Higher Order Repetitive Control for External Signals with Uncertain Periods

Repetitive control (RC) was proven to enable high performance for systems that are subject to periodically repeating signals by enhancing an existing feedback control system so that it produces zero tracking error to a periodic command, or zero tracking error in the presence of a periodic disturbance of known period. Periodic signals are very common in many applications like robotics, disk drive systems, power converters, photolithography, jitter or vibration elimination in spacecraft and many more. Due to the growth in micro-processor and micro-controller technologies, most of the controllers are implemented in digital domain. Digital RC is typically designed by assuming a known constant period of command/disturbance signal, which then leads to the selection of a fixed sampling period that keeps it synchronized with the command/disturbance signal. However, in practice, the period for these signals might not be accurately known or might vary with time. In order to overcome this problem, higher order RC (HORC) was proposed as one method to make RC less sensitive to period error or period fluctuations. This dissertation investigates HORC, specifically second and third order RC designs (SORC and TORC), to identify the limitations, gaps, and design tradeoffs that a control system designer faces. New designs and methods are developed to address such gaps including stability, designer tradeoffs, robustness and other related performance characteristics. This dissertation has three major parts: SORC designs and stability, SORC design tradeoffs, and TORC designs and stability.