Robust repetitive control and applications

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. This thesis aims to develop novel RC designs for a tracking/ rejecting periodic signal with time-varying frequency. We present three main designs in this thesis: a robust RC design, an adaptive RC design, and a MIMO RC design. The first design developed was the robust RC for linear systems with time varying sampling periods. Firstly, it develops a new frequency domain method for the nominal sampling period to design a low order, stable, and causal IIR repetitive compensator that uses an optimization method to achieve fast convergence and high tracking accuracy. A new stable and causal compensator can be implemented independently to reduce the design complexity, as most existing repetitive compensators are either unstable or non-causal, which makes the implementation difficult. A comprehensive analysis and comparison study is presented. Then this thesis extends the method to design a robust RC, which compensates time varying periodic signals in a known range. In the design, the time-varying parts due to sampling period interval variation are treated as parametric uncertainties, and the robust RC is designed as close as possible to the nominal one, thus ensuring that the system is stable for any sampling period in the given interval. A complete series of experiments on a servo motor was successfully carried out to demonstrate the effectiveness of the proposed algorithms. The second design developed was the Adaptive Repetitive Control (ARC) for unknown linear systems subject to time varying periodic disturbances. It was assumed that the sampling period would be locked to the period of disturbance signal to preserve a constant number of samples per disturbance period, as required by the RC. The sampling period adjustment results in a discrete plant with time-varying coefficients. By considering the direct adaptive control, it is possible to adapt the parameters of the controller to handle the time varying plant. Thus, the ARC has been proposed, based on the direct adaptive control and the internal model principle. 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. The effectiveness of the ARC has been verified in simulations and experiments on a servo motor system. The third design developed was the decentralized RC (DRC) for linear multiple inputs multiple outputs (MIMO) systems. The design is based on decentralized control that treats the MIMO system as a set of single input single output (SISO) systems. A Relative Gain Array (RGA) analysis is first performed to determine the dynamics that result in dominant interactions. A set of low order, stable and causal repetitive compensators are then designed to compensate the dominant dynamics that have been determined by the RGA. The compensators, which ensure the system stability, are obtained by solving an optimization. Various numerical examples are presented to demonstrate the effectiveness of the proposed DRC. The comprehensive analysis and comparison study is given. The novelty of the design was also verified in experiments on a 2 DOF robot.