DESIGNING PID CONTROLLERS WITH A MINIMUM IAE CRITERION BY A DIFFERENTIAL EVOLUTION ALGORITHM

Although the integral of absolute error (IAE) has long been used as a performance measure for controller evaluation, a systematic approach is still lacking for the design of optimal PID controller with the minimum IAE performance criterion. This may be ascribed to the nonsmoothness of the IAE objective function and the lack of closed-form expression for the IAE performance index. In this paper, we propose the use of a differential evolution algorithm (DEA) to design a minimum-IAE PID controller to overcome the nondifferentiability of the IAE objective function. To achieve also a specified least relative stability margin and least damping ratio, the D-partition technique is used to identify the allowable domain in the tuning parameter space. Three examples are provided to illustrate the effectiveness of the DEA.