Experimental evaluation of design strategies in repetitive control for high-precision mechanical motion.

摘要

Learning and repetitive control develop controllers that learn from experience performing a task, in order to improve performance as the task is repeated. Learning control applies when the task restarts from the same initial condition. Repetitive control applies when the command is periodic, or there is a periodic disturbance. Here, several effective learning control laws are adapted for use as repetitive control laws. In addition, several related frequency response based repetitive control design techniques are studied. Experiments are performed on a double reduction timing belt drive fixture. The aim is to obtain high precision constant output velocity by eliminating a rich spectrum of small repeating errors produced by imperfect machining of the gears, speed fluctuations related to tooth meshing, etc.;The research is divided into four parts. The first studies implementation of learning in a batch mode, making the repetitive control application as similar to learning control as possible, and eliminating any real-time computation constraints. Three designs are tested: phase cancellation, contraction mapping, and a linear phase lead design with a non-causal zero-phase low-pass filter. The first of these gave essentially perfect results, eliminating all error peaks up to the 500 Hz Nyquist frequency.;The second part performs experiments using these algorithms in a real-time repetitive control implementation, plus another method using linear phase lead with a Bartlett window. Real time implementation, and replacement of some frequency domain computations results in performance degradation at high frequencies, and the need to stabilize. The most effective repetitive control designs differ from these for learning control, with these effective designs exhibiting long term stable behavior due to finite word length. In the third part of the thesis, finite word length is studied as a methodology for stabilizing repetitive control laws.;The fourth part of the thesis applies similar learning concepts to a different class of problems in which there is an unknown measurement disturbance with a known fundamental frequency and many harmonics. The technique is shown experimentally to be very effective.