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1998 | Buch

Introduction Kapitel lesen Erstes Kapitel lesen

Fuzzy Modeling for Control

verfasst von: Robert Babuška

Verlag: Springer Netherlands

Buchreihe : International Series in Intelligent Technologies

Enthalten in: Professional Book Archive

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Über dieses Buch

Rule-based fuzzy modeling has been recognised as a powerful technique for the modeling of partly-known nonlinear systems. Fuzzy models can effectively integrate information from different sources, such as physical laws, empirical models, measurements and heuristics. Application areas of fuzzy models include prediction, decision support, system analysis, control design, etc. Fuzzy Modeling for Control addresses fuzzy modeling from the systems and control engineering points of view. It focuses on the selection of appropriate model structures, on the acquisition of dynamic fuzzy models from process measurements (fuzzy identification), and on the design of nonlinear controllers based on fuzzy models.
To automatically generate fuzzy models from measurements, a comprehensive methodology is developed which employs fuzzy clustering techniques to partition the available data into subsets characterized by locally linear behaviour. The relationships between the presented identification method and linear regression are exploited, allowing for the combination of fuzzy logic techniques with standard system identification tools. Attention is paid to the trade-off between the accuracy and transparency of the obtained fuzzy models. Control design based on a fuzzy model of a nonlinear dynamic process is addressed, using the concepts of model-based predictive control and internal model control with an inverted fuzzy model. To this end, methods to exactly invert specific types of fuzzy models are presented. In the context of predictive control, branch-and-bound optimization is applied.
The main features of the presented techniques are illustrated by means of simple examples. In addition, three real-world applications are described. Finally, software tools for building fuzzy models from measurements are available from the author.

