工業界常見之伺服控制系統如XY平台及CNC工具機皆存在許多非線性外擾，其中摩擦力為其最常見之外擾，對於整體循跡精度上有著很大的影響。有鑑於此，本論文之研究主題將針對摩擦力抑制問題進行控制器設計與基於觀測器之外擾補償，藉以提升伺服機構循跡精度。本論文將比較六種不同之控制器於兩種不同軌跡之循跡控制精度，利用位置誤差及輪廓誤差作為性能判斷指標。比較之控制器分別有PID、SMC、STC、FSTC及本論文提出之MFSTC與Fuzzy MFSTC。其中MFSTC主要是透過sig函數減緩抖振現象，而Fuzzy MFSTC則是針對靜摩擦力抑制問題採用模糊邏輯理論來調整增益值。除了控制器外，本論文之另一研究主題為基於觀測器之外擾補償，為了提升循跡控制精度，本論文使用觀測器估測集總外擾，並進行即時補償。本論文共比較三種不同之觀測器，分別是STSMO、FSTSMO，及本論文提出之透過sig函數減緩抖振現象的MFSTSMO。為驗證本論文所提出之控制演算法可行性，本論文透過XY平台進行兩種不同軌跡之實作驗證。模擬及實驗結果顯示，本論文所提出之Fuzzy MFSTC控制演算法不僅可改善抖振現象，亦可同時抑制靜摩擦力的影響，在所有受測之控制器中表現最佳。在基於觀測器之外擾補償部分，本論文所提出之MFSTSMO，在三種不同觀測器中，其觀測誤差最小。最後本論文將所設計之控制器與觀測器進行結合，進一步改善循跡精度。

“Friction” is the most common external disturbance in X-Y tables and CNC machine tools, leading to a deterioration of contour following accuracy. Consequently, the major research themes of this thesis will focus on suppressing the friction effect by “controller design” and “observer-based disturbance compensation” so as to improve contour following accuracy. In this thesis, the position error and contour error are used as the performance indices when comparing the contour following accuracy of six different controllers in two different trajectory following tasks. These six controllers are PID, SMC, STC, FSTC, the proposed MFSTC and the proposed Fuzzy MFSTC. In particular, the proposed MFSTC suppresses the chattering effect by replacing the sign function with the sig function, and the proposed Fuzzy MFSTC exploits fuzzy logic theory to adjust the control gain to suppress the adverse effects caused by static friction.
Another research theme of this thesis is observer-based disturbance compensation. To improve contour following accuracy, an observer is employed in this thesis to estimate the value of external disturbance which will be used in disturbance compensation. In this thesis, three different disturbance observers—STSMO, FSTSMO and the proposed MFSTSMO are compared. In particular, the proposed MFSTSMO improves estimation accuracy by replacing the sign function with a sig function. To verify the feasibility of the proposed approach, this thesis not only conducts Matlab simulation, but also uses an XY table to perform contour following experiments. Simulation and experimental results show that the proposed Fuzzy MFSTC is superior to other controllers in contour following accuracy. In addition, the proposed MFSTSMO has the best estimation accuracy of the three different disturbance observers. Finally, the proposed Fuzzy MFSTC is combined with the proposed MFSTSMO to further improve contour following accuracy.

[1] M. Y. Cheng, M. C. Tsai, J. C. Kuo, “Real-time NURBS command generators for CNC servo controllers,” International Journal of Machine Tools and Manufacture, vol. 42, no. 7, pp. 801-813, May. 2002.
[2] 蘇科翰，輪廓誤差控制於參數式自由曲線循跡運動之研究，博士論文，國立成功大學電機工程學系，台灣，2008.
[3] S. V. DRAKUNOV, V. I. UTKIN, “Sliding mode control in dynamic systems,” International Journal of Control, vol. 55, no. 5, pp. 1029-1037, 1992.
[4] A. LEVANT, “Sliding order and sliding accuracy in sliding mode control,” International Journal of Control, vol. 58, no.6, pp. 1247-1263, 1993.
[5] W. Gao, “Theory and design method of variable structure control,” Science Press, 1996.
[6] L. Zhang, S. Wang, J. Bai, “Fast-super-twisting sliding mode speed loop control of permanent magnet synchronous motor based on SVM-DTC,” IEICE Electronics Express, vol. 18, no. 1, pp. 20200375-20200375, Jan. 2021.
