Repetitive Control of Two-mass Systems based on the Singular Perturbation Technique and Periodical Disturbance Observer

In this paper, a repetitive learning control strategy for two-mass systems is proposed based on the singular perturbation technique (SPT) and a periodical disturbance observer (PDOB). Firstly, the original higher order system is decomposed into two lower order subsystems using the SPT. Then PDOBs are designed for each subsystem, and sliding mode controllers are designed using the estimation results to achieve exponential convergence. Compared to other methods where the controller is designed based on the high order system model, the developed control method combines the SPT and PDOB together, thus the controller design problem is simplified and the control accuracy is improved because the periodic nature of the system is exploited. Furthermore, to reduce the oscillation at the beginning of each period when the PDOB is employed, a new repetitive learning law is developed, where an additional parameter is introduced to adjust the damping effect during the disturbance observation. The stability of the PDOB and the closed-loop system is analyzed via the Lyapunov approach and the effectiveness of the proposed PDOB and controller is verified by simulations.