On repetitive control

Abstract: This thesis will concern control systems ability to enhance performance by repeating, while maintaining a stable and sufficiently fast closed loop performance. Iterative techniques can be divided into repetitive and learning control. In principle these techniques only differ in that the learning systems initial condition is reset at the beginning of each cycle while the repetitive system runs continuously. Repetitive controllers, the main theme of this thesis, can be used for rejecting periodic disturbances as well as tracking periodic references with ideally zero error. To accomplish this an internal signal model is utilized. This model is either a delay with a positive feedback around it modeling a general periodic signal, or a combination of harmonic frequencies adding up to a band-limited signal. The delay internal model has some uncomplicated, easy to grasp interpretation. Robustness properties may however not be the best. But if the plant is well determined over a frequency band this may be an excellent approach. With increased sampling rate the robustness properties of the delay model controller will however deteriorate. To cure this, disturbance rejection/tracking properties may be traded against robustness using lowpass filtering. As an alternative the internal model consisting of a number of isolated frequencies is exploited. This model has better robustness properties while preserving the zero error property for a bandlimited input signal. In addition it is shown how fundamental frequency adaptation can be incorporated for the case of unknown or drifting input signal frequencies. In this thesis repetitive controllers have successfully been implemented with two test plants; a peristaltic blood pump used in dialysis treatments, and a process where vibrations caused by a motor with an imbalance are suppressed.