本論文目標為開發一種具有高強健性、高精度之智慧型遞迴終端滑動模式控制器，用於音圈馬達雙軸運動平台定位控制，論文中首先介紹音圈馬達雙軸運動平台架構和運作原理，並對運動平台進行系統鑑別，得出系統模型參數並建立其動態模型。接著，本論文先以傳統滑動模式控制設計一雙軸運動平台控制系統，再以非線性滑動面之遞迴終端滑動模式控制解決傳統滑動模式控制無法在有限時間收斂之問題。為了降低控制力的高頻震盪，本論文引入雙曲正切函數取代符號函數的不連續性，改善控制過程中的抖顫現象。由於切換控制力需要得知不確定項的上限才可確保系統收歛，實務上並不容易取得，故引入單維度卷積神經網路估測器對系統不確定項進行估測與補償，提出智慧型遞迴終端滑動模式控制器，消除系統參數變化和外部干擾等不確定性影響，提高系統的強健性，最終採用Lyapunov函數證明系統的穩定性並得到網路權重之更新律。
本研究以數位訊號處理器實現上述控制法則，並設計出兩種控制軌跡和雜訊，組合成四種控制情境進行分析對比，實驗結果得知與傳統滑動模式控制相比遞迴終端滑動模式控制最高改善了28.5%；智慧型遞迴終端滑動模式控制最高改善了39.3%，最終實驗證實所設計之控制系統具備優異的控制精密度的同時依然保有較佳的強健性。

This paper aims to develop an Intelligent Recursive Terminal Sliding Mode Controller (IRTSMC) characterized by high robustness and precision for the positioning control of a Voice Coil Motor (VCM) two-axis motion platform. The paper begins by introducing the architecture and outlining the operational principles of the VCM dual-axis motion platform, followed by system identification to extract system model parameters and establish its dynamic model. Subsequently, a control system for the two-axis motion platform is designed using traditional Sliding Mode Control (SMC) in this paper. To address the convergence issue within a finite time associated with traditional SMC, we introduce Recursive Terminal Sliding Mode Control (RTSMC) with a nonlinear sliding surface. To reduce high-frequency oscillations in the control force, a hyperbolic tangent function is employed to replace the discontinuity of the sign function, improving the control process's jitter phenomenon. Since the switching control force requires knowledge of the upper limit of uncertainties for system convergence, which may not be easily obtained in practice, an One-Dimensional Convolutional Neural Network (1D-CNN) estimator is introduced to estimate and compensate for system uncertainties. This leads to the development of the IRTSMC, aiming to eliminate the impact of uncertainties such as system parameter variations and external disturbances, thereby enhancing system robustness. The stability of the system is ultimately proven using Lyapunov functions, accompanied by the update law for network weights.
The implementation of the proposed control strategies is realized using a digital signal processor in this study. Two control trajectories and corresponding noise profiles are designed, creating four control scenarios for thorough analysis and comparison. Experimental results reveal that compared to traditional SMC, RTSMC demonstrates an improvement of up to 28.5%, while IRTSMC shows an even greater improvement of up to 39.3%. The final experiment validates that the designed control system exhibits outstanding control precision while maintaining superior robustness.

[1] Y. Qiao, T. Zhao, and X. Gui, “Overview of Position Servo Control Technology and Development of Voice Coil Motor,” CES Transactions on Electrical Machines and Systems, vol. 6, no. 3, pp. 269-278. 2022.
[2] X. Zhang, and Q. Xu, “Design, fabrication and testing of a novel symmetrical 3-DOF large-stroke parallel micro/nano-positioning stage,” Robotics and Computer-Integrated Manufacturing, vol. 54, pp. 162-172. 2018.
[3] C. L. Hsieh, C. S. Liu, and C. C. Cheng, “Design of a 5 degree of freedom–voice coil motor actuator for smartphone camera modules,” Sensors and Actuators A: Physical, vol. 309, pp. 112014. 2020.
