The Iterative Learning Control of a Stewart Platform System 劉翰綸、陳志鏗
E-mail: [email protected]
ABSTRACT
An iterative learning controller (ILC) adjusts the learning parameters by repeating control operations. Tracking error from a
previous stage is used as the correction factor for the next control action. By this way, a ILC can minimize the tracking error within a limited number of iterations. In this study, a Stewart Platform is built to implement tracking control experiments. The kinematic equations of the Stewart Platform are found by considering the relationship between the center of the upper-plate, which has six degrees of freedom, and six hydraulic legs. The extension lengths obtained by solving the kinematic equations of the Stewart Platform are then used as reference inputs for tracking control of the six hydraulic legs. By controlling extension lengths of the six hydraulic legs of the Stewart Platform, we can force the center of the upper-plate to follow a given trajectory. In our study, a ILC is used to improve tracking errors of the six hydraulic legs of a Stewart Platform. A PD-typed ILC with delay parameters are also used to control the upper-plate of the Stewart Platform to follow a repeated path until the tracking errors are minimized. We also propose a system identification scheme to identify our plant and to find the transfer function of the system. This transfer function is then used to yield the time histories of the system and to design controller. Finally, experiment results are verified by simulations. We can find out results in path tracking of experiment differing from results in path tracking of simulation. Basically, all errors are in acceptable region, and we can know from the data of experiment the larger amplitude, the slower error converging.
Keywords : Stewart Platform, hydraulic, ILC
Table of Contents
封面內頁 簽名頁 授權書... iii 中文摘要...v 英文摘要...vi 誌謝... vii 目
錄... viii 圖目錄...x 表目 錄... xiii 符號說明...xiv 第一章 緒 論...1 1.1 前言...1 1.2 文獻回
顧...2 1.3 研究目的與本文架構...5 第二章 史都華平台實 驗架構與系統模型...7 2.1 實驗架構...7 2.2 實驗儀器與設 備...8 2.3 伺服油壓系統識別...13 2.3.1 ARX 識別結 果...15 2.3.2 ARMAX 識別結果...17 2.3.3 OE 識別結
果...18 2.3.4 BJ 識別結果...19 第三章 史都華平台之運動學與 控制理論...21 3.1 運動學之推導...21 3.1.1 座標之選
定...21 3.1.2 逆向運動學...27 3.1.3 順向運動
學...27 3.2 反覆式學習控制理論...29 第四章 史都華平台實驗 流程...33 4.1 控制實驗流程與程式發展...33 4.2 史都華平台單軸軌 跡跟隨控制實驗...34 第五章 史都華平台路徑跟隨控制實驗...38 5.1 史都華 平台圓軌跡跟隨控制實驗...39 5.2 史都華平台旋轉軌跡控制實驗...45 第六 章 結論...61 參考文獻...62
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