Robust stabilization of an inverted cart-pendulum: A second order continuous sliding mode approach

This manuscript uses two continuous sliding mode controllers to stabilize a cart-pendulum system. The nonlinear model of the cart-pendulum system is, at the first stage, transformed into its regular form. Then, the control input designed via continuous sliding mode strategies uses a sliding variable with relative degree two, which reduces the number of stages of the design. The implemented control techniques are the discontinuous integral action and a continuous nested algorithm. The proposed robust control strategies are insensitive against unknown matched perturbations with bounded derivatives. Since the proposed controllers require the knowledge of the successive time derivatives of the sliding surface, a Levant's Differentiator is introduced to estimate such derivatives. The performance of both controllers is contrasted using the mean square error of the sliding surface as comparison criteria.