1 Introduction

Abstract

Since Ziegler and Nichols’ PID tuning rules had been published in 1942 [68], the PID control has survived the challenge of advanced control theories, e.g., LQG an Open image in new window control [20, 67], adaptive (backstepping) control [28, 38] and so forth. The PID’s long life force comes from its clear meaning and effectiveness in practice. In PID control, the P-control (Proportional control) is the present effort making a present state into desired state, I-control (Integral control) is the accumulated effort using the experience information of bygone state and D-control (Derivative control) is the predictive effort reflecting the tendency information for ongoing state. Also, PID control has been utilized irrespective of linear system or nonlinear one, electrical system or mechanical one, time-invariant system or time-varying one. Though the PID control has been widely accepted in industry, PID control itself is still short of the theoretical basis, e.g., the optimality of PID control, performance tuning rules of PID control, automatic performance tuning method and the PID state observer have not been clearly presented especially for the trajectory tracking control of mechanical systems.