本論文以個人電腦作為控制單元，嘗試做出具有高精度、高強健性之智慧型分數階超扭曲滑動模式控制演算法，不僅自製3-PRP型並聯式機械平台上並實作驗證。並聯式機械平台是基於並聯式機械手臂，透過三顆旋轉伺服馬達加上連桿結構形成關節，根據連接的關節不同，在組合上相當靈活，可以被設計為3-RPP、3-PRP、3-PPR亦或上述的任意組合，而本論文選用3-PRP的架構進行自製。
由於許多研究都指出並聯式機械平台都有著複雜耦合的動態特性，為了有效進行控制，透過拉格朗日方程式建立機械平台之動態模型。控制器部分，透過雅可比矩陣將 、 和 方向的目標軌跡進行轉換，將運動軌跡進行解耦合，再將命令輸入控制器。將傳統的滑動模式加入超扭曲的特性，除了保留傳統滑動模式優點外，也降低系統抵達滑動面之後的小範圍抖動，並將超扭曲滑動模式演算法引入分數階微積分概念，增加控制參數的自由度以提升控制效果。最後為了消除系統在外部干擾、參數變化等影響使其提升強健性，再提出循環神經網路估測器補償系統之不確定性誤差，發展出智慧型分數階超扭曲滑動模式控制系統，此系統也通過李亞普諾夫穩定性來證明穩定性及權重更新。經過實驗證實，本研究設計之控制演算法可以有效控制自製之3-PRP型並聯機械平台。

This study mainly uses a personal computer as the algorithm control unit to make an intelligent fractional-order super-twist sliding mode control algorithm with high precision and high robustness and implement the algorithm on a self-made 3-PRP parallel mechanical platform for verification.The parallel mechanical platform is based on a parallel mechanical arm, which forms joints through three rotary servo motors and the link structure. Depending on the connected joints, the combination is quite flexible and can design as 3-RPP, 3-PRP, 3 -PPR, or any combination of the above, and this thesis uses the 3-PRP architecture by self-made.
Since many studies have pointed out that the parallel mechanical platform has complex coupled dynamic characteristics, in order to control it effectively, this thesis establishes the dynamic model of the 3-PRP parallel mechanical platform through Lagrange mechanics. In the controller part, after decoupling target trajectories in x,y, and theta directions through the Jacobian matrix, the decoupled commands are the controller's inputs. In addition, the traditional sliding mode is added with super-twisting characteristics, which retains the advantages of the traditional sliding mode and reduces the phenomenon of small-scale shaking after the system state reaches the sliding surface. Then, adding the fractional-order concept into the super-twisting sliding mode algorithm increases the degree of freedom of the control parameters to improve the control effect. Finally, to eliminate the influence of external disturbance and parameter changes to improve the system's robustness, a recurrent neural network estimator is proposed to compensate uncertainty of the system, and an intelligent fractional-order super-twist sliding mode control system is developed. Furthermore, stability prove and weight updates are divided by the Lyapunov theorem.The experiment result confirmed that the proposed control algorithm designed in this study could effectively control the self-made 3-PRP parallel mechanical platform.

