3 Optimality of PID Control

Abstract

The conventional PID controller for automated machines is widely accepted by industry. According to a survey reported in [3, 66], more than 90% of control loops used in industry use PID. There are many types of PID controllers, e.g., PID plus gravity compensator, PID plus friction compensator, PID plus disturbance observer, etc. The wide acceptance of the PID controller in industry is based on the following advantages: it is easy to use, each term in the PID controller has clear physical meanings (present, past and predictive), and it can be used irrespective of the system dynamics. A optimal controller that is robust and performs well has been developed for nonlinear mechanical control systems; however, it has not been widely accepted in industry since it is not immediately clear which partial diMerential equations should be solved. To transfer control theory to industry, it is worthwhile to describe the relationship between control and PID. In this chapter, we analyze the optimality of a PID controller, especially for Lagrangian systems.