臺灣博碩士論文加值系統

線性感應馬達具有旋轉式感應馬達所缺乏的優點，兩者特性相近，差別在於運動方式不同；線性感應馬達是一個多階非線性時變耦合系統，在控制上具有其難度，另外還受到邊際效應的影響，使得在模型化及控制器設計上加入些許難度；本篇論文將針對線性感應馬達，提出考慮邊際效應的數學模型，並利用適應性控制及被動性控制設計速度追蹤控制器。
利用電路特性和能量觀點兩種方法推導線性感應馬達的數學模型，線性感應馬達的結構如同旋轉式感應馬達切開坦平後的結構，兩者相像度極高，因此利用十分成熟的感應馬達模型推導方式套用於線性感應馬達上，兩者的差別在於運動方式不同，及線性感應馬達受到邊際效應的影響；運動方式的不同可藉由簡單的轉換式變換，邊際效應的影響以磁通的觀點討論，由於磁通必須是連續的，因此當線性感應馬達移動時，對應於一次側(移動體)邊端的二次側(感應體)會產生電流來抵抗突然變化的磁通，將此電流量化，並討論其對磁場及能量損失的影響，如此即可得到完整的線性感應馬達模型。
針對兩種方式所推導的數學模型分別利用適應性控制及被動性控制設計速度控制器；線性感應馬達為機電系統，可分成電氣子系統和機械子系統，在控制器設計上，亦針對兩個子系統獨立設計，電氣子系統以電流或電壓來控制推力，機械子系統控制器以推力來控制速度。第三章假設機械參數未知，在估測磁通時也有一未知常數，利用適應性控制估測這些未知常數，並完成速度控制的目的。第四章使用被動性控制，兩子系統皆利用到加入阻尼(damping injection)和能量塑形(energy shaping)的方式設計控制器，這裡亦假設機械參數未知，因此在機械子系統控制器中加入適應性控制來解決未知常數的問題。最後，針對這兩個控制器各自定義Lyapunov函數來證明整個系統的穩定性。
以Matlab的Simulink對兩控制器進行模擬，初步驗證其可行性，以PC-Based視覺化控制系統對實際的馬達進行控制，可由結果得知控制器可使其速度達到追蹤效果。

A linear induction motor (LIM) is a kind of special electrical machines that convert electrical energy directly into mechanical energy of linear motion. Owing to the nonlinear, time-varying, coupled model of LIM, the speed control becomes a complex problem. A challenge arises on the modeling and controller design of LIM due to the existence of the end effect. The aim of this thesis is to derive the mathematical model of an LIM where the end effect is considered, and then two schemes,namely adaptive control and passivity based control (PBC), are proposed to design the LIM speed controller.
Form the circuit and energy point of view, the mathematical model of an LIM can be derived based on Kirchhoff’s voltage law and Euler-Lagrange equations, respectively. An LIM can be regarded as an unrolled rotary motor by cutting the rotary motor along a radial plane. Hence, the structure is similar to the induction motor. However, when we model the LIM, the end effect should be emphasized. When the primary of an LIM moves, the secondary under the edge of primary will create the eddy current to resist a sudden increasing or disappearing fluxes. After modelling the end effect due to eddy current, we obtain the complete mathematical model of an LIM.
Based on the two forms of the derived models, adaptive control and passivity based control(PBC) are, respectively, proposed to design the LIM speed controller. LIM is an electromechanical system and can be decomposed into a mechanical subsystem and an electrical subsystem. Therefore, a two-stage control design, namely torque controller and speed controller are developed. An adaptive controller with a nonexplicit flux observer is applied to handle the speed tracking problem when the mechanical parameters and the flux of secondary are unknown. The PBC design includes two main parts, namely damping injection and energy shapping to form the controller. Lyapunov direct method is used to analyize the stability of the closed-loop systems. Finally, numerical simulation and hardware experiments are carried out to verify the performance of the proposed controller.

中文摘要
英文摘要
目錄
第一章緒論1
1.1 簡介 1
1.2 研究動機5
1.3 論文架構6
1.4 論文貢獻7
第二章線性感應馬達之數學模型 8
2.1 前言 8
2.2 線性感應馬達之結構 9
2.3 線性感應馬達在電路上的特性 12
2.4 三相系統與二維座標系統之間的轉換 15
2.5 線性感應馬達之動態方程式 16
2.5.1 電氣方程式 16
2.5.2 推力方程式 18
2.5.3 機械方程式 19
2.5.4 線性感應馬達之初步模型 19
2.6 邊際效應對線性感應馬達的影響 20
2.7 線性感應馬達之完整模型 24
2.8 由能量觀點推導線性感應馬達模型 26
2.8.1 Euler-Lagrange方程式 26
2.8.2 電氣系統和機械系統的能量與外部作用力26
2.8.3 未考慮邊際效應之線性感應馬達模型29
2.8.4 考慮邊際效應之線性感應馬達模型 31
2.8.5 線性感應馬達系統之被動性 32
2.8.6 轉換為傳統五階方程式 33
第三章線性感應馬達簡化模型之適應性速度控制 35
3.1 前言 35
3.2 線性感應馬達之簡化模型 36
3.3 二階段式控制器設計(Two-Stage Design Method)37
3.4 最佳推力的產生與磁通命令 37
3.5 二次側磁通重建 39
3.6 適應性速度控制 40
3.6.1 速度控制器之設計 41
3.6.2 推力控制器之設計 42
3.6.3 穩定度分析 44
3.7 模擬結果 46
第四章線性感應馬達完整模型之被動性速度控制57
4.1 前言 57
4.2 外迴圈速度控制器 58
4.3 內迴圈推力控制器 60
4.3.1 加入阻尼(damping injection) 60
4.3.2 能量塑形(energy shaping) 62
4.4 穩定性分析 66
4.5 模擬結果 68
第五章控制器軟硬體設計環境與實作結果78
5.1 前言 78
5.2 軟硬體設計環境 79
5.3 實作結果 81
第六章結論與未來展望 89
6.1 結論 89
6.2 未來展望 90
參考文獻 92

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