Sliding repetitive control with adaptive bound estimation for motion systems liable to periodic exogenous signals

Periodic exogenous signals often exist in motion systems, especially those involving one or more rotating elements. These periodic exogenous signals deteriorate the performance of motion systems, and these adverse effects cannot be practically eliminated by straightforwardly increasing feedback control gains due to sensor noise, actuator saturation, and unmodeled plant dynamics. This paper describes a sliding repetitive controller for motion systems subject to periodic exogenous signals. Moreover, an adaptive law for bound estimation is devised to ensure the presence of a sliding motion for both repetitive learning and disturbance observation. The tracking motion system of a disk drive is considered in practice, and a traditional repetitive controller is also implemented for performance comparisons with the proposed scheme. Experimental results are reported in this paper, showing the efficacy of the proposed scheme.

Padé-Approximation-Based Preview Repetitive Control for Continuous-Time Linear Systems

This paper concerns a Padé-approximation-based preview repetitive control (PRC) scheme for continuous-time linear systems. Firstly, the state space representation of the repetitive controller is transformed into a nondelayed one by Padé approximation. Then, an augmented dynamic system is constructed by using the nominal state equation with the error system and the state equation of a repetitive controller. Next, by using optimal control theory, a Padé-approximation-based PRC law is obtained. It consists of state feedback, error integral compensation, output integral of repetitive controller, and preview compensation. Finally, the effectiveness of the method is verified by a numerical simulation.

Using Repetitive Control with Force Feedback to Reduce Impedance of Exoskeletons for Gait Training

Transparent interaction, or the reduction of human-robot interaction forces, is an important quality of gait training exoskeletons. In this paper, we investigate the feasibility of using a repetitive controller for reducing impedance of gait training exoskeletons using force feedback. We used a two-mass spring damper model system, and simulated the application of repetitive force controllers with the objective of reducing the end-point impedance of the distal mass. We designed and applied three repetitive controllers: a 1st order, a 2nd order designed for random signal period error, and a 2nd order designed for constant signal period error. We compared these three repetitive controllers subject to plant model parameter error, random signal period error, and constant signal period error. Numerical simulations under nominal conditions show that via repetitive force control, it is possible to reduce the endpoint impedance to the targeted magnitude and RMSE force below the limit achievable with force controllers while guaranteeing passivity. Furthermore, we established that the application of a 2nd order repetitive controller designed for random period error is highly robust to random period error - exceeding the performance of the passive proportional controller up to 30% error of nominal frequency. Furthermore, this 2nd order repetitive controller designed for random period error maintains a 100% convergence rate through 60% plant parameter error.