[4] J. Xu, W. Zhou, and J. Jing, “An electromagnetic torsion active vibration absorber based on the FxLMS algorithm,” Journal of Sound and Vibration, vol. 524, pp. 116734. 2022.
[5] Y.-L. Chen, Y. Tao, P. Hu, L. Wu, and B.-F. Ju, “Self-sensing of cutting forces in diamond cutting by utilizing a voice coil motor-driven fast tool servo,” Precision Engineering, vol. 71, pp. 178-186. 2021.
[6] R. Cao, Z. Hou, Y. Zhao, and B. Zhang, “Model free adaptive iterative learning control for tool feed system in noncircular turning,” IEEE Access, vol. 7, pp. 113712-113725. 2019.
[7] G. Peng, F. Xu, J. Chen, Y. Hu, H. Wang, and T. Zhang, “A cost-effective voice coil motor-based portable micro-indentation device for in situ testing,” Measurement, vol. 165, pp. 108105. 2020.
[8] M. Mutluer, “Analysis and design optimization of tubular linear voice coil motor for high thrust force and low copper loss,” IEEE Canadian Journal of Electrical and Computer Engineering, vol. 44, no. 2, pp. 165-170. 2021.
[9] R. Wang, X. Yin, Q. Wang, and L. Jiang, “Direct amplitude control for voice coil motor on high frequency reciprocating rig,” IEEE/ASME Transactions on Mechatronics, vol. 25, no. 3, pp. 1299-1309. 2020.
[10] B. Zhao, Y. Liu, D. Jia, T. Zhang, H. Zhang, H. Yan, and X. Lu, “Application of Fuzzy Sliding Mode Control in Voice Coil Motor Control System,” in Proc. Journal of Physics: Conference Series, 2022, pp. 012009.
[11] C.-F. Hsu, and W.-F. Kao, “Perturbation wavelet neural sliding mode position control for a voice coil motor driver,” Neural Computing and Applications, vol. 31, pp. 5975-5988. 2019.
[12] U. Itkis, Control systems of variable structure, New York: John Wieley, 1976.
[13] V. Utkin, “Variable structure systems with sliding modes,” IEEE Transactions on Automatic control, vol. 22, no. 2, pp. 212-222. 1977.
[14] H. Jin, and X. Zhao, “Approach angle-based saturation function of modified complementary sliding mode control for PMLSM,” IEEE Access, vol. 7, pp. 126014-126024. 2019.
[15] A. Eltayeb, M. F. a. Rahmat, M. A. M. Basri, M. M. Eltoum, and S. El-Ferik, “An improved design of an adaptive sliding mode controller for chattering attenuation and trajectory tracking of the quadcopter UAV,” IEEE Access, vol. 8, pp. 205968-205979. 2020.
[16] Q. Hou, S. Ding, and 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. 2020.
[17] H. Hou, X. Yu, L. Xu, K. Rsetam, and Z. Cao, “Finite-time continuous terminal sliding mode control of servo motor systems,” IEEE Transactions on Industrial Electronics, vol. 67, no. 7, pp. 5647-5656. 2019.
[18] H. Du, X. Chen, G. Wen, X. Yu, and J. Lü, “Discrete-time fast terminal sliding mode control for permanent magnet linear motor,” IEEE Transactions on Industrial Electronics, vol. 65, no. 12, pp. 9916-9927. 2018.
[19] Y. Feng, F. Han, and X. Yu, “Chattering free full-order sliding-mode control,” Automatica, vol. 50, no. 4, pp. 1310-1314. 2014.
[20] K. Shao, J. Zheng, H. Wang, F. Xu, X. Wang, and B. Liang, “Recursive sliding mode control with adaptive disturbance observer for a linear motor positioner,” Mechanical Systems and Signal Processing, vol. 146, pp. 107014. 2021.
[21] B. Deng, K. Shao, and H. Zhao, “Adaptive second order recursive terminal sliding mode control for a four-wheel independent steer-by-wire system,” IEEE Access, vol. 8, pp. 75936-75945. 2020.
[22] F. Rosenblatt, “The perceptron: a probabilistic model for information storage and