Filtered Repetitive Control of Robot Manipulators

In this paper, a filtered repetitive controller (FRC) is proposed for robot manipulator tracking. Error dynamics are obtained first, leaving an unknown periodic signal to be compensated. A new model to describe the periodic signal is proposed then. By this model, an FRC is designed to compensate for the unknown periodic signal. The resulting closed-loop error dynamics are analyzed with the help of a Lyapunov-Krasovskii functional. In order to compare stability of the closed-loop error dynamics with the FRC and corresponding repetitive controller, the convergence rate is proposed to measure their stability. It is shown that the resulting closed-loop error dynamics with the FRC is more stable. In comparison with existing repetitive controllers, the proposed controller provides the flexibility to choose parameters to achieve a tradeoff between tracking performance and stability. Numerical simulations demonstrate the effectiveness of the proposed controller.