that the proposed ASMC is guaranteed to be uniformly ultimately bounded with arbitrarily small bound.