Robust immersion and invariance adaptive coordinated control for a class of biaxial gantry systems

Abstract

This paper proposes a robust Immersion and Invariance (I&I) adaptive coordinated controller for a class of uncertain linear-motor-driven biaxial gantry system subject to external disturbances for high-accuracy contour tracking. Firstly, the dynamic model of the gantry system is transformed into task coordinate frame, through which the contour tracking can be regarded as a regulation problem. Based on the transformed system dynamics, an I&I-based adaptation law with smooth projection is proposed to estimate the unknown parameters. Different from traditional adaptive control, the proposed robust I&I adaptive control introduces a new term called tuning function in adaptation law to shape the dynamic behaviour of the estimation vector. Then the stability of the closed-loop system is proved by Lyapunov theory. Finally, comparative experiments are executed on an industrial biaxial gantry system with two different cases to verify the effectiveness of the proposed control law.