Inhaltsverzeichnis

Frontmatter
1. Introduction
Abstract
This book addresses the modeling of complex, nonlinear, or partially unknown systems by means of techniques based on fuzzy set theory and fuzzy logic. This approach, termed fuzzy modeling, is shown to be able to cope with systems that pose problems to conventional techniques, mainly due to nonlinearities and lack of precise knowledge about these systems. Methods are described for the development of fuzzy models from data, and for the design of control systems which make use of an available fuzzy model. The presented framework allows for an effective use of heterogeneous information in the form of numerical data, qualitative knowledge, heuristics and first-principle models for the building, validation and analysis of models, and for the design of controllers. The obtained model can be a part of a real-time control algorithm, or can serve for analysis of the process, in order to gain better understanding, and to improve the operation, monitoring and diagnosis.
Robert Babuška
2. Fuzzy Modeling
Abstract
The concepts of fuzzy-set theory and fuzzy logic can be employed in the modeling of systems in a number of ways. Examples of fuzzy systems are rule-based fuzzy systems (Zadeh, 1973; Driankov, et al., 1993), fuzzy linear regression models (Tanaka, et al., 1982), or fuzzy models using cell structures (Smith, et al., 1994). This book focuses only rule-based fuzzy systems, i.e., systems where the relationships between variables are represented by a means of fuzzy if-then rules of the form:
If antecedent proposition then consequent proposition.
Robert Babuška
3. Fuzzy Clustering Algorithms
Abstract
An effective approach to the identification of complex nonlinear systems is to partition the available data into subsets and approximate each subset by a simple model. Fuzzy clustering can be used as a tool to obtain a partitioning of data where the transitions between the subsets are gradual rather than abrupt. This chapter gives an introduction to the basic concepts of fuzzy clustering, and simultaneously serves as a reference to clustering algorithms that can be used to construct fuzzy models from data. The basic notions of clustering and the different types of partitions are defined in Sections 3.1 and 3.2. Section 3.3 presents the basic idea of fuzzy clustering with objective function and the fuzzy c-means algorithm. Sections 3.4 and 3.5 address algorithms which can detect clusters contained in linear subspaces of the data space. These methods include clustering with an adaptive distance measure, clustering with linear prototypes, and fuzzy regression clustering. Section 3.6 presents the approach known as possibilistic clustering. Section 3.7 addresses the determination of an appropriate number of clusters and Section 3.8 deals with pre-processing of the data. The aim of this chapter is to explain clustering at a level necessary to understand the subsequent chapters. For a more detailed treatment of the subject, the reader may refer to the classical monographs by Duda and Hart (1973), Bezdek (1981) and Jain and Dubes (1988). A more recent overview can be found in a collection of Bezdek and Pal (1992), and the monograph by Backer (1995). The notation and terminology in this chapter closely follows Bezdek (1981).
Robert Babuška
4. Product-Space Clustering for Identification
Abstract
This chapter addresses the decomposition of a nonlinear identification problem into a set of locally linear models by means of product-space fuzzy clustering. The identification procedure is first outlined in Section 4.1. Structure selection and the choice of regressors in the modeling of dynamic systems are discussed in Section 4.2. Section 4.3 describes the principle of identification of nonlinear systems by product-space clustering. The choice of clustering algorithms is discussed in Section 4.4. Section 4.5 deals with the determination of the number of clusters by means of validity measures and compatible cluster merging.
Robert Babuška
5. Constructing Fuzzy Models from Partitions
Abstract
As shown in the previous chapter, a class of fuzzy clustering algorithms can be used to approximate a set of data by local linear models. Each of these models is represented by a fuzzy subset in the data set available for identification. In order to obtain a model useful for prediction or controller design, an additional step must be applied to generate a model independent of the identification data. Such a model can be represented either as a rule base or as a fuzzy relation. This chapter presents methods and algorithms for constructing fuzzy rule-based and relational models from the fuzzy partitions obtained by product-space clustering.
Robert Babuška
6. Fuzzy Models in Nonlinear Control
Abstract
This chapter addresses the design of different nonlinear controllers based on a fuzzy model of the process. In the presence of strong nonlinearities, nonlinear controllers can offer significant advantages over linear control techniques, and sometimes may be the only solution to develop a reliable controller. The previous chapters dealt with methods to obtain fuzzy models of dynamic systems. Once a reasonably accurate fuzzy model of the considered process is available, it can be used off-line to design a nonlinear controller for that process, or it may become a part of a model-based control scheme. Most methods for off-line control pertain to the homogenous or affine Takagi-Sugeno structure. Standard methods from linear system theory can be applied to design local feedback controllers for the individual consequent models. Stability of the closed loop can be analyzed by the Lyapunov method (Tanaka and Sugeno, 1992). Furthermore, the control design problem can be formulated by using linear matrix inequalities (Tanaka, et al., 1996). As quite an extensive literature is available on this topic (Palm, et al., 1997), this chapter will be devoted to the latter approach, i.e., model-based fuzzy control. Two particular techniques are considered: model inverse control and model-based predictive control.
Robert Babuška
7. Applications
Abstract
This chapter describes three selected real-world applications of the fuzzy modeling, identification and control methods presented in this book. Section 7.1 describes the development of a knowledge-based linguistic fuzzy model for predicting the performance and tool wear of a rock-excavation machine. The model has been developed purely on basis of expert knowledge, but it allows for tuning and adjustment by using numerical data. Different facets of the approach, such as translation of the expert knowledge into the linguistic rules and membership functions, the hierarchical organization of knowledge, and validation of the model are discussed. Section 7.2 deals with nonlinear identification based on fuzzy clustering. Takagi-Sugeno, singleton and relational fuzzy models have been developed to model highly nonlinear pressure dynamics. Experimental results of real-time predictive control based on the fuzzy model are presented. The last application, given in Section 7.3, demonstrates a modeling approach based on the combination of a fuzzy model with a first-principles model. A linguistic fuzzy model which represents the kinetic term in enzymatic Penicillin-G conversion is developed from numerical data. This fuzzy model is then incorporated in macroscopic balance equations describing the overall conversion process. It is shown that this approach gives good predictions, and at the same time allows for qualitative interpretation of the unknown relationships learnt from data.
Robert Babuška
Backmatter
Metadaten
Titel
Fuzzy Modeling for Control
verfasst von
Robert Babuška
Copyright-Jahr
1998
Verlag
Springer Netherlands
Electronic ISBN
978-94-011-4868-9
Print ISBN
978-94-010-6040-0
DOI
https://doi.org/10.1007/978-94-011-4868-9