This paper presents repetitive control laws in real time using matched basis functions. These laws adjust the command given a feedback control system in order to eliminate tracking errors, resulting from in general a periodic disturbance and a non-periodic disturbance. The periodic error can be reduced by linear basis functions while the non-periodic error by the projection algorithm along with the wavelet filtering. The control laws do not use a system model, but instead the control action is chosen to be a linear combination of chosen input basis functions, and the corresponding output basis functions are obtained, nominally by experiment. The repetitive control laws use the projection algorithm to compute the output components on the output basis functions, and then the corresponding input components are adjusted accordingly. The output signals are reconstructed via the wavelet filtering before they are feedback to the controller. Numerical experiments show that the repetitive controllers are quite effective. In particular, the output tracking errors are further reduced because of the introduction of the wavelet filtering when compared to the previous work. In general, the repetitive control laws developed here can be used for the purpose of precision machinery control.

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