| The thesis addresses three problem areas within repetitive control. Firstly, it addresses issues concerning the ability of repetitive control and feedback control systems to eliminate periodic disturbances occurring above the Nyquist frequency of the hardware. Methods are developed for decomposing and unfolding notch filter or comb filter feedback control so that disturbances above Nyquist frequency can be canceled. Phenomena affecting final error levels are discussed, including error in unfolding, coarseness of zero-order hold cancellation, and waterbed effects in the feedback control system frequency response for different sample rates.; Secondly, matched basis function repetitive control laws are developed for batch mode and real time implementation to converge to zero tracking error in the presence of periodic disturbances. For both control methods, conditions are given that guarantee asymptotic and monotonic convergence. Stability tests are formulated to examine stability when the period of a disturbance is not an integer number of sample times, and when there are multiple unrelated periods whose common period is too long to use.; Thirdly, an understanding is developed of the optimum division of labor between the objectives accomplished by feedback and the objectives accomplished by repetitive control action. Some experimental results of the particle accelerator testbed at Thomas Jefferson National Accelerator Facility, Newport News, Virginia, are reported. |
