Multi-rate digital control and signal processing: Theory and applications to motion control systems

In this dissertation, multi-rate control is studied for performance enhancement of motion control systems under measurement constraints. A multi-rate feedback/feed-forward control structure is proposed and analyzed. For feedback control systems, multi-rate digital redesign methods are considered from both the analysis and design points of view.; In the multi-rate feedback/feed-forward control scheme, the feedback controller is updated at the same rate as the sampling rate of the output measurements. The feedforward controller processes the desired output signal for high accuracy tracking, and its output is updated at a rate N-times faster than the sampling rate of the output measurements. When compared with the single rate feedback/feed-forward control scheme, the proposed scheme has at least two advantages. When the sampling rate of the output measurements is fixed, the plant output remains closer to the desired output by increasing the update rate of the feed-forward control input. In certain cases, the proposed multi-rate scheme can avoid the fundamental problem in the design of feed-forward controllers arising from unstable zeros of the discrete time transfer function model of the system.; Digital redesign by multi-rate sampling and high order holds are studied for recovering the performance of the continuous time controller which may be lost by discretization, especially for feedback control systems with large measurement sampling period. The controller output is updated at a frequency N times faster than the measurement sampling frequency, and at the same time the evolution of the error signal between two consecutive sampling instances is estimated by utilizing present and past error measurements. General equations for analyzing such multi-rate control systems are presented. It is shown that multi-rate control and high order holds are useful for recovering the performance of the original continuous time compensator. Also studied is a multi-rate H_∞ optimal digital redesign of continuous time controllers. It focuses on the performance of the closed loop system under digital control. The discrete time controller is obtained through minimization of H_∞ norm of the lifted system. The stability of the closed loop system with the redesigned controller is guaranteed. The proposed approaches are applied to track following control of a hard disk drive (HDD) servo system.