[7] L. Freidovich, A. Robertsson, A. Shiriaev, R. Johansson, “LuGre-model-based friction compensation,” IEEE Transactions on Control Systems Technology, vol. 18, no. 1, pp. 194-200, Jan. 2010.
[8] F. Al-Bender, V. Lampaert and J. Swevers, “The generalized Maxwell-slip model：a novel model for friction Simulation and compensation,” IEEE Transactions on Automatic Control, vol. 50, no. 11, pp. 1883-1887, Nov. 2005.
[9] J. Han, “From PID to active disturbance rejection control,” IEEE Transactions on Industrial Electronics, vol. 56, no. 3, pp. 900-906, Mar. 2009.
[10] A. Chalanga, S. Kamal, L. M. Fridman, B. Bandyopadhyay, J. A. Moreno, “Implementation of super-twisting control：super-twisting and higher order sliding-mode observer-based approaches,” IEEE Transactions on Industrial Electronics, vol. 63, no. 6, pp. 3677-3685, Jun. 2016.
[11] Yang, Y., Yan, Y., Xu, X., Gong, B, “Super-twisting algorithm with fast super-twisting disturbance observer for steer-by-wire vehicles,” Proceedings of the Institution of Mechanical Engineers, Part D： Journal of Automobile Engineering, vol. 235, no.8, pp. 2324-2340, Jan. 2021.
[12] J. Zheng, H. Wang, Z. Man, J. Jin, M. Fu, “Robust motion control of a linear motor positioner using fast nonsingular terminal sliding mode,” IEEE/ASME Transactions on Mechatronics, vol. 20, no. 4, pp. 1743-1752, Aug. 2015.
[13] 蔡維哲，基於適應性非線性滑模控制之循跡精度改善研究，碩士論文，國立成功大學電機工程學系，台灣，2017.
[14] Y. Chu, F. Fei, S. Hou, “Dynamic global proportional integral derivative sliding mode control using radial basis function neural compensator for three-phase active power filter,” Transactions of the Institute of Measurement and Control, vol. 40, no. 12, pp. 3549-3559, Nov. 2017.
[15] 林宏憲，應用基於NURBS之強健遞回模糊類神經網路干擾量補償於動態快速非奇異終端滑模控制之循跡精度改善，碩士論文，國立成功大學電機工程學系，台灣，2018.
[16] H. -H. Lin, M. -Y. Cheng, Y. -T. Chen, C. -Y. Huang, “Contour following accuracy improvement—a dynamic fast nonsingular terminal sliding mode control approach,” IEEE Access, vol. 10, pp. 34185-34195, Mar. 2022.
[17] T. Issac, F. Thomas, S. J. Mija, “Trajectory tracking of unmanned helicopter using super twisting control,” in Proceedings of the 2020 International Conference for Emerging Technology (INCET), Belgaum, India, pp. 1-4, Jun. 2020.
[18] M. Mat-Noh, M. R. Arshad, R. Mohd-Mokhtar, “Nonlinear control of autonomous underwater glider based on super-twisting sliding mode control (STSMC),” in Proceedings of the 2017 7th IEEE International Conference on System Engineering and Technology (ICSET), Shah Alam, Malaysia, pp. 71-76, Oct. 2017.
[19] Q. Hou, S. Ding, “Finite-time extended state observer-based super-twisting sliding mode controller for PMSM drives with inertia identification,” IEEE Transactions on Transportation Electrification, vol. 8, no. 2, pp. 1918-1929, Jun. 2022.
[20] Q. Hou, S. Ding, X. Yu, “Composite super-twisting sliding mode control design for PMSM speed regulation problem based on a novel disturbance observer,” IEEE Transactions on Energy Conversion, vol. 36, no. 4, pp. 2591-2599, Dec. 2021.
[21] J. Gil, S. You, Y. Lee, W. Kim, “Super twisting-based nonlinear gain sliding mode controller for position control of permanent-magnet synchronous motors,” IEEE Access, vol. 9, pp. 142060-142070, Oct. 2021.
