本論文提出了重複適應性互補式滑動模式控制(RACSMC)應用於X-Y軸伺服線性馬達定位平台，以開發一套高精密運動之雙軸控制平台。首先我們先針對單軸的線性馬達系統模型建立，然後進行控制器設計，在本研究中RACSMC將主要運用適應性互補式滑動模式控制(ACSMC)來進行主要的控制動作，其主要特性在於有兩個滑動面的設計，而滑動面的狀態收斂條件是沿著兩滑動面的交線移動到最終收斂位置，而在動態響應部分比起一般傳統的滑動模式控制(SMC)，有更好的誤差收斂效果，接著加入適應控制讓不確定性的參數估測不必全部都藉由SMC的強健控制切換函數項進行抑制，進而減少切跳現象(chattering)，最後再加入重複控制原理，讓系統在週期性的精密運動的時候，可以抑制週期性的誤差，反覆學習的一種概念，使系統的穩態誤差在經由反覆的學習再更加的降低，進而提升此系統的精確度。
　　在本論文中將會建立出一個線性馬達的雙軸定位平台數學模型，首先會把使馬達驅動的三相電流轉換為d-q軸控制電流，接著將此線性馬達推力方程式與機械模型整合後推導出兩軸的定位平台運動方程式，而系統的運動方程式將會考慮不確定性的問題，因此將會藉由此運動方程式，進行控制器的推導來設計適合此定位平台之控制器。在實驗中本研究將會對兩軸個別的做控制，以了解論文中設計的SMC及RACSMC對於此控制平台的性能差異，藉由定位以及追跡的實驗結果，可以證明本論文提出的RACSMC可以在此控制平台中有降低切跳現象，以及增加誤差收斂的效果，最後將使用RACSMC對雙軸做圓追跡、螺紋和葉子軌跡來呈現控制器的效能。

In this paper, a repetitive adaptive complementary sliding mode control (RACSMC) is proposed for the X-Y-axis servo linear motor positioning platform develop the high precision motion double-axis platform. First, it focus on the developing of the single-axis linear motor system model. Then it will program the design of the controller. In this study, RACSMC will mainly use adaptive complementary sliding mode control (ACSMC) to carry out the main control action. The main feature is the design of two sliding surfaces. Its state of convergence is to move along the intersection of the two sliding surfaces to the final convergence position. The error convergence effect in the part of dynamic response is better than the traditional sliding mode control (SMC). This study add the adaptive control so that the parameter estimation of the uncertainty does not have to be all by the SMC robust control switching function to suppress in addition to reduce the chattering. At last, combining the principle of repeated control to inhibit the cyclical error and repeat learning a concept in the system in the periodic. Then steady-state error of the system will reduce through the repeated learning, and moreover enhance the accuracy of the system.It will derive a dual axis positioning platform mathematical model of the linear motor in the paper. It will convert the three-phase current which drives the motor into the dq-axis control current. This study can derive the motion equations of the two-axis positioning platform by integrating the linear motor thrust equation and the mechanical model. However, the system motion equations will take into account the problem of the uncertainty, so the motion equation will be used to derive the controller to design the controller for this positioning platform. In the experiment, this study will respectively control two-axes to learn the difference of performance between our designed SMC and RACSMC in this control platform. By the experimental results of positioning and tracking, it can prove that the RACSMC which our proposed will produce reduction in the phenomenon of switching and increase the effect of error convergence in this control platform. Finally, this study will present the performance of the controller by using the RACSMC on the dual axis to make circle tracking.

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