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標題: 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
Fuzzy Modeling and Robust Adaptive Control for Three-Dimensional Magnetic Bearings Using LMI Approach
作者: 黃仕璟
關鍵字: 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
出版社: 機械工程學系
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。

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.
Appears in Collections:機械工程學系所

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