Design And Analysis Of 3-Domain Fuzzy Logic Controller For Spatially Distributed Systems

Many of industrial processes and systems are inherently characterized by the presence of strong spatial variations, however, in the actual application the spatial distribution is usually ignored and the traditional control methods developed for lumped parameter systems are used. With the development of modern industry, higher requirements are brought forward for those industrial processes, including safety regulation, increasingly stringent environmental regulation, tighter product quality, and energy specification. For the spatially distributed systems that commonly exist in the industrial processes, control methods used for traditional lumped parameter systems couldn't satisfy the actual control requirement any more, thus, research on the control theory of spatially distributed systems has become one of the highlights in the modern control theory. Classical distributed parameter control methods were developed for spatially distributed systems during the past several decades. Since the methods require the precise mathematical models of the systems to be controlled and expect the control designers to grasp plentiful, complicated mathematical knowledge involved in the theory of distributed parameter systems, they are difficultly employed in the practical engineering applications. In contrast, fuzzy logic control has achieved worldwide success in countless commercial products and applications, because it has two practical advantages: no requirement of the mathematical model of the system, and satisfactory nonlinear controller developed by utilizing human control knowledge and experience without a complicated mathematics. However, due to the inherent two-dimensional feature of the traditional fuzzy set, the traditional fuzzy logic controller cannot solve the control problem of spatially distributed systems effectively. Fuzzy logic control for spatially distributed system is still an open problem. Thus, on the basis of the spatial distribution nature, this dissertation begins with new fuzzy set and new fuzzy logic control strategy, and then concentrates on the study on the fuzzy logic control for spatially distributed systems.The main contents are as follows:A novel three-dimensional fuzzy set, called as spatial fuzzy set, is proposed, since traditional two-dimensional fuzzy set is not able to express the spatial information effectviely. The spatial fuzzy set is inherently defined to express the spatial information, and has three coordinates: one is for the universe of discourse of the variable, another is for the spatial information, and a third is for the membership degree. Additionally, the set-theoretic operation of spatial fuzzy sets is introduced, and then spatial input variable and spatial fuzzification,two concepts extended from the spatial fuzzy set, are given. In terms of the feature of spatial distribution, a novel fuzzy logic control strategy based on spatial fuzzy set is proposed. The fuzzy logic control strategy can make a fuzzy logic controller control a spatially-distributed field by emulating human knowledge and experience from the point of view of the entire space domain. As a tentative application of the fuzzy logic control strategy based on spatial fuzzy set, an interval-valued fuzzy logic controller is designed. An example is illustrated to verify the effectiveness of the controller by simulation experiments.A three domain fuzzy logic controller (3-D FLC) is proposed based on the spatial fuzzy set for the spatially distributed systems with one control source. The controller is designed under the framework of the fuzzy logic control strategy based on spatial fuzzy set, and it has a self-contained structure. Similar to the traditional FLC, the 3-D FLC consists of spatial fuzzification, 3-D fuzzy rule inference, and defuzzifier, however, it has its unique nature:â‘ it takes the spatially distributed inputs from multiple sensors in the space domain and expresses the spatial information with the help of the spatial fuzzy set.â‘¡it processes the inference mechanism which can cope with the spatial information.â‘¢rules will not increase as sensors increase for spatial measurement. The 3-D FLC is designed with a simple configuration. Additionally, the spatial fuzzy set as well as the 3-D rule inference has certain physical meanings, and the involved computation is not complicated. Thus, 3-D FLC can be further investigated analytically. An example is finally illustrated to verify the effectiveness of the controller by simulation experiments.The analytical mathematical model of the 3-D two-term fuzzy logic controller is derived, and then controller structure is explained with the help of the existing conventional control techniques. The graphic analytical method (rule base plane decomposition) for the traditional two-term fuzzy logic controller is used for the analytical model derivation. The derived results expose that on the one hand, the 3-D FLC has a global sliding mode structure over the spatial domain; on the other hand, it has a spatial equivalent structure with the traditional fuzzy logic controller over the space domain. In terms of the spatial equivalent structure, some properties of the controller are further presented.The stability issue of the 3-D fuzzy logic control system is discussed, based on the analytical mathematical model of the 3-D FLC. In virtue of the global sliding mode feature of 3-D FLC, the Lyapunov stability of fuzzy logic control system is investigated, where a global stability condition is derived and an approach for designing the controller parameters is given. Utilizing the spatial equivalent structure and some feature of discrete time systems, the BIBO stability of discrete time fuzzy logic control system is investigated, where a global BIBO stability condition is derived and an approach for designing the controller parameters is given. Two examples are presented respectively to demonstrate the effectiveness of the two kinds of controller parameter designs by simulation experiments.A 3-D fuzzy logic control strategy based on decomposition and coordination is proposed for the spatially distributed systems with multiple sources. It extends the 3-D FLC to solve the control problem of the general spatially distributed systems. The control system has a hierarchical structure with three hierarchies. Firstly, the decomposition module decomposes the whole space domain into sub-space domains and decomposes the complex spatially-distributed process with multiple sources into several relatively simple subsystems. Then, on the middle layer, a 3-D FLC is used for each subsystem. Finally, on the top layer, the coordination module carries out a strategy of local coordination among adjacent subsystems, and formulates a coordinated 3-D fuzzy logic control. The proposed control method is successfully applied to a Rapid Thermal Chemical Vapor Deposition (RTCVD) system, and the simulation results demonstrate its effectiveness.