Adaptive Repetitive Control for linear systems subject to time varying periodic disturbances

What is it about?

Repetitive Control (RC) has been widely used to track a periodic reference signal, or to reject periodic disturbance. Digital RC is usually designed by assuming a constant period of reference/disturbance signal, which then leads to the selection of a fixed sampling period. However, in practice, both reference signal and disturbance may vary in period. In order to overcome this problem, the sampling period is carefully adjusted to maintain a constant number of samples per period. This sampling period adjustment causes a change in the parametric model of the plant. Then, we propose an Adaptive Repetitive Control for linear systems subject to time varying periodic disturbances with time-varying sampling periods. The internal model can reject the disturbance perfectly, since the number of samples per period remains fixed. The time-varying plant parameters are handled by the direct adaptive control, as it tunes the controller parameters such that the closed-loop system is stable and the plant output tracks the reference.

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Photo by Will Swann on Unsplash

Photo by Will Swann on Unsplash

Why is it important?

We design an Adaptive Repetitive Control for linear systems subject to time varying periodic disturbances with time-varying sampling periods. In the design, the sampling period will be locked to the period of disturbance signal to preserve a constant number of samples per disturbance period, as required by Repetitive Control. This design based on direct adaptive control and the internal model principle. The internal model can reject the disturbance exactly, since the number of samples per period remains fixed. The time-varying plant parameters are handled by the direct adaptive control, as it tunes the controller parameters such that the closed-loop system is stable and the plant output tracks the reference.