[1]S. Mohan , J. K. Mohanta, “Dual integral sliding mode control loop for mechanical error correction in Trajectory-Tracking of a Planar 3-PRP Parallel Manipulator,” Journal of Intelligent & Robotic Systems, vol. 89, pp. 371-385, 2018
[2]S. Y. Chen , Y. H. Liu , S. J. Hwang , K. H. Tan, “Motion control of a 3-PRP Planar Parallel Robot using Dual-Loop PID Controller,” 2021 International Symposium on Intelligent Signal Processing and Communication Systems (ISPACS), Hualien, Taiwan, Oct. 2021
[3]A. Ghosal, “Robotics: Fundamental concepts and analysis,” Oxford University Press, 2006
[4]A. Sabanovic, K. Ohnishi, “Motion Control Systems,” John Wiley and Sons, 2011
[5]Y. Chen, F. Dong, “Robot machining: recent development and future research issues,” Int. J. Adv. Manuf. Tech, vol. 66, pp. 1489–1497, 2013
[6]X. W. Chen, S. Y. Nof, “Error detection and prediction algorithms: Application in robotics,” The International Journal of Advanced Manufacturing Technology volume, vol. 48, pp. 225–252, 2007
[7]A. Yu, I. A. Bonev, P. Zsombor-Murray, “Geometric approach to the accuracy analysis of a class of 3-DOF planar parallel robots,” Mechanism and Machine Theory, vol. 43, pp. 364–375, 2008
[8]J. Lang, L. Chen, “Dual-loop integral sliding mode control for flexible space manipulator,” China Mechanical Engineering, vol. 22, pp. 1906– 1912, 2011
[9]A. Agarwal, C. Nasa, S. Bandyopadhyay, “Dual-Loop Control for Backlash Correction in Trajectory-Tracking of a Planar 3-RRR Manipulator,” Proceedings of 15Th National Conference on Machines and Mechanisms (NaCoMM2011), Chennai, pp. 189:1-8, 2011
[10]M. Karnam, R. Kalla, A. Nag, S. Agarwal, S Bandyopadhyay, “Improved Tracking Performance Using Dual and Double Dual Feedback Loops,” Indian Control Conference, Chennai, India, Jan. 2015
[11]J. Lamaury, M. Gouttefarde, A. Chemori, P.E. Herve, “Dual-Space Adaptive Control of Redundantly Actuated Cable Driven Parallel Robots,” Proceedings of International Conference on Intelligent Robots and Systems (IROS 2013), Tokyo, pp. 4879–4886, 2016
[12]SM12165D, https://img.ruten.com.tw/s2/e/b2/ec/21518228090604_957.jpg
[13]A. Agarwal, C. Nasa, and S. Bandyopadhyay, “Dual-loop control for backlash correction in trajectory-tracking of a planar 3-RRR manipulator,” in Proceedings of 15th National Conference on Machines and Mechanisms (NaCoMM 2011), Chennai, India, Nov. 30-Dec. 2, 2011, pp. 189.
[14]Y. Singh and S. Mohan, “Development of a Planar 3PRP Parallel Manipulator using Shape Memory Alloy Spring based Actuators,” In Proceedings of the Advances in Robotics (AIR '17), no. 10, 1–6. 2017
[15]X. Y. Wu, Z. J. Xie, J. A. Kepler, S. P. Bai, “A parametric model of 3-PPR planar parallel manipulators for optimum shape design of platforms,” Mechanism and Machine Theory, Vol. 118, pp. 139-153, 2017
[16]V. Vinoth, Y. Singh, and M. Santhakumar, “Indirect disturbance compensation control of a planar parallel (2-PRP and 1-PPR) robotic manipulator,” Robotics and Computer-Integrated Manufacturing, vol. 30, no.5, pp. 556-564, Oct. 2014.
