254 IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS—PART C: APPLICATIONS AND REVIEWS, VOL. 28, NO. 2, MAY 1998 An Experiment in Automatic Modeling an Electrical Drive System Using Fuzzy Logic P. J. Costa Branco, Member, IEEE, and J. A. Dente Abstract— Electrical drives are usually modeled using circuit theory, with currents or linking fluxes chosen as state variables for its electrical part and rotor speed or position chosen for its mechanical part. Often, its internal structure contains nonlinear relations difficult to model as dead-time, hysteresis, and satura- tion effects. On the contrary, if the available model is accurate enough, its parameter values are generally difficult to obtain and/or be estimated in real time. Therefore, this paper inves- tigates the use of fuzzy logic for automatic modeling electrical drive systems. An experimental system composed by a DC motor supplied from a DC–DC converter is used. We underline the unsupervised learning characteristics of the fuzzy algorithm, its memory and generalization capabilities. Some learning situations with critical effects in model performance are presented and discussed, pointing out some results and conclusions concerning the fuzzy modeling process in practice. Index Terms— Fuzzy logic, fuzzy systems, learning systems, modeling, motion control, pattern recognition. I. INTRODUCTION T HE CLASSIC approaches to modeling electrical drive systems do not provide enough representation for actual drive systems. The models are not sufficiently complete to represent the system since simplifications are made in the modelization process, and frequently, their structure contains nonlinear relations that are difficult to model or are even unknown. Recent papers [9], [10], [12] show that fuzzy logic is a powerful tool for representing complex relations in state space. Therefore, it introduces a methodology into electrical drive systems to automatically extract their dynamic behavior [3], [4]. Fuzzy modeling allows the incorporation of self-learning ca- pabilities into the system and design learning control schemes to compensate nonlinear terms affecting system dynamics. When parameter uncertainties are large, the use of feedback control with fixed coefficients may not be adequate. So, it is useful to identify on-line the complex relations represent- ing the drive’s behavior. In this paper, we investigate the capabilities of automatic modeling electrical drive systems by using fuzzy logic. Important situations, such as modeling when the variables are not sufficient to describe a system’s dynamic, the problem of a bad learning set not covering all of a system’s operating domain, and noise influence in modeling performance, are presented and discussed. Manuscript received October 15, 1996; revised October 22, 1997. The authors are with the Instituto Superior T´ ecnico, CAUTL/Laborat´ orio de Mecatr´ onica, Technical University of Lisbon, 1096 Lisboa Codex, Portugal (e-mail: pbranco@alfa.ist.utl.pt). Publisher Item Identifier S 1094-6977(98)02522-X. Fig. 1. Fuzzy model characterizes simple or complex relations between system variables, regardless of their analytical relationship. This paper is organized as follows. Section II presents the fuzzy learning algorithm used to extract the fuzzy model and resumes its main steps. Section III briefly describes the ex- perimental system and its controller, and Section IV discusses different aspects of the drive modeling process using the fuzzy algorithm. II. FUZZY LEARNING ALGORITHM Fuzzy modeling expresses qualitatively the system charac- teristics by using fuzzy reasoning [2]. It characterizes simple or complex relations between system variables, regardless of their analytical dependence, by a set of rules: “IF a set of conditions is satisfied, THEN a set of conclusions is inferred” (Fig. 1). In this work, rules have the form of (1). The symbol represents the th model rule among a total of rules, is the chosen system variables expressing its condition, is the system output variable, and is the inferred value from the extracted fuzzy model if is and is and is then is (1) For electrical drives, the rules usually express the relation- ship between current, voltage, speed, or position reference, with the output signal being the angular speed, position, or electrical torque. In each rule, represents a linguistic term (or fuzzy set) characterized by a membership function, denoted by , and composing the condition rule part. Fuzzy set represents the conclusion rule part. The antecedent variables representing a system’s condi- tion make active each rule by some degree computed using (2). The condition terms and in this expression are the numerical values acquired from system sensors being 1094–6977/98$10.00  1998 IEEE