PID auto-tuning for simultaneously fulfilling the requirements of relative stability and steady-state error

Proportional-integral-derivative (PID) control is commonly used in industrial automatic control systems. However, it is not straightforward to determine control gains in a PID controller for satisfactory closed-loop performance. Many research works have been devoted to the auto-tuning of PID control gains. In contrast to previous studies, this paper develops an auto-tuning rule for PID controllers to simultaneously satisfy specifications of both steady-state error and relative stability, in which stability is specified in terms of phase margin. To illustrate the proposed auto-tuning rule, a focus servo of an optical disk drive is used, in which a voice coil motor drives a lens to focus a laser beam on a data layer of an optical disk. Experimental results show the effectiveness of the proposed PID auto-tuning process.