[17]Y. Singh, M. Santhakumar, “Inverse dynamics and robust sliding mode control of a planar parallel (2-PRP and 1-PPR) robot augmented with a nonlinear disturbance observer,” Mechanism and Machine Theory , 2015, 92: 29-50
[18]S. H. Saheb and G. S. Babu, “Mathematical Modeling and Kinematic analysis of 3-RRR Planar Parallel Manipulator,” EAI Endorsed Transactions on Energy Web, vol. 8, no. 35, Jan. 2021
[19]G. Wu, S. Bai, J. Kepler, and S. Caro, “Error Modeling and Experimental Validation of a Planar 3-PPR Parallel Manipulator With Joint Clearances,” Journal of Mechanisms and Robotics, vol. 4, pp. 041008, Nov. 2012
[20]V. Vinoth, Y. Singh, J. K. Mohanta and M. Santhakumar, “Robust disturbance observer based sliding mode control of a planar parallel (3-PPR) manipulator,” in 2014 Students Conference on Engineering and Systems, pp. 1-6, 2014
[21]V. Vinoth, Y. Singh, M. Santhakumar, “Indirect disturbance compensation control of a planar parallel (2-PRP and 1-PPR) robotic manipulator,” Robotics and Computer-Integrated Manufacturing, Vol. 30, Issue 5, pp. 556-564, 2014
[22]Y. Singh, V. Vinoth, Y. R. Kiran, J. K. Mohanta and S. Mohan, “Inverse dynamics and control of a 3-DOF planar parallel (U-shaped 3-PPR) manipulator,” Robotics and Computer-Integrated Manufacturing, Vol. 34, pp. 164-179, 2015
[23]Z. Zhu, S. Zhen, Z. Chen and H. Sun, “Udwadia-Kalaba Control Approach for 3-DOF Planar Parallel Manipulator,” 2019 1st International Conference on Industrial Artificial Intelligence (IAI), pp. 1-6, 2019
[24]S. Yogesh and M. Santhakumar, “PID-like Fuzzy Logic Control Scheme for Control of a Planar Parallel (3PPR U-base) Manipulator,” in 2nd international and 17th National Conference on Machines and Mechanisms, 2015
[25]V. Utkin, “Variable Structure systems with sliding modes,” IEEE Trans. Automatic Control, vol. 22, no. 2, pp. 212-222, 1977.
[26]吳冠緯, “基於積分型終端滑動模式控制之三軸音圈馬達定位平台,” 國立臺灣師範大學電機工程學系, 碩士論文, 2017
[27]方君強, “二階滑動模式控制器設計原理與應用,” 國立雲林科技大學工程科技研究所, 博士論文, 2016年6月
[28]S. D. Lee, B. K. Lee, and S. S. You, “Sliding Mode Control with Super-Twisting Algorithm for Surge Oscillation of Mooring Vessel System,” Journal of the Korean Society of Marine Environment and Safety, vol. 24, pp. 953-959, 2018
[29]C. Mu, C. Sun, C. Qian and R. Zhang, “Super-twisting sliding mode control based on Lyapunov analysis for the cursing flight of hypersonic vehicles,” in 2013 10th IEEE International Conference on Control and Automation (ICCA), pp. 522-527, 2013
[30]F. Rosenblatt, “The perceptron, a perceiving and recognizing automaton Project Para,” Cornell Aeronautical Laboratory, 1957
[31]L. Barhoumi, H. Bemri and D. Soudani, "Discretization of uncertain linears systems with time delay via Euler's and Tustin's approximations," 2016 4th International Conference on Control Engineering & Information Technology (CEIT), pp. 1-6, 2016
[32]A. H. Khan, S. Li and X. Luo, “Obstacle Avoidance and Tracking Control of Redundant Robotic Manipulator: An RNN-Based Metaheuristic Approach,” in IEEE Transactions on Industrial Informatics, vol. 16, no. 7, pp. 4670-4680, July 2020
[33]A. H. Khan, S. Li and X. Cao, “Tracking control of redundant manipulator under active remote center-of-motion constraints: an RNN-based metaheuristic approach,” Science China Information Sciences, vol. 64, no. 132203, 2021
[34]N. Federici, D. Pau, N. Adami and S. Benini, “Tiny Reservoir Computing for Extreme Learning of Motor Control,” in 2021 International Joint Conference on Neural Networks (IJCNN), pp. 1-8, 2021
