在自動化工業演進的過程中，傳動系統無疑扮演重要的角色，不論在機械手臂的伺服系統，又或是風力發電與飛行器的制動器等，都能看到它的身影，其主要的功能是將馬達的力量或是速度以機構的方式傳遞到目標的位置。由於傳動機構在運作的過程時常產生高溫，為了能夠加入潤滑劑且避免機構熱膨脹造成元件變形，在設計上往往會透過預留一小段空隙作為緩衝，該空隙也就是所謂的背隙。隨著使用的時間越長，機台元件的損耗皆會導致背隙區間逐漸變大，除了會影響被動端的追蹤誤差外，過大的背隙甚至會造成系統過度振動。若能從已知的資訊透過一連串的鑑別流程獲得背隙區間的大小，除了可以作為機台元件是否要更換的依據外，更可將鑑別結果整合至控制架構進行補償以改善背隙對系統造成的影響。理想的情況下可直接利用主動端與被動端兩者位置資訊的差距判斷出背隙區間的大小，但在真實情況下被動端的位置資訊較難取得，因此如何僅由主動端資訊去估測出正確的背隙區間大小便是需要解決的問題之一。本論文建立一套完整的技術，透過主動端轉矩判斷背隙發生的時機，並利用2-step法鑑別出主動端與被動端的慣量與摩擦力，再透過預測被動端在背隙過程中的速度以積分速度差的方式鑑別出精確的背隙區間大小，整套技術僅會使用到主動端的資訊。此外，本論文亦透過建立數位孿生模型以預測運動過程中系統的接觸狀態，並設計出背隙補償命令改善被動端的追蹤誤差。簡言之，本論文提出的方法包含系統的參數鑑別、背隙區間大小的鑑別以及背隙補償命令的設計，除了可用於機台的健康診斷以外，亦可以有效改善運作過程中因為背隙造成的追蹤誤差，藉此改善機台的加工精度。

Transmission systems are crucial in modern industrial processes such as servo systems of robot manipulators, power generation systems, and aircraft actuators. In general, the purpose of a transmission system is to transmit the force or velocity of the motor to the target position through a mechanism. Because the operation is usually conducted at high temperature, a space is left between the gear teeth in a transmission system—known as backlash—for the purpose of lubrication and also providing the margin of the thermal expansion of gears. The backlash would get wider with time because of the wear of machine components, leading to the tracking errors on the load side as well as the vibration of the system. If the backlash size can be identified by known information, it can not only be used as the index of a maintenance strategy, but also used in a control scheme to compensate for the effects of the backlash. As a result, this thesis proposes an approach for identifying the size of the backlash using motor-side information only. Timing of the backlash is determined by the motor-side torque, while the inertia and friction are identified by a 2-step method. With the estimation of load-side velocity in the backlash process, accurate size estimation of the backlash can be achieved by integrating the velocity difference. In addition, a digital twin model is constructed for predicting the contact states during the system motion, helping to design the backlash compensation command to reduce tracking errors and also suppress the vibration of the system. Simulations and experimental results verify the accuracy of identification results and the effectiveness of the compensation methods.

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