本論文提出了具有數種干擾之五軸主動式磁浮軸承(AMB)系統的完整狀態空間模型，做為一個具有挑戰性的基準問題，並針對五軸AMB採樣系統提出強建最佳線性二次數位追蹤器(LQDT)。此外，本文的其他目標為: (i) 針對一個極度不穩定的未知非線性時變AMB系統，藉由觀測器/卡爾曼濾波器鑑別方法建構一個基於額定轉速和採樣頻率下的等效離散時間線性非時變系統及其狀態估測器; (ii) 建構一個自調式干擾估測器以得到等效未知干擾(EID)，當一些未知系統干擾發生在一些不可預期的時間段時，可以補償受到未知系統干擾的伺服機構之性能; 以及 (iii) 針對一個預先規劃之時變轉速及未知干擾的採樣AMB系統，建構一個強健最佳LQDT，當轉子位移偏離其預定軌跡時，控制器可以將轉子位移回復到預定軌跡上。

A complete state-space modelling of the five-degree-of-freedom (five-DOF) active magnetic bearing (AMB) system with various disturbances has been presented in this thesis as a challenge benchmark problem. Then, a robust observer-based optimal linear quadratic digital tracker (LQDT) for the five-DOF sampled-data AMB system is proposed. In addition, the other objectives of this thesis are to: (i) Construct an equivalent discrete-time linear time-invariant model of the highly unstable unknown nonlinear time-varying AMB system and its state estimator for some specified rotation speed and sampling rate by Observer/Kalman filter identification; (ii) Construct an adaptive disturbance estimator to have the equivalent input disturbance (EID), whenever some unexpected system disturbances occur during some unexpected time periods, so that the performance compensation of the servomechanism subjected to the unexpected disturbances can be achieved; and (iii) Construct a robust observer-based optimal LQDT for the sampled-data AMB system subjected to a pre-specified time-varying rotation speed as well as unexpected disturbances, so that the controller can recover the displacements of the rotor to the pre-specified position trajectory whenever it deviates from the pre-specified position trajectory.

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