H<inf>∞</inf> tracking adaptive fuzzy integral sliding mode control for parallel manipulators

Abstract

In this paper, an H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> adaptive fuzzy integral sliding mode control scheme is proposed for controlling parallel manipulators with nonlinear unmodeled dynamics, external disturbances, and approximation errors. First, the parallel manipulator is formulated as an error dynamics according to a specified reference model. Then, an adaptive fuzzy integral sliding mode control scheme is developed to tackle the unmodeled dynamics and approximation errors. The integral sliding mode control with time-varying exponent in terms of error is proposed to eliminate the reaching phase in the sliding manifold such that the error state approach the equilibrium point in a finite time period as quickly as possible. Based on Lyapunov stability theorem, the proposed control scheme can guarantee the stability of the closed-loop system and achieve the H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> performance. Finally, we will use a 2-dof parallel robot system to verify the effectiveness of the proposed control scheme.