單輸入模糊控制器與基底函數之探討

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姓名

陳明裕(Ming-Yu Chen) 查詢紙本館藏

畢業系所

電機工程學系

論文名稱

單輸入模糊控制器與基底函數之探討
(A Single-input Fuzzy Controller and Basis Functions)

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摘要(中)

本論文以模糊控制器為基本架構，發現大多數模糊控制器之模糊規則庫均具有反對稱的性質，所以我們根據此特性設計一個單數入模糊控制器，比較可得傳統雙輸入模糊控制器與單輸入模糊控制器之響應圖近似，但是單輸入模糊規則數卻大大地減少，因此更加利於修改。接著，我們應用基因演算法來調整比例因子，經由此方法可使的上升時間和最大超越量均有所改善。此外，我們又另外提出模糊基底函數與其它連續型基底函數做比較，因而發現模糊基底函數的性能相較於其他連續型基底函數更加優越。

摘要(英)

We find that rule tables of most fuzzy logic controllers have skew-symmetry property. In this thesis, we will propose a new variable, which is a sole fuzzy input variable. The single-input fuzzy logic controller can greatly reduce the total number of rules. Hence, generations and the adjustment of control rules are easier. Control performance is nearly the same as that of conventional fuzzy logic controllers. In order to improve the performance of the transient state and the steady state of single-input fuzzy logic controller, we develop a method to tune the scaling factors based on genetic algorithms. The simulations of this new method show the better performance in the response. Next, we will discuss the fuzzy basis function and other continuous basis functions. Then, it is seen that the fuzzy basis function has the better performance than other continuous basis functions.

關鍵字(中)

★ 單輸入模糊控制器
★ 基底函數

關鍵字(英)

