On the Design of Adaptive Robust Repetitive Controllers

Abstract

A new perspective on dealing with the noise sensitive problem of repetitive control algorithms is given in the paper. It is firstly shown that, in continuous-time domain, what the conventional repetitive learning algorithm does is equivalent to adapting all the values of the periodic uncertainties over one period. Such an endeavor means very high bandwidth of the learning algorithm as an infinite number of parameters need to be adapted, which puts a great demand on microprocessor memory in implementing the algorithms. At the same time, such a formulation also makes the algorithm very sensitive to noise as it treats the values of the periodic uncertainties over the same period totally independent from each other, just like a random noise. Based on this new perspective on the noise sensitive problem of repetitive algorithm, a simple remedy is provided for the recently proposed adaptive robust repetitive control (ARRC) design by recognizing the physical dependence of the values of the periodic uncertainties over the same period and using certain known basis functions to capture these physical dependence. By doing so, only the amplitudes of these known basis functions need to be adapted on-line. The net results are that, not only the number of the parameters to be adapted is reduced drastically, but also the noise sensitive problem of the conventional learning algorithm is overcome. The precision motion control of a linear motor drive system is used as an application example. The comparative experimental results demonstrate that, with the new adaptive robust repetitive control design, not only the noise sensitive problem of repetitive learning is completely eliminated, but also a much improved tracking performance is achieved due to the built-in extrapolation capability of the basis functions used.