各式倒單擺系統之強韌控制器設計與性能分析

Design and Performance Analysis of the Robust Controller for Inverted Pendulum Systems

陳家慧(Chia-Hui Chen)

指導教授 ： 王富正

國立臺灣大學/工學院/機械工程學研究所/碩士(2012年)

https://doi.org/10.6342/NTU.2012.02223

摘要

本文將探討二種旋轉型倒單擺系統：Furuta與Pendubot系統，首先，我們推導系統的動態方程式，並藉由SimMechanics及AutoSim來驗證數學模型之正確性，再來為了控制器設計，我們利用SimMechanics建構更複雜的多擺系統模型，然後利用能量法設計甩上控制器，以及四種平衡控制器：LQR控制、Pole placement控制、及 強韌控制及 定階控制器。最後，我們將控制器安裝於 PC-based 系統進行性能驗證，並進一步將其安裝於單晶片系統，達到系統微小化及降低成本的目的。

關鍵字

倒單擺 ； 雙連桿倒單擺 ； 強韌控制 ； 平衡控制

並列摘要

This thesis discusses two kinds of rotational inverted pendulum systems: Furuta and Pendubot systems. First, we derive the dynamics of these systems, and compare them with the SimMechanics and AutoSim models for verification. Second, we use the software to build the complex models of multi-pendulum systems for controller design. Third, we design the swing-up controller and balance controllers (LQR, Pole placement,Robust, fixed-order robust control.) for these systems. Lastly, we implemented the designed controllers on a PC-based system to verify system performance. In addition, we also use a micro-chip system for system miniaturization and cost reduction. Based on the results, the proposed systems are deemed effective.

並列關鍵字

Inverted pendulum ； Furuta ； Pendubot ； H-infinity control ； balance control

參考文獻

[38]吳建諭,“永磁馬達特性快速檢測系統設計”,國立成功大學計械工程學系碩士論文,2010.

[42]呂育儒,“倒單擺系統模型之建立與控制”,國立台灣大學計械工程學系碩士論文,2007.

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[2]P.J. Larcombe and B. Torsney, “On the control of a two-dimensional uniform multi-link inverted pendulum: the enumeration and identification of equilibrium states”, International Journal of Systems Science, vol. 23, no. 12, pp. 2291-2308, Jan. 1992

[3]I. Fantoni and R. Lozano,“Non-linear Control for Underactuated Mechanical Systems”, pp. 53-72, Springer-Verlag, London, 2002.