FUZZY LOGIC CONTROLLER WITH INTERVAL-VALUED INFERENCE FOR DISTRIBUTED PARAMETER SYSTEM

It is worth noting that, in the past three decades, a kind of fuzzy set called type-2 fuzzy set is developed as an extension of the concept of an ordinary fuzzy set (also called as type1 fuzzy set) for handling extra uncertainties. The type-2 fuzzy set was first introduced by Zadeh [10] and studied intensively by other people: Yager [11], Turksen [12], Gorzalcznay [13], Karniak [14], Mendel [15,16], etc. Type-2 fuzzy logic systems have been applied to many fields such as classification of coded video streams [17], forecasting of time-series [18], and autonomous mobile robots [19].
1. Introduction. In the real world, most physical processes are inherently characterized by the presence of strong spatial variations [1], and are usually called distributed parameter systems. The mathematical models describing these distributed processes are represented by partial differential equations and the control problems will involve the regulation by using spatially-distributed control actuators and measurement sensors. Most control methods for distributed parameter systems are based on mathematical models. There exist two approaches to control distributed parameter systems. The first one is to control a distributed parameter system using a conventional control method based on ‘lumped’ system model (called as ‘early lumping’ in [2]), i.e. simply discretizing the partial differential equation by using the finite-difference or finite-element techniques and leading to a approximate system of thousands of ordinary differential equations. The other one is to control a distributed parameter system by fully utilizing control theory of distributed parameter systems (called as ‘late lumping’ in [2]), requiring plenty of complex mathematical knowledge.
International Journal of Innovative Computing, Information and Control Volume 2, Number 6, December 2006
ICIC International °c 2006 ISSN 1349-4198
pp. 1197—1206
syli@
Received May 2005; revised December 2005
Abstract. A fuzzy logic controller with interval-valued inference mechanism is presented for the control of distributed parameter system (DPS). Interval-valued fuzzy set, a special case of type-2 fuzzy set, is innovatively designed to cope with the spatial information of distributed parameter systems. The proposed fuzzy logic controller is composed of six modules: fuzzifier, fuzzy composition, rules, inference engine, type-reducer, and defuzzifier. The fuzzy composition maps actual spatial information to an interval-valued fuzzy set - the fuzzy information that the FLC can identify, and then the interval-valued rule inference operates on the interval-valued fuzzy set that contains spatial information and produces control action. The application of the FLC with interval-valued inference to a catalytic reactor demonstrates its effectiveness to a class of distributed parameter systems. Compared with the ordinary FLC, the proposed FLC can improve its control performance due to its spatial expression and interval-valued inference mechanism. Keywords: Interval-valued fuzzy set, Fuzzy logic controller, Distributed parameter system, Fuzzy set, Type-2 fuzzy set
2. Fuzzy Logic Controller with Interval-valued Inference. The fuzzy logic controller consists of fuzzifier, fuzzy composition, rules, inference engine, type-reducer and defuzzifier as shown in Figure 1.
Most fuzzy controls [3-5] in the real world are also found to be designed on lumped systems. There are fewer literatures devoted to the fuzzy controls for distributed parameter systems. In [6-8], the fuzzy control designs were based on exact mathematical models of distributed parameter systems under the structure of the control theory of distributed
The paper is organized as follows. Section 2 presents configuration and design of fuzzy logic controller with interval-valued inference for a distributed parameter system. An application of the proposed fuzzy logic controller to a catalytic reactor is given in Section 3. In section 4, conclusions are giveHANG
parameter systems. In literature [9], a hierarchical fuzzy control structure was designed for a flexible robot, where the high level was a fuzzy classifier used for space feature extraction and the lower level was a traditional fuzzy logic controller. Those applications of FLC to distributed parameter systems show that the ordinary fuzzy logic controller is not inherently designed for distributed parameter systems since the ordinary fuzzy set cannot express spatial information.