近年來，由於磁浮軸承能有效減少系統因為摩擦力所產生之磨耗、震動、噪音與能量損失…等問題，已被廣泛的利用在各種應用之中。然而由於磁浮軸承系統具有高度非線性與時變之控制特性，因此必須針對磁浮軸承發展具優異強健性之控制系統以達到良好之控制性能。
為了達到非線性磁浮軸承系統之精密定位與追蹤控制功能，本論文首先提出遞迴式小波類神經網路(Recurrent Wavelet Neural Network, RWNN)控制器來控制磁浮軸承系統的轉子位置。雖然控制器之參數值可經由負梯度下降法進行線上學習，但不適當之參數初始值會使得線上學習落入局部最佳值，限制了控制性能。有鑑於此，本論文進一步提出最佳化遞迴式小波類神經網路(Optimal Recurrent Wavelet Neural Network, ORWNN)，運用適應性差分進化演算法(Adaptive Differential Evolution, ADE)來優化網路參數初始值。由實驗結果可知，優化後的遞迴式小波類神經網路確實可得到更佳之控制效果。
此外，本論文以利用適應性差分進化演算法最佳化差動驅動模式中之偏置電流(Bias Current, io)之概念，提出具最佳化差動驅動模式之遞迴式小波類神經網路(Optimal Recurrent Wavelet Neural Network with Differential Driving Mode, ORWNN-DDM )控制器，以進一步降低磁浮軸承系統之耗能。最後由實驗可知，本論文所提出之ORWNN-DDM控制器確實可在達到良好定位控制情況下，同時達到降低能量消耗之效果。

In recent years, magnetic bearings (MB) with noncontact and frictionless characteristics have been widely applied in various kinds of applications. However, since the MB systems are with highly nonlinear and time-varying control characteristics, it is very important to develop the robust controllers for MB to achieve favorable control performances.
To achieve precise positioning and tracking control performances of the nonlinear MB control system, a recurrent wavelet neural network (RWNN) controller is firstly proposed to control the position of the rotor in this study. Though the network parameters including connective weights, translations and dilations of the RWNN controller can be adjusted online through the gradient descent method, they may reach the local optimal solutions due to the inappropriate initial values. Therefore, an optimal RWNN (ORWNN) controller with adaptive differential evolution (ADE) is further proposed, in which the initial network parameters are optimized via the ADE algorithm. From the experimental results, the tracking performances of the ORWNN are much improved compared with the ones of RWNN.
In addition, the ADE algorithm is used to optimize the bias current of the differential drive mode system for saving energy consumption. It is called ORWNN-DDM controller in this study. Experimental results demonstrate the high-accuracy control and significant energy saving performances of the proposed ORWNN-DDM controlled MB positioning system.

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