[35]S. C. Yogi, V. K. Tripathi, A. K. Kamath and L. Behera, “Real-time Trajectory Tracking of a Quadrotor using Adaptive Backstepping Controller and RNN based Uncertainty Observer,” in 2020 International Joint Conference on Neural Networks (IJCNN), pp. 1-8, 2020
[36]Y. S. Quan and C. C. Chung, “Approximate Model Predictive Control with Recurrent Neural Network for Autonomous Driving Vehicles,” 2019 58th Annual Conference of the Society of Instrument and Control Engineers of Japan (SICE), pp. 1076-1081, 2019
[37]G. Venu and S. T. Kalyani, “Design of Fractional Order based Super Twisting Algorithm for BLDC motor,” 2019 3rd International Conference on Trends in Electronics and Informatics (ICOEI), pp. 271-277, 2019
[38]V. Kumar, S. R. Mohanty and M. Banafer, “Fractional Order Control with Super Twisting Observer for AC Microgrid,” 2021 29th Mediterranean Conference on Control and Automation (MED), pp. 1013-1018, 2021
[39]P. Gao, G. Zhang, H. Ouyang and L. Mei, “An Adaptive Super Twisting Nonlinear Fractional Order PID Sliding Mode Control of Permanent Magnet Synchronous Motor Speed Regulation System Based on Extended State Observer,” in IEEE Access, vol. 8, pp. 53498-53510, 2020
[40]J. Fei and Z. Feng, “Fractional-Order Finite-Time Super-Twisting Sliding Mode Control of Micro Gyroscope Based on Double-Loop Fuzzy Neural Network,” in IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 51, no. 12, pp. 7692-7706, Dec. 2021
[41]X. Zhang and Y. Quan, “Adaptive Fractional-Order Non-Singular Fast Terminal Sliding Mode Control Based on Fixed Time Disturbance Observer for Manipulators,” in IEEE Access, July 2022
[42]A. El-Bakly, A. Fouda, W. Sabry, “A Proposed DC Motor Sliding Mode Position Controller Design using Fuzzy Logic and PID Techniques,” AEROSPACE SCIENCES & AVIATION TECHNOLOGY, vol. 13, pp. 1-9, May 2009
[43]THK官方手冊螺桿選定要點, https://tech.thk.com/ct/products/pdf/tc_b17_009.pdf
[44]W. Y. Lee, C. L. Shih, C. T. Chi, “直流馬達電流、速度與位置控制硬體電路之設計與製作,” Journal of Technology, vol. 14, no. 3, pp. 453-461, 1999
[45]Advantech, https://www.advantech.tw/products/
[46]雅可比矩陣的意義, https://blog.csdn.net/yu_223/article/details/121487033
[47]雅克比矩陣理解, https://blog.csdn.net/qq_28087491/article/details/115620590
[48]A. R. Husain, M. N. Ahmad, A. H. M. Yatim, “Chattering-free sliding mode control for an active magnetic bearing system,” World Academy of Science, Engineering and Technology, vol. 39, pp. 385-391, 2008
[49]F. F. M. El-Sousy, F. A. F. Alenizi, “Optimal Adaptive Super-Twisting Sliding-Mode Control Using Online Actor-Critic Neural Networks for Permanent-Magnet Synchronous Motor Drives,” IEEE Access, vol. 9, pp. 82508-82534, 2021
[50]M. D. Ortigueira, “On the “walking dead” derivatives: Riemann-Liouville and Caputo,” International Conference on Fractional Differentiation and Its Applications (ICFDA), pp. 907-912, 2016.
[51]D. E. Rumelhart, G. Hinton and R. Williams, “Learning representations by back-propagating errors,” Nature, vol. 323, pp. 533–536, 1986
[52]F. Lin, L. Teng and P. Shieh, “Intelligent Sliding-Mode Control Using RBFN for Magnetic Levitation System,” IEEE Transactions on Industrial Electronics, vol. 54, no. 3, pp. 1752-1762, 2007
[53]S. C. Yogi, V. K. Tripathi and L. Behera, “Adaptive Integral Sliding Mode Control Using Fully Connected Recurrent Neural Network for Position and Attitude Control of Quadrotor,” IEEE Transactions on Neural Networks and Learning Systems, vol. 32, no. 12, pp. 5595-5609, Dec. 2021
[54]A. Sabanovic and K. Ohnishi, “Motion Control Systems,” Wiley, 2011