Date of Award:

5-1995

Document Type:

Thesis

Degree Name:

Master of Science (MS)

Department:

Electrical and Computer Engineering

Committee Chair(s)

Robert W. Gunderson

Committee

Robert W. Gunderson

Committee

Todd K. Moon

Committee

R. Rees Fullmer

Abstract

Fuzzy control has met with a tremendous interest in applications over the past few years. Despite its application potential, a broader industrial exploitation of fuzzy control has been hindered by the lack of standard design methods for fuzzy control systems. Fuzzy controllers have had to be designed on a case-by-case basis employing heuristics and reflecting the designer's limited insight into the control object's behavior. A number of fuzzy theorists have investigated the fuzzy system theoretic problems and results reported in the literature have been encouraging.

This thesis research has explored the notion that fuzzy control, despite being a rule-based control strategy, can be approximated in the limit by a linear control scheme and can, further, be reconciled with more conventional design and analysis methods. By extending the results of the "natural law" theorems by Bouslama and Ichikawa to the control of digital servo-systems, this thesis presents a systematic design procedure for a fuzzy controller by utilizing the considerable resources and well-developed techniques of linear control theory.

The preliminary contribution of this thesis has been to show that the "natural law" limit theorem remains valid for the more widely used scaled (correlation-product) inference with the faster center-of-sums defuzzification. By relating the theoretical results obtained to conventional control theory, a systematic design scheme has been proposed based on linear state feedback and direct digital design. A unique method of relating the state-feedback gains to the partitions of the fuzzy sets has also been presented. By employing a modified MRAC scheme, direct adaptation capability has been provided to modify the fuzzy sets on-line. To the author's knowledge, this adaptive "natural law" fuzzy controller (ANFC) is a novel attempt at applying advanced techniques directly from linear systems theory to fuzzy control.

This research has resulted in a coherent procedure for the design of adaptive fuzzy controllers for digital servo-systems. This design method has been implemented as a control algorithm and used successfully to balance an inverted pendulum. The performance comparisons of the ANFC with other control schemes offer definite encouragement for future research along these lines.

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