[22] P. Gao, G. Zhang, X. Lv, “Model-free hybrid control with intelligent proportional integral and super-twisting sliding mode control of PMSM drives,” Electronics, vol. 9, no. 9, pp. 1427, Sep. 2020.
[23] 王國欽，T-S型式之非奇異終端順滑模態控制在機械手臂之應用，碩士論文，交通大學電機與控制工程系所學位論文，台灣，Jan, 2013.
[24] 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, Jun. 2021.
[25] .N. P. Nguyen, H. Oh, Y. Kim, J. Moon, J. Yang and W. -H. Chen, “Fuzzy-based super-twisting sliding mode stabilization control for under-actuated rotary inverted pendulum systems,” IEEE Access, vol. 8, pp. 185079-185092, Oct. 2020.
[26] J. Song, W. X. Zheng, Y. Niu, “Self-triggered sliding mode control for networked PMSM speed regulation system：A PSO-optimized super-twisting algorithm,” IEEE Transactions on Industrial Electronics, vol. 69, no. 1, pp. 763-773, Jan. 2022.
[27] Y. Wang, F. Yan, J. Chen and B. Chen, “Continuous nonsingular fast terminal sliding mode control of cable-driven manipulators with super-twisting algorithm,” IEEE Access, vol. 6, pp. 49626-49636, Sep. 2018.
[28] P. Gao, G. Zhang, H. Ouyang, 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,” IEEE Access, vol. 8, pp. 53498-53510, Mar. 2020.
[29] Y. Rong, R. Jiao, S. Kang, “Sigmoid super-twisting extended state observer and sliding mode controller for quadrotor UAV attitude system with unknown disturbance,” in Proceedings of the IEEE International Conference on Robotics and Biomimetics, Dali, China, Dec. 2019.
[30] Y. Zhang, S. Tang, J. Guo, “Adaptive-gain fast super-twisting sliding mode fault tolerant control for a reusable launch vehicle in reentry phase,” ISA Transactions, vol. 71, part 2, pp 380-390, Nov. 2017.
[31] Z. Gao, “Scaling and bandwidth-parameterization based controller tuning,” in Proceedings of the 2003 American Control Conference, pp. 4989-4996, Jun. 2003.
[32] Z. Xu, T. Zhang, Y. Bao, H. Zhang, C. Gerada, “A nonlinear extended state observer for rotor position and speed estimation for sensorless IPMSM drives,” IEEE Transactions on Power Electronics, vol. 35, no. 1, pp. 733-743, Jan. 2020.
[33] Wameedh Riyadh Abdul-Adheem, Ibraheem Kasim Ibraheem, “Improved sliding mode nonlinear extended state observer based active disturbance rejection control for uncertain systems with unknown total disturbance,” Proceedings of the International Journal of Advanced Computer Science and Applications (IJACSA), vol. 7, no. 12, pp.80-93, 2016.
[34] 陳彥君，基於摩擦力模型及適應性PI滑模擴張狀態觀測器之循跡運動精度改善研究，國立成功大學電機工程學系，台灣，2019
[35] A. Chalanga, S. Kamal, L. M. Fridman, B. Bandyopadhyay and J. A. Moreno, “Implementation of super-twisting control：super-twisting and higher order sliding-mode observer-based approaches,” IEEE Transactions on Industrial Electronics, vol. 63, no. 6, pp. 3677-3685, Jun. 2016.
[36] S. R, B. Singh, “Sensorless predictive control of SPMSM-driven light EV drive using modified speed adaptive super twisting sliding mode observer with MAF-PLL,” IEEE Journal of Emerging and Selected Topics in Industrial Electronics, vol. 2, no. 1, pp. 42-52, Jan. 2021
[37] A. Vargas, J. A. Moreno, A. V. Wouwer, “A weighted variable gain super-twisting observer for the estimation of kinetic rates in biological systems,” Journal of Process Control, vol. 24, no. 6, pp.957-965, Jun. 2014.
[38] F. Piltan, J. Kim, “Bearing fault diagnosis by a robust higher-order super-twisting sliding mode observer,” Sensors, vol. 18, no. 4, Apr. 2018.
[39] Y. -C. Liu, S. Laghrouche, D. Depernet, A. Djerdir and M. Cirrincione, “Disturbance-observer-based complementary sliding-mode speed control for PMSM drives：a super-twisting sliding-mode observer-based approach,” IEEE Journal of Emerging and Selected Topics in Power Electronics, vol. 9, no. 5, pp. 5416-5428, Oct. 2021.
