Design of adaptive and basis function based learning and repetitive control.

摘要

In engineering practice there are many situations in which a feedback control system is given the same command repeatedly, or the command is periodic, or the control system is subject to periodic disturbances. Typical feedback control systems will produce repeating deterministic errors under such circumstances. Learning and repetitive control create methods to examine the tracking error of the system from each repetition or period, and then adjust the command the next repetition or period in order to make the error go to zero. Thus, by simply changing the command given to a feedback controller the next repetition or period, these methods can substantially increase the accuracy of an existing feedback control system.; The thesis is divided into four parts. The first part shows how indirect adaptive control ideas can be applied to the learning control problem. We introduce the assumptions needed in the theory of indirect adaptive control, with the aim of eliminating as many of them as possible in the development of indirect learning control algorithms. In the second part, basis functions are introduced into the repetitive control problem. Using batch updates, under appropriate conditions it is shown that basis functions can make the learning and repetitive control problems look mathematically the same. Matched basis functions are shown to be particularly advantageous, producing simple system models and guaranteeing stability of the learning process. The third part of the thesis develops the mathematics governing real time basis function repetitive control. Different mathematical methods of finding components of the error on basis function in real time are studied, and a method based on Floquet stability concepts is developed to determine convergence and stability of real time basis function repetitive controllers. In repetitive control, especially when there are periodic external disturbances, there is no reason for the period to be an integer multiple of the sample time. This causes difficulties to digital implementation of repetitive control, and in the fourth part of the thesis, methods are developed to address this problem.