★ a single input fuzzy logic controller
★ basis function

論文目次

Table of Content
Abstract Ⅰ
Table of Content Ⅱ List of Figures Ⅳ
List of Tables Ⅶ
ChapterPage
Chapter 1 Introduction 1
1.1 Background 1
1.2 Motivation 2
1.3 Organization 3
Chapter 2 Notions of the Fuzzy Logic Controller4
2.1 The Basic Notion of the Ordinary Fuzzy Controller4
2.2 The Basic Structure of the PID-type Controller6
2.3 The Simulations of Comparison9
Chapter 3 A Single-input Fuzzy Logic Controller via the
Tuning of Scaling Factors Based on Genetic Algorithms12
3.1 Introduction 12
3.2 Design of the Single-input FLC13
3.2-1 Problem Formulation 13
3.2-2 Design of S-FLC 15
3.3 The Performance-oriented Objective Function for Genetic Algorithms18
3.3-1 The Basic Concept of Genetic Algorithms18
3.3-2 The Scaling Factor Based on Genetic Algorithms 19
3.4 Simulation Results20
3.4-1 Example 1 20
3.4-2 Example 2 23
3.5 Conclusions 28
Chapter 4 Comparison of Adaptive Controllers Using Different Basis Functions29
4.1 Introduction 29
4.2 Basis Functions 30
4.2-1 Fuzzy Basis Functions 30
4.2-2 Gaussian Radial Basis Functions 31
4.2-3 Orthogonal Basis Functions 32
4.2-3-A Legendre Polynomials 33
4.2-3-B Laguerre Polynomials 33
4.2-3-C Hermitte Polynomials 34
4.2-3-D Tchebycheff Polynomials of the First Kind 35
4.2-3-E Tchebycheff Polynomials of the Second Kind 35
4.3 The Problem Formulation and the Adaptive Controller Design Using Different Basis Functions36
4.4 Simulation and Discussion39
4.5 Conclusions 51
Chapter 5 Conclusions and Recommendations 52
References 54
List of Figures
Page
Fig. 2.1 The basic structure of fuzzy controller4
Fig. 2.2 Four types of the fuzzy membership functions 5
Fig. 2.3 The fuzzy PD-type control system 6
Fig. 2.4 The fuzzy PI-type control system6
Fig. 2.5 Time domain7
Fig. 2.6 Phase plane8
Fig. 2.7 The fuzzy PID-type control system9
Fig. 2.8 The membership function of antecedent and consequent 9
Fig. 2.9 Comparison of the fuzzy PD-type and PID-type controller system 10
Fig. 2.10 Comparison of the fuzzy PI-type and PID-type controller system 10
Fig. 3.1 Rule table with infinitesimal quantization levels 15
Fig. 3.2 Derivation of a signed distance 16
Fig. 3.3 The algorithm structure of SGA 18
Fig. 3.4 The scaling factor on S-FLC used genetic algorithms 19
Fig. 3.5 The membership function of antecedent and consequent 20
Fig. 3.6 The response of of S-FLC21
Fig. 3.7 The response of of S-FLC22
Fig. 3.8 The response of of S-FLC based on genetic algorithms22
Fig. 3.9 The response of of S-FLC based on genetic algorithms23
Fig. 3.10 Structure of an inverted pendulum system 24
Fig. 3.11 Time response of of S-FLC25
Fig. 3.12 Time response of of S-FLC25
Fig. 3.13 Time response of of S-FLC based on genetic algorithms26
Fig. 3.14 Time response of of S-FLC based on genetic algorithms26
Fig. 3.15 The control input of S-FLC 27
Fig. 3.16 The control input of S-FLC based on genetic algorithms27
Fig. 4.1 Basic configuration of fuzzy systems 30
Fig. 4.2 Six fuzzy membership functions defined over the state space41
Fig. 4.3(a) The response of the different positive initial states using the fuzzy basis functions41
Fig. 4.3(b) The response of the different negative initial states using the fuzzy basis functions42
Fig. 4.4(a) The control inputs of different positive initial states using the fuzzy basis functions 42
Fig. 4.4(b) The control inputs of different negative initial states using the fuzzy basis functions 42
Fig. 4.5(a) The response of the different positive initial states using the radial basis functions43
Fig. 4.5(b) The response of the different negative initial states using the radial basis functions43
Fig. 4.6(a) The control inputs of different positive initial states using the radial basis functions 43
Fig. 4.6(b) The control inputs of different negative initial states using the radial basis functions 44
Fig. 4.7(a) The response of the different positive initial states using the Legendre polynomial functions44
Fig. 4.7(b) The response of the different negative initial states using the Legendre polynomial functions44
Fig. 4.8(a) The control inputs of the different positive initial states using the Legendre polynomial functions45
Fig. 4.8(b) The control inputs of the different negative initial states using the Legendre polynomial functions45
Fig. 4.9 The response of the different initial states using the Laguerre polynomial functions45
Fig. 4.10 The control inputs of the different initial states using the Laguerre polynomial functions46
Fig. 4.11(a) The response of the different positive initial states using the Hermite polynomial functions46
Fig. 4.11(b) The response of the different negative initial states using the Hermite polynomial functions46
Fig. 4.12(a) The control inputs of the different positive initial states using the Hermite polynomial functions47
Fig. 4.12(b) The control inputs of the different negative initial states using the Hermite polynomial functions47
Fig. 4.13(a) The response of the different positive initial states using the Tchebycheff polynomial of the first kind functions47
Fig. 4.13(b) The response of the different negative initial states using the Tchebycheff polynomial of the first kind functions48
Fig. 4.14(a) The response of the different positive initial states using the Tchebycheff polynomial of the second kind functions48
Fig. 4.14(b) The response of the different positive initial states using the Tchebycheff polynomial of the second kind functions48
Fig. 4.15 The response of the positive initial state using the Walsh functions 50
Fig. 4.16 The response of the positive initial using the Walsh functions 50
Fig. 4.17 The response of the negative initial state using the Walsh functions 50
Fig. 4.18 The response of the negative initial using the Walsh functions 51

參考文獻

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指導教授

鍾鴻源(Hung-yuan Chung)

審核日期

2000-7-5

推文