Adaptive Sliding Mode Control for Underactuated Euler-Lagrange Systems

This paper proposes an adaptive sliding mode controller based on time-delay estimation for underactuated Euler-Lagrange systems. The proposed controller has a simple structure, being able to deal with the complex nonlinear dynamics and unknown disturbances by applying the time-delay estimation technology. The controller adopts a new adaptive law, which allows the control gain to be automatically increased or decreased according to the distance of the sliding variable from the sliding surface. Using the Lyapunov method, we prove that the tracking errors and sliding variable are uniformly ultimately bounded. Through numerical simulations in an overhead crane system, it is shown that the proposed method has good tracking performance and robustness to external disturbances.