有限行程下的線性致動器參數估測與快速定位控制之穩定性研究; Identification of Linear Actuators within Limited Stroke and Stability Analysis on Fast-Pointing Systems

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题名:	有限行程下的線性致動器參數估測與快速定位控制之穩定性研究;Identification of Linear Actuators within Limited Stroke and Stability Analysis on Fast-Pointing Systems
作者:	李永瑤;Yun-Yao Lee
贡献者:	電機工程研究所
关键词:	運動方程式;非線性;摩擦;可動噴嘴;倒單擺;致動器;系統鑑別;friction;nonlinear systems;pointing control;stick-slip;simulation;modeling;identification
日期:	2009-06-24
上传时间:	2009-09-22 11:48:11 (UTC+8)
出版者:	國立中央大學圖書館
摘要:	本論文主要研究致動器在不同負載下的動態行為。首先推導致動器外接不同負載時的運動方程式，本文發展出獨特的模組式架構，將負載與致動器分離，使致動器在外接不同負載時完全不需要修改致動器本身的運動方程式，而以負載抗力作為致動器與負載之間的連結。所得到的運動方程式簡潔，極易轉換成系統或模擬所需的方塊圖，但最大的好處為，致動器或負載本身所含的非線性可個別鑑別，不需面對複雜而有行程限制的致動器與負載系統。繼而提出致動器在無外加負載下的鑑別程序。本文提出一種新的鑑別方式，可在有限行程中鑑別致動器的阻尼、庫倫摩擦，以及系統轉動慣量等三大參數，其中轉動慣量的鑑別特別考慮到庫倫摩擦影響，並提出模擬與實驗結果，證實本方法的有效與正確性。在建立制動器之參數鑑別後，繼續討論致動器與負載連結時，系統整體機械效率(hm)的鑑別方式。本文將與外力成正比的摩擦以機械效率來建模，詳細推導hm對系統運動方程式的影響，並提出hm 與致動器內部庫倫摩擦的鑑別方式。並提出實驗結果與理論模型比較，理論分析的正確性。另外針對線性致動器中常見的非線性元素，特別是摩擦引起的死域(dead zone)非線性以及任意的非線性增益(nonlinear gain)，再提出一種補償方式。本文利用非線性增益調整(nonlinear gain compensation)方式，針對非線性的特性曲線，設計一前置補償器，先行調整依照線性模型設計的控制器產生的控制量，此調整過的控制量經功率放大器放大後驅動致動器，雖同樣受致動器非線性影響而減損部分訊號強度，但因已經事先做過適當放大補償，致動器實際輸出結果會如線性模型所預期。最後以一個針對線性致動器精密定位系統的三階段非線性PPR (Proportional,Pulse, Ramp)控制器的穩定性提出證明。此PPR 控制器於2004 年提出，以簡單的控制法則，克服致動器的摩擦、背隙、死域等非線性，快速達成精度1 μm 的定位控制。此控制器性能雖優異，但其穩定性證明尚未於期刊中正式提出。本文除以Lyapunov 方法證明PPR 的穩定性之外，並深入分析斜坡控制的穩定性。 In this Dissertation, studies on actuators connected to various types of load are investigated, particularly on the topics of modeling, identification, compensation, controller design, and stability analysis. First we present a systematic approach to construct the equations of motion for various load types driven by a linear actuator. In this approach, the equations of motion for the actuator and the load are separated which enables the reader to derive the equations of motion of various types of load without being coupled with those of the linear actuator. Next, we present a novel method for estimating the parameters of electro-mechanical systems, or known as actuators, within limited stroke. A sequence of pulses with various levels is designed to estimate the viscous damping coefficient and the Coulomb friction torque within the limited stroke of the actuator. Then an optimal algorithm based on the interior-reflective Newton method is applied to search the moment of inertia of the overall system. We also examine the effect of mechanical efficiency on the performance of the actuator. In our research, we derive the equations of motion involving the mechanical efficiency hm and describe the procedure to estimate this important parameter of the actuator when connected to various types of load. To the best of the authors’knowledge, this topic has not been published in current research. As regards the compensation for nonlinear elements inherent in the linear actuator,a novel approach to linearize such nonlinearities is proposed. This approach solves the inverse of the nonlinearity without requiring its I/O relations as a one-on-one map, which is necessary for the current inverse-model method. Finally, we investigate the stability of a newly proposed ultra precise fasting pointing controller. This research investigates the sufficient stability condition of a three-phase (proportional gain, pulse, and ramp, PPR) controller for pointing systems under the influence of friction. With the ramp and pulse schemes integrated, the PPR controller has been demonstrated to be an effective control strategy for fast and precise pointing applications. The Lyapunov direct method is applied to prove the stability of the PPR controller.
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