本篇論文對於非線性系統與模糊系統引用LMI為基礎之精確已近似控制理論，並用已達成控制目標。首先，將非線性系統以數個具線性系統為後件部的模糊子系統作為表示，再融合所有子系統精確表示原先的非線性系統。針對此精確模糊受控系統，設計具相同前件部之模糊狀態迴授控制器，另用穩定性分析方法找出閉迴路系統穩定之充分條件，將充分條件轉換為 LMI 條件後，控制器達成目的所需之控制增益等等，可由電腦以數值模擬方式運算出結果。
為驗證所提出的控制方法，首先利用 Matlab 完成控制器在電壓穩定性的數據模擬。接著，用電子電路實做直流對直流降壓型電源轉換器，利用 dSPACE 1104 控制晶片以及 Matlab toolbox 實現 LMI為基礎的非線性控制器。時做結果也證明此控制理論確實能應用於降壓型電源轉換器的控制，並增加輸入變動以及負載變動實驗，證明此控制理論在不同狀態下仍能達到電壓穩壓之效果。

In this thesis, according LMI-based Control for Fuzzy and nonlinear systems to implement the DC-DC buck converter output voltage regulation. First, the nonlinear system is represented by several fuzzy subsystems where the consequent parts are linear dynamical systems. Then by blending these rules, we exactly represent the original nonlinear dynamical systems. Following the modeling stage, a fuzzy state feedback controller for each linear subsystem is designed with same variables as that of the fuzzy plant model representation. Using Lyapunov’s direct method, the stability analysis is carried out on the overall closed-loop system. The sufficient conditions arising from the stability analysis is then formulated into linear matrix inequalities.
 We using MATLAB to simulate the LMI voltage output and then make electronic circuit DC-DC buck converter. In the end use DS1104 controller and MATLAB Simulink toolbox to achieve LMI-based controller, and the experiment result indicates LMI-based theory can implement into PWM DC-DC buck converter, and it can also can regulate the voltage on load changes or voltage changes situation

Contents I
List of Figures II
List of Tables IV
1 Introduction 1
1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.1 Mamdani fuzzy System . . . . . . . . . . . . . . . . . . . . . . . 2
1.1.2 T-S fuzzy System . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1.3 Linear Martix Inequalities . . . . . . . . . . . . . . . . . . . . . 3
1.2 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2 LMI-based Control for Nonlinear Systems 6
2.1 Modeling of Nonlinear System . . . . . . . . . . . . . . . . . . . . . . . 6
2.1.1 Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.1.2 Dynamic Output Feedback Controller . . . . . . . . . . . . . . . 9
2.1.3 Robust Output Tracking and Regulation . . . . . . . . . . . . . 20
I
3 Conventional PWM Buck Converter 24
3.1 Basic Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.2 Modeling for PWM Buck Converter . . . . . . . . . . . . . . . . . . . . 26
3.3 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
4 Experiment Results 29
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
4.2 DS1104 controller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
4.2.1 DS1104 A/D . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
4.2.2 DS1104 PWM signal . . . . . . . . . . . . . . . . . . . . . . . . 31
4.2.3 MOSFET gate drive circuit design . . . . . . . . . . . . . . . . 31
4.2.4 Implementation using DS1104 . . . . . . . . . . . . . . . . . . . 33
4.2.5 Experiment 1 : Change different voltage inputs . . . . . . . . . 33
4.2.6 Experiment 2 : Switch different Resistances . . . . . . . . . . . 36
5 Conclusions and future work 39
References 40
II
List of Figures
3.1 Conventional PWM buck converter circuit . . . . . . . . . . . . . . . . 24
3.2 PWM buck converter circuit when the switch is on . . . . . . . . . . . 25
3.3 PWM buck converter circuit when the switch is off . . . . . . . . . . . 25
4.1 DS1104 Architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
4.2 DS1104 experiment flow chart . . . . . . . . . . . . . . . . . . . . . . . 30
4.3 DS1104 A/D figure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
4.4 DS1104 PWM signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
4.5 Resistor–Capacitor circuit . . . . . . . . . . . . . . . . . . . . . . . . . 33
4.6 Output voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
4.7 Output iL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
4.8 error when the voltage at 20V . . . . . . . . . . . . . . . . . . . . . . . 35
4.9 V of loading change from 6Ω to 16Ω at 20V . . . . . . . . . . . . . . . 36
4.10 Ampere of loading change from 6Ω to 16Ω at 20V . . . . . . . . . . . . 37
4.11 Error of loading change from 6Ω to 16Ω at 20V . . . . . . . . . . . . . 37
III
List of Tables
4.1 Parameter value of DC-DC PWM buck converter . . . . . . . . . . . . 38
IV

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