Direct Adaptive Fuzzy PI Sliding Mode Control of Systems with Unknown but Bounded Disturbances

An asymptotically stable direct adaptive fuzzy PI sliding mode controller is proposed for a class of nonlinear uncertain systems. In contrast to other existing approaches of handling disturbances, the proposed approach does not require this bound to be known, only requiring that it exists. Moreover, a PI control structure is used to attenuate chattering. The approach is applied to stabilize an open-loop unstable nonlinear system as well as the Duffing forced-oscillation chaotic nonlinear system amid significant disturbances. Analysis of simulations reveals the effectiveness of the proposed method in terms of a significant reduction in chattering while maintaining asymptotic convergence.