Abstract: An optimal PID controller with incomplete derivation is proposed based on fuzzy inference and genetic algorithms. It consists of the off-line part and the on-line part. In the off-line part, by taking the overshoot, rise time, and setting time of system response as the performance indexes and by means of the genetic algorithm, a group of optimal PID parameters K_p^*, T_i^*, and T_d^* are obtained, which are used as the initial values for the on-line tuning of PID parameters. In the on-line part, based on K_p^*, T_i^*, and T_d^* and according to the system's current error e and its time derivative, a dedicated program is written, which is used to optimize and adjust the PID parameters on-line through a fuzzy inference system to ensure that the system response has optimal dynamic and steady-state performances. This controller has been used to control the executive motor of the intelligent bionic artificial leg designed by the authors. The result of computer simulation shows that this kind of optimal PID controller possesses good control performance and robust performance.