本論文目標是研究一種最佳化的分數階比例-積分-微分(PID)控制策略，用來控制於X-Y音圈馬達定位平台。首先介紹音圈馬達平台之系統架構和運作原理，以系統鑑別的方式推導出馬達數學模型中的系統參數。接著，基於分數階微積分設計一個分數階PID控制，透過控制系統參數額外自由度，分數階PID可改善傳統的PID控制響應和穩健性，為了增加系統的控制平滑度，本論文以模糊理論提出了分數階模糊PID控制，可解決傳統分數階PID的抖動現象，調整這些額外的分數運算也增加控制系統設計的複雜性，因此，本論文進一步提出了最佳化分數階模糊PID控制器，其中五個參數包括比例增益、積分增益、微分增益、分數階積分和分數階微分，均利用自適應布穀鳥搜索算法調整。在自適應布穀鳥中，本論文再提出以動態調整步長及發現率來增加全域和局部的搜尋能力，並以音圈馬達追隨過程中X軸和Y軸的最小誤差的絕對值作為布穀鳥演算之適應函數。本論文以數位訊號處理器(TMS320F28377xD)實現上述控制策略，並且比較兩種追蹤軌跡和兩種測試模式，最後由實驗結果驗證所設計的控制器確實能有效的控制音圈馬達定位平台。

The object of this study is to develop an optimal fractional-order proportional-integral-derivative (OFOPID) control strategy for controlling the mover position of a voice coil motor (VCM)-based x-y motion stage. First, the operating principle and dynamics of the VCM-based x-y motion stage are described. Then, a design of the fractional-order proportional-integral-derivative (FOPID) control is introduced on the basis of the fractional calculus. With the additional degree of freedom to the control system parameters, the FOPID control can improve the control responses and robustness of the conventional proportional-integral-derivative (PID) control. In order to improve the robustness of the system, a fuzzy fractional-order PD control is proposed based on fuzzy theory, which can solve jitter phenomenon of the traditional fractional-order PID. However, tuning these extra fractional operators increases the complexity of the control system design. In this regard, the FOPID controller is further proposed in which five interdependent control parameters including proportional gain, integral gain, derivative gain, fractional operator of integral, and fractional operator of derivative are all online optimally determined via an adaptive cuckoo search algorithm (ACSA). In the ACSA, the step size and discovery probability are dynamically adjusted to regulate the abilities of global and local searches. The summation of integral absolute errors in x and y axes of the VCM-based x-y motion stage during tracking process is chosen as a performance index for minimization. In this study, all of the control strategy were implemented via the digital signal processor (DSP). In addition, two reference trajectories and three control modes were provided to evaluate the control performances of different control systems. the experimental results can be verified that the designed controller can effectively control the voice coil motor positioning platform.

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