Decoupled variable structure control design for trajectory tracking on mechatronic arms

This brief presents a variable structure control (VSC) algorithm to achieve the prespecified trajectory tracking on mechatronic arms. The tracking trajectory is composed of a set of sequentially-operated piecewise continuous sliding surfaces which the system´s state can follow to the equilibrium in phase plane. Some sliding mode controllers corresponding to the piecewise continuous sliding surfaces are designed to achieve the hitting motion and ensure the system´s state traveling on the trajectory. The algorithm using the boundary layer technique is capable of handling the reaching phase (RP) of the trajectory and chattering effects inherent to the VSC easily and effectively. The advantages of the proposed algorithm are that 1) the state would follow the sliding surfaces in turn so that the tracking control purpose is achieved, 2) the total tracking time by adding up the traveling time for each sliding surface can be evaluated explicitly, and 3) the robustness is as excellent as that of the conventional VSC scheme. A rotational inverted pendulum system subject to external disturbances is illustrated to show the validity of the proposed algorithm.