線性馬達平台誤差補償之順滑模態觀測器設計

Abstract

本文主要研究方向在於設計一順滑模態觀測器來觀測線性馬達中無可避免的摩擦力及非線性干擾現象，進而迴授補償至系統輸入力矩，達到精準的控制效果。文中在動態摩擦力模型中的LuGre Model架構下設計觀測器，並利用各種不同的實驗方法來估測摩擦力模型的參數以得到精確的摩擦力模型。並利用Lie derivative的方法，針對系統狀態進行了可觀測性分析。而對於摩擦力模型所無法涵蓋的部分，以及馬達運動過程中的一切非線性干擾，引進順滑模態控制理論的概念於觀測器中，設計一個令誤差動態為零的狀態空間為順滑面，一旦誤差動態到達此順滑面，將不會再離開。經過實驗的驗證，順滑模態觀測器確實可以對摩擦力進行有效的補償，不論是起動區亦或是換向區的部分，響應與命令的誤差都能夠有效的減少百分之五十以上。

A sliding-mode observer is proposed in this thesis to estimate the unavoidable friction and undesired disturbance of motion. Then, it is used to feedback for compensation to achieve precise control. In this research, the design of observer is based on a dynamic friction model, LuGre Model, which can estimate friction more accurately. Several kinds of experimental methods are used to identify the parameters of the friction model. The observerbility of the nonlinear system is also verified by Lie derivative method. For the rest part of nonlinear friction force which is not included in the dynamic friction model and any other nonlinear disturbance which occurred in motor motion, the sliding-mode observer were devised. The sliding surface is defined as the state errors are zeros. Once the error dynamics reaches the sliding surface, it will not move off any more. It means this observer can accurately estimate the nonlinear term. The experimental results show that the errors are reduced to 50% of the value of the original errors.