應用自適應滑動模式實現於機械手臂之位置控制器設計

Design of Position Controller for Delta Robot Applying Adaptive Sliding Mode Control

蔡岱桓(Tsai Tai-Huan)

指導教授 ： 陳美勇

國立臺灣師範大學/科技與工程學院/機電工程學系/碩士(2017年)

https://doi.org/10.6345/NTNU202202531

摘要

本論文主要研究之目的是設計三相無刷直流馬達的位置控制器，並實現於機械手臂上。在位置控制器設計方面，本論文克服了機械手臂當中的不確定性與外界干擾的問題，並且提出強健且穩定的自適應滑動控制器設計方法。本研究選擇具有良好強健性的滑動模式控制器為主控制器。而在滑動模式控制當中有負責將系統狀態拉至滑動平面的(sign function)sgn(.)。但此函數會造成在滑動平面上 0- 、0+ 附近變化，隨著滑動增益量造成滑動模式中的跳切現象。因此本研究以飽和函
數(saturation function)sat(.) 替換符號函數，來去除滑動模式的跳切現象。但在系統在穩態時，存在穩態誤差。因此本文研究加入適應控制，對於系統附載進行估測，以消除系統在穩態時出現的穩態誤差。

本研究提出的位置控制器，可以有效率的使我們所控制的三相無刷直流馬達追上我們的目標位置。並實際解決傳統滑動控制當中的跳切現象，與系統在穩態時的穩態誤差，使目標位置與馬達位之誤差值趨近於零。在控制器設計當中，本文以 Lyapunov 函數證明系統穩定性。在馬達位置控制精確的情況下，本文結合機械手臂之正逆向運動學，以機械手臂目標位置推算馬達必須實際轉動之角度，使目標移動更加精確，並驗證控制器性能。

最後本實驗以 C#程式語言，建立三相無刷直流馬達與與電腦之間的溝通。並設計控制機械手臂之 UI 介面，並實際運作在 Windows10 作業系統中。介面內容包含馬達相對與絕對位置控制、馬達轉速設定、馬達與電腦通訊方法。調整機械手臂當中三顆馬達同時做動狀態，使機械手臂完成目標命令。

關鍵字

三相無刷直流馬達 ； 機械手臂 ； 自適應滑動控制

並列摘要

In this study, we design an adaptive sliding mode position controller, which is applying on the three-phase DC brushless motor and using in the Delta robot arms. We remove the uncertainty and the external disturbances of a robot arm in the controller design, and proposed robust and the stability adaptive sliding mode (ASMC) control method. In this study, we choose sliding mode control (SMC) as our major controller, which has good robust appearance. There is an (sign function)sgn(.) in the sliding mode control, it is using to let the system status get on the sliding surface. But the function would let the changing between the -0 and +0 on the sliding surface. And there would have some chattering, because the changing sliding gain. So in our study, we change the function into (saturation function)sat(.) to remove the chattering in the sliding mode. But there are still have some steady state error, so we used the adaptive control to estimate the system’s load torque to remove the steady state error.

The position control we proposed can made the three-phase DC brushless motor get on our target position. The error between the target position and the motor’s position is near to zero, because we remove the chattering and the steady state error. We use the
Lyapunove function to prove our controller design in the system was stability. In the study, we us the positive inverse kinematics to calculate the motor moving angle in the robot arm.

In the experiment result, communicate between the three-phase DC brushless motor and the computer is set up by the C# language. We design an UI interface working in
the windows 10 system to control the robot arm. There are the relatively, absolute positon control, motor’s speed setting and the communication method in the UI interface. Let the robot arm move to our target position.

並列關鍵字

Three-phase DC brushless motor ； robot arm ； adaptive sliding mode control

參考文獻

參考文獻

[1] Xuewen Yang, Zuren Feng, Chenyu Liu, and Xiaodong Ren, “A Geometric Method for Kinematics of Delta Robot and its Path Tracking Control,” International Conference on Control Automation and System, Gyeonggi-do, Korea, Oct. 2014, pp.509-514.

[2] Atushi Ishigame, Tadashi Furukawa, Shunji Kawamoto, and Tsuneo Taniguchi, “Sliding Mode Controller Design Based on Fuzzy Inference for Nonlinear System,” IEEE Transactions on Industrial Electronics, vol. 40, no. 1, Feb. 1993.

[3] Oscar Barambones, Patxi Alkora, Jose Maria Gonzalez de Durana, and Enrique Kremers, “A Robus Position Control for Induction Motors using a Load Torque Obsever,” Mediterranean Conference on Control and Automation, Barcelona, Spain, pp.278-283. July. 2012.

[4] Oscar Barambones, and Patzi Alkorta, “Position Control of the Induction Motor Using an Adaptive Sliding-Mode Controller and Observers,” IEEE Transations on Industrial Electronics, vol. 61, no. 12, pp. 6556-6565, Dec. 2014.