___________________________________________ 0-7803-8560-8/04/$20.00©2004 IEEE INPUT WEIGHTING OPTIMIZATION FOR PID CONTROLLERS BASED ON THE ADAPTIVE TABU SEARCH D. Puangdownreong * T. Kulworawanichpong * * and S. Sujitjorn * * * Department of Electrical Engineering, South-East Asia University, Bangkok, THAILAND * * Control and Automation Research (CAR) Group, School of Electrical Engineering, Suranaree University of Technology, Nakhon Ratchasima, THAILAND ABSTRACT Eitelberg introduced a useful method to recover system performance when a direct tuning of the PID’s parameters was prohibited in 1987 [1]. Our work herein proposes the use of adaptive tabu search (ATS) [11] to optimally tune the input-weight factors according to Eitelberg’s. We illustrate the effectiveness of our proposed method via two motor control problems. 1. INTRODUCTION Over decades, PID controllers have been increasingly employed in feedback control systems for industrial applications. The three-term parameters are appropriately designed at the beginning by a number of design methods or tuning rules. In general, design of the PID controllers assumes that neither the controlled plant’s nor the controller’s parameters are changed due to working environment or use. This may thus degrade the system performance in long term. For industrial use, most controllers are hard- wired or prohibited from adjustment. On the other hand, the fixed configuration type control system has been commonly used in industries. The method to keep the system response at or near optimum whenever the parameter variation occurs in the control loop was introduced by Eitelberg [1] in 1987. Employing the leveling of input signals, called input weighting, the structure of the control system introduced by Eitelberg is shown in Fig.1. Due to the special feature of input-weighting parameter adjustment, the Eitelberg’s method is extended to several applications such as feedback analog PID control [2], fuzzy-PID for DC motor speed regulation [3-4], performance adjustment of a fixed configuration type control system [5], and novel control strategy under alias situation [6]. Nowadays, artificial intelligent (AI) techniques have been accepted and widely used for the controller design in various industrial control applications. For example, designing of an adaptive PID controller by Genetic Algorithm (GA) [7], a self-tuning PID controller by GA [8], and a finite-precision PID controller by GA [9]. Although the GA is efficient to find the global minimum of the search space, it consumes too much calculation time. By literature, the ATS (Adaptive Tabu Search) method is an alternative, which also has global convergence property. Interestingly, it requires less time consumed, comparative to that spent by the GA method [10]. In addition, it is extended to linear and nonlinear identifications for some complex systems [11]. In this paper, the ATS method is exploited for the PID controller design problems proposed by Eitelberg. Fig. 1 Input weighting introduced by Eitelberg This paper consists of five sections. Section 2 describes the problem formulation of the input weighting optimization. Section 3 provides the ATS method used in this work. The test of the proposed optimization method is illustrated in Section 4, while Section 5 gives the conclusions. 2. PROBLEM FORMULATION Consider the structure of the control system introduced by Eitelberg as shown in Fig. 1. The parallel type PID controller receives the error signal E p (s), E i (s), and E d (s) as shown in Eq. (1) – (3), respectively. Then, the controller generates the control signal, U(s), to regulate the output response, C(s), referred to the input, R(s), where G p (s) and G c (s) are the plant and the controller transfer functions, respectively. The transfer function of the system introduced by Eitelberg is shown in Eq. (4), () () () p p E s FRs Cs (1) () () () i i E s FR s Cs (2) () () () d d E s FRs Cs (3) 451