[40] Y. Wu, F. Ma, X. Liu, Y. Hua, X. Liu, G. Li, “Super twisting disturbance observer-based fixed-time sliding mode backstepping control for air-breathing hypersonic vehicle,” IEEE Access, vol. 8, pp. 17567-17583, Jan. 2020.
[41] Q. D. Nguyen, “Robust sliding mode control-based a novel super-twisting disturbance observer and fixed-time state observer for slotless-self bearing motor system,” IEEE Access, vol. 10, pp. 23980-23994, Feb. 2022.
[42] J. Qiang, L. Liu, M. Xu, Y. Fang, “Fixed-time backstepping control based on adaptive super-twisting disturbance observers for a class of nonlinear systems,” International Journal of Control, vol. 95, no. 9, pp.2294-2306, Apr. 2021.
[43] L. Cui, X. Hou, Z. Zuo, H. Yang, “An adaptive fast super-twisting disturbance observer-based dual closed-loop attitude control with fixed-time convergence for UAV,” Journal of the Franklin Institute, vol. 359, no. 6, pp. 2514-2540, Apr. 2022.
[44] C. T. Johnson and R. D. Lorenz, “Experimental identification of friction and its compensation in precise, position controlled mechanisms,” IEEE Transactions on Industry Applications, vol. 28, no. 6, pp. 1392-1398, Nov. 1992.
[45] 吳仁哲，伺服控制系統之摩擦力與干擾補償研究，碩士論文，國立成功大學電機工程學系，台灣，2009
[46] M. C. Tsai, M. Y. Cheng, K. F. Lin, N. C. Tsai, “On acceleration/deceleration before interpolation for CNC motion control,” in Proceedings of the IEEE International Conference on Mechatronics, Taipei, Taiwan, pp. 382-387, 2005.
[47] A. Satici, D. Tick, J. Shen, N. Gans, “Path-following control for mobile robots localized via sensor-fused visual homography,” in Proceedings of the 2013 American Control Conference, pp. 6287-6293, 2013.
[48] J. Dong, T. Wang, B. Li, Y. Ding, “Smooth feedrate planning for continuous short line tool path with contour error constraint,” International Journal of Machine Tools and Manufacture, vol. 76, pp.1-12, Jan,2014
[49] Y. Shtessel, M. Taleb, F. Plestan, “A novel adaptive-gain super twisting sliding mode controller：Methodology and application,” Automatica, vol. 48, no. 5, pp. 759-769, May. 2012.
[50] LA. Zadeh, GJ. Klir, B. Yuan, “Fuzzy sets, fuzzy logic, and fuzzy systems：selected papers,” World Scientific Publishing, Singapore,1996
[51] J. J. E. Slotine and W. Li, Applied Nonlinear Control, New Jersey, Prentice Hall, 1991.
[52] W. D. Chang, R. C. Hwang and J. G. Hsieh, “A self-tuning PID control for a class of nonlinear system based on the Lyapunov approach,” J. Process Control, vol. 12, no.2, pp. 233-242, Feb. 2002.
[53] G. Tao, “Adaptive Control Design and Analysis,” Wiley-IEEE Press, 2003.
[54] H. Celik and T. Yigit, “Field-oriented control of the PMSM with 2-DOF PI controller tuned by using PSO,” in Proceedings of the 2018 International Conference on Artificial Intelligence and Data Processing (IDAP), pp. 1-4, Sep. 2018.
[55] J. Song, Y. -K. Wang, Y. Niu, H. -K. Lam, S. He, H. Liu, “Periodic event-triggered terminal sliding mode speed control for networked PMSM system: A GA-optimized extended state observer approach,” IEEE/ASME Transactions on Mechatronics, pp. 1-12, Mar. 2022.
[56] S. -I. Kim, J.-Y. Lee, Y.-K. Kim, J.-P. Hong, Y. H, Y.-H. Jung, “Optimization for reduction of torque ripple in interior permanent magnet motor by using the Taguchi method,” IEEE Transactions on Magnetics, vol. 41, no. 5, pp. 1796-1799, May. 2005.