史都華平台之順滑模態控制器設計

The Design of Sliding Mode Controller for Stewart Platforms

夏瑞宏(Ruei-Hong Sia)

指導教授 ： 鄒忠全 ； 吳向宸

崑山科技大學/工程學院/機械工程研究所/碩士(2008年)

https://doi.org/10.6828/KSU.2008.00002

摘要

史都華(Stewart)平台的結構是由一個活動平台、基座平台與六根致動器支柱組合而成，而致動器支柱是使用伺服馬達驅動滾珠螺桿，並利用編碼器(Encoder)作為回授(Feedback)信號，因此成為一個閉迴路的系統。本論文研究目的是針對史都華平台的控制，設計一個理想的順滑模態控制器，以更精確的達到期望的運動軌跡，將實際車輛的運動姿態呈現出來。
本文首先推導出史都華平台的逆向運動學與致動器支柱的運動學，逆向運動學可將輸入的活動平台的位置轉換成六支致動器支柱的位移。依據推導出的活動平台與致動器支柱的動力學分析，利用Lyapunov定理證明系統的穩定性，就可設計出順滑模態控制器。
本文使用MATLAB/Simulink套裝軟體撰寫控制器和史都華平台的模擬程式，進行史都華平台位移運動的模擬分析。在實驗部份則使用C++語言撰寫程式並在DOS環境下執行，確保能達到即時(Real-Time)的動作。控制器利用馬達上的編碼器所提供的位置與速度作為回授信號，使活動平台能更精確地將運動軌跡呈現出來。最後依據模擬與實驗的結果，進行順滑模態控制器與PID控制器的性能比較。

關鍵字

史都華平台 ； 順滑模態控制器 ； PID控制器

並列摘要

The structure of a Stewart platform is constituted with a moving platform, a base platform and six actuating struts. The actuating strut is made with a ball screw powered by a servomotor. The encoder behind the servomotor provides the feedback of the position and velocity of the strut. These platforms, actuating struts and encoders form a close-loop system. The paper presents how to design a sliding mode controller to control the motion of the Stewart platform to precisely follow the desired trajectory and the attitude of the vehicle.
This paper first derives the inverse kinematics of the Stewart platform and kinematics of the actuating strut. The inverse kinematics can convert the position of the moving platform into the lengths of six actuating struts. According to the derivation of the dynamic analysis of the moving platform and the actuating struts, a sliding mode controller can be designed by using the Lyapunov theory to guarantee stability.
The simulation program for the Stewart platform and the controller is written by using MATLAB/Simulink package software. Then the position analysis of the Stewart platform is preceded using the simulation results. Because the experiments are done by using C++ language and worked in the DOS environment, the Real-Time motion was guaranteed. Because the controllers use the position and speed signal from the encoders as feedback signals, more precise trajectory of the Stewart platform can be achieved. Finally, according the simulation and experimental results, the performance of the sliding mode controller and that of PID controller can be compared with.

並列關鍵字

Stewart platform ； sliding mode controller ； PID controller

參考文獻

[3] D. C. Yang, and T. W. Lee, “Feasibility Study of a Platform Type of

[1] D. Stewart, “A Platform with Six Degrees of Freedom”, Proceedings of

freedom workstation for mechanized assembly”, 5th World Congress

on Theory of Machines and Mechanisms, Montreal, 1979.

[4] E. F. Fichter, “A Stewart Platform-Based Manipulator: General Theory and Practical Construction”, Int. Journal of Robotics Research, Summer 1986, pp. 157-182.