Fuzzy Logic Controller Scale Factor Optimization

Abstract

The fuzzy logic controller based on fuzzy set theory provides a useful tool for converting the linguistics control strategy from the expert knowledge into automatic control rules. However, systematic tuning methods for fuzzy logic controllers have remained still under investigation. Usually FLC elements are tuned by trial and error method. In this paper, a new systematic method based on the optimization theory is used to tune the FLC scale factors. The objective functions based on the deviation from set point in the time response are optimized to achieve this goal. Simulation examples of aircraft longitudinal approach control are presented to illustrate the proposed method. INTRODUCTION For complex control problems, the fuzzy control algorithm can be obtained without a mathematical model of the plant, but the main disadvantage of using FLC seems to be the lack of systematic procedure for the design of FLC. The general method for designing FLC is to use trial and observation. No useful mathematical tool has yet been developed for the design of FLC because of its fuzziness, complexity and nonparameterization. There are three significant elements that have notable influence on the behavior of an FLC: 1)The control rule expressed in linguistic language, 2)The membership functions defined for fuzzy sets, and 3)The scale factors attached to the input and the output. Many researchers have investigated the tuning of FLC using these elements. Most of them concentrate on tuning FLC by adjusting control rules, the tuning of these rules is done by introducing self organizing fuzzy logic controller that can change the rules with respect to the process under control and its environment. The influence of scale factor values on the system response have been investigated by many researchers. However, proper control rules cannot always easily be obtained and suitable scale factors cannot always be achieved. Therefore, fixed fuzzy rules based on analyzing the behavior of a controlled process are used. For designing this kind of fuzzy logic controller, the tuning of fuzzy logic controller scale factors is considered one of the most important steps, especially when FLC output and. _________________________________ * AIAA member, Assistant Professor input parameters have the same range for the universe of discourse. In this paper, an optimization method will be used to find the optimal values of FLC scale factors. These values are achieved by minimizing proposed objective functions. These functions measure the deviation from the desired set point in different forms, since the deviation is related to scale factor selected values, the objective function form is explicitly function of deviation and implicitly is function of scale factors. The scale factors of the controller inputs and output may have been initially selected to have arbitrally initial values. FUZZY LOGIC CONTROLLER STRUCTURE The principle approach to the derivation of fuzzy control rules, in this research, is based on system response of the process to be controlled as shown in Fig. (1), where the input variables of the FLC are the error E and the change of error CE. While, the FLC output is the change of process input U. Fig. (1) System time response of a regulating system The input universe of discourse for the tracking error E or derivation error CE is divided into 7 degrees connected with the number of fuzzy sets by membership functions. In this study, E and CE can each range from –3 to +3 and the seven degrees are -3, -2, -1, 0, +1, +2, +3 and the fuzzy sets are defined as ( NB Negative Big, NM Negative Medium, NS Negative Small, AZ Zero, PS Positive Small, PM Positive Medium, PB Positive Big ). A similar analysis is given to the output for the control action, which uses the same fuzzy sets for the same universe of discourse. The fuzzy rules used to implement the controller are the standard IF.....THEN American Institute of Aeronautics and Astronautics 1 AIAA Guidance, Navigation, and Control Conference and Exhibit 16 19 August 2004, Providence, Rhode Island AIAA 2004-5003 Copyright © 2004 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. type. The controller rule base is consisted of 49 rules of the form: IF (E is NS) AND (CE is NM) THEN (U is NB) ¦ ¦ ¦ ¦ ¦ ¦ IF (E is PM) AND (CE is NS) THEN (U is PS) The membership functions for fuzzy rules are illustrated in Fig. (2) and the prototype of fuzzy control rules is tabulated in Table (1). -3 -2 -1 0 1 2 3 NB NM NS PM PB