Designing Pid Controllers With a Minimum Iae Criterion by a Differential Evolution Algorithm

Abstract

Although the integral of absolute error (IAE) has long been used as a performana: measure for controller evaluation, a systematic approach is still lacking for the design of optinlal 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 lo 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 spnce. Three examples are provided to illustrate the effectiveness of the DEA.

ACS algorithm-based adaptive fuzzy PID controller and its application to CIP-I intelligent leg

“…To evaluate the performance of the Fuzzy-ACS PID controller, as the comparison objects, other three typical evolutionary algorithms, including the differential evolution (DE) algorithm [3] , real-coded genetic algorithm (GA) [4] , and simulated annealing (SA) algorithm [4] , are also used to design the optimal PID controller, and the designed PID controllers are called the DE-PID, GA-PID, and SA-PID controller, respectively. The parameter settings of the four algorithms are shown in Table 2.…”

“…About this problem, many researchers conducted research [1−2] . With the development of artificial intelligence, recently many new methods has been used to design PID controllers, such as the differential evolution (DE) algorithm [3] , genetic algorithm(GA) [4−6] , simulated annealing(SA) algorithm [4] , and fuzzy logic control [6−8] . In these methods, the fuzzy logic control has a good control effect especially for the objects with nonlinear and/or uncertain properties or the objects whose models are very difficult to be established accurately.…”

Digital redesign of analog controllers based on minimizing integral of squared errors

“…In order to obtain digital controllers that are globally optimal, the differential evolution algorithm described in References [25,26] is used in the following examples to search the optimal controller coefficients. Like many other evolutionary algorithms, the differential evolution algorithm has been successfully used to solve global optimization problems related to some concrete multimodal, nondifferentiable, and combinatorial functions [25][26][27][28][29].…”

“…Using the above expression for the evaluation of performance index, we found with a differential evolution algorithm described in Reference [26] the following optimal digital controllers and the corresponding performance indices: …”

PID compensation of time delayed processes 1998-2002: a survey

“…Finally, alternative design methods may be used to determine the controller parameters, such as fuzzy logic Patranabis 1998, 2001;Blanchett et al 2000;Xu et al 1998Xu et al , 2000Tso 1999, 2000;Mudi and Pal 1999;Visioli 1999Visioli , 2001bWang et al 1999d;Tao and Taur 2000;Mann et al 2001a), genetic algorithms (Cheng and Hwang 1998;Wang et al 1999d) or neural networks Sbarbaro et al 2000;Shu and Pi 2000).…”