Predefined-Time Control with Prescribed Performance for Multi-Motor Servo System Based on Generalized Coupling Error

This paper proposes a predefined-time coordinated control scheme for multi-motor servo systems based on a generalized coupling error (GCE). By introducing the GCE, the motor tracking and synchronization errors are unified into a single error variable, through which the coupled tracking and synchronization problem is transformed into the convergence of the GCE. This formulation significantly simplifies the controller design and effectively avoids the mutual coupling between tracking and synchronization control loops. To explicitly guarantee the transient performance of multi-motor servo systems, a GCE-based fractional-form error transformation function is constructed, which enables direct regulation of the transient behavior of motor tracking and synchronization errors while avoiding the numerical singularities commonly encountered in traditional performance transformation methods. On this basis, a predefined-time control strategy is systematically developed to simultaneously achieve load tracking and motor synchronization. By incorporating the control framework, both the load tracking error and motor synchronization are guaranteed to converge within a predefined time. Rigorous Lyapunov-based analysis is provided to establish the predefined-time stability of the overall closed-loop system. Simulation results on a four-motor servo system validate the effectiveness of the proposed control strategy.