The Novel Singular-Perturbation-Based Adaptive Control with σ-Modification for Cable Driven System

Due to their large working space and fast response, cable driven systems have been widely applied in manufacturing, robotics and motion simulators, etc. However, the cable is flexible and tends to resonate at high frequencies, which raises challenges for the motion control of the cable driven system. To solve this problem, this paper proposes a singular-perturbation-based adaptive control method with $\sigma$-modification. Taking advantage of the multi-time scale characteristics, the flexible system is approximately decomposed into two subsystems, and then the damping compensation is designed in the boundary layer subsystem to enhance the tension stability. In addition, estimated parameters drift may occur for the reduced-order system. Thus, the $\sigma$-modification is proposed to ensure that the tracking and estimation errors converge to a bounded residual set. The Lyapunov stability theorem proves that the closed-loop system is stable and errors are ultimately uniformly bounded. A research prototype of a twin-motor cable driven system is developed, and experimental investigation is conducted on it. The experimental results show that the proposed control method can effectively suppress cable resonance at high frequencies. Compared with the conventional adaptive control method, it can significantly increase the system bandwidth.