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研究生:黃仕璟
論文名稱:三維磁浮軸承之模糊建模與強健適應控制-使用線性矩陣不等式法
論文名稱(外文):Fuzzy Modeling and Robust Adaptive Control for Three-Dimensional Magnetic Bearings Using LMI Approach
指導教授:林麗章
學位類別:博士
校院名稱:國立中興大學
系所名稱:機械工程學系
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2004
畢業學年度:92
語文別:中文
中文關鍵詞:錐形磁浮軸承系統T-S模糊模式線性參數近似器假設模態平行分散補償動態輸出回授控制器線性矩陣不等式偏心適應補償
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本論文考慮具偏心及撓性效應之錐形磁浮軸承系統(轉軸含剛性中段與兩側撓性軸),以假設模態(assumed modes)法表示兩側撓性軸之彈性變形,於建立整體轉軸之動能與位能表示式後,利用拉格蘭奇(Lagrange)方程式推導整體轉軸的三維(六自由度)動力學模式,再引入磁力與軸承間隙之關係式,建構整體磁浮軸承系統之撓性解析模式。
為了達到磁浮軸承系統暫態及穩態的性能要求,應用傳統控制理論,常使得控制策略過於複雜且需要龐大的計算量。因此,本論文先考慮一僅含偏心效應之剛性磁浮軸承,推導其解析T-S模糊模式,其中偏心效應以一線性參數(linear in the parameters)近似器加以處理,再以平行分散補償(PDC)方式建立各局部區域之狀態回授控制架構,並據以建構全域之強健適應模糊控制器。因系統狀態並非皆可量測,狀態回授控制器的實現有其困難,故本論文另提出一含偏心適應補償之動態輸出回授控制器。因為使用輸出回授,提高了控制器實現的可行性。當轉軸高速運轉時,除了轉軸偏心不平衡力所造成振動問題外,轉軸之撓性效應也將對系統的性能產生嚴重的破壞,因此基於前述所提含適應偏心補償之動態輸出回授控制,再引入一抗撓性效應之補償策略,期望能同時抑制偏心及撓性效應對系統的影響。
本論文針對含偏心效應之剛性磁浮軸承系統或撓性磁浮軸承系統所提出之強健適應模糊控制器,均可經由穩定化及抑制干擾之強健性分析,將控制器的設計化為解線性矩陣不等式(LMI)的問題,再經由最佳化方法解LMI,以求得控制器參數的最佳解。前述適應模糊控制器,所需的計算量較直接使用原來複雜模式設計的傳統非線性控制器簡單,因此將更容易實現。經由大量電腦模擬結果顯示,本論文所提之強健適應控制律皆有優異之轉軸速度追蹤、旋轉定位控制,以及氣隙調節的性能,對於由偏心及撓性效應所引起的振動,以及外部干擾具有極佳的主動抑制能力。
This thesis considers the modeling and control for conical magnetic bearings with flexible shaft, at whose center is fixed rigid circular rotor. The two lateral deflections of each flexible part can be considered as cantilever beams and expressed using the assumed-modes method. After deriving the kinetic and potential energy expressions, the whole rotor dynamics model is derived using Lagrange’s equations. Magnetic levitation force equations are then integrated with the rotor model to construct a complete model for the magnetic bearing system.
To meet the stringent transient and steady-state performance requirements, control design based on the original complex dynamics model is highly difficult. For simplicity, an analytical T-S (Takagi-Sugeno) fuzzy model with simplified mass-unbalance model expressed with a linear in the parameter approximator for a complex nonlinear rigid magnetic bearing system is first constructed. Based on the T-S fuzzy model, a stable fuzzy control including adaptive unbalance compensation for the high speed and high accuracy control of the complex magnetic bearing systems is then proposed. Since the states of the controlled system are not all measurable in practice, this thesis further presents a dynamic output feedback control with adaptive rotor-imbalance compensation based on the analytical T-S fuzzy model. Since the control design adopts output feedback, the derived controller can be more easily implemented. Furthermore, since the flexibility will also introduce severe oscillation of the rotor at high speed, based on the above proposed dynamic output feedback control, this thesis also suggests an energy-based active damping control design for further enhancing the vibration suppression capability of the whole control system.
Through the robust analysis for disturbance rejection, the suggested state feedback and dynamic output feedback fuzzy control design approaches for nonlinear magnetic bearings can be cast into a linear matrix inequality (LMI) problem, and the LMI problem can be solved efficiently using the convex optimization techniques. Based on the suggested fuzzy design, the controller will be much easier to implement than conventional nonlinear controllers. Simulation validations are presented for illustrating that the proposed control laws can suppress the rotor vibration due to the mass imbalance and rotor flexibility, and have excellent capability for high-speed tracking, angular positioning control and gap deviations regulation.
中文摘要......................... Ⅰ
英文摘要......................... Ⅲ
誌謝........................... Ⅴ
目錄........................... Ⅵ
圖表目錄......................... Ⅷ
符號說明......................... Ⅹ
第一章 緒論....................... 1
1.1 研究動機..................... 1
1.2 文獻回顧..................... 2
1.3 論文大綱..................... 6
第二章 考慮偏心及撓性效應之錐形磁浮軸承系統數學模式... 8
2.1 機械系統之數學模式................ 8
2.2 電磁系統模式................... 18
2.2.1 電磁系統之方程式................ 18
2.2.2 氣隙厚度偏差量之推導.............. 19
第三章 含適應偏心補償之剛性磁浮軸承系統強健模糊控制... 23
3.1 含偏心效應之剛性磁浮軸承系統之模糊建模...... 23
3.2 考慮適應偏心補償之強健模糊控制設計........ 30
第四章 含適應偏心補償之動態輸出回授控制......... 40
第五章 含撓性效應之錐形磁浮軸承動態輸出回授控制..... 51
第六章 電腦模擬與討論.................. 66
6.1 電腦模擬時使用之系統參數值............ 66
6.2 結果與討論.................... 69
第七章 結論與建議.................... 142
附錄 A 撓性軸側向變形之運動方程式........... 146
A-1 撓性軸變形運動方程式推導............. 146
A-2 轉軸系統動能與位能之推導............. 154
附錄 B 剛性磁浮轉軸之數學模式............. 159
B-1 剛性磁浮轉軸系統之動力學模式.......... 159
B-2 剛性磁浮轉軸系統之狀態方程式.......... 165
附錄 C 電腦模擬實例之控制器參數............ 167
C-1 剛性系統時,狀態回授控制器之參數........ 167
C-2 剛性系統時,動態輸出回授控制器之參數...... 170
C-3 撓性轉軸時,動態輸出回授控制器之參數...... 178
參考文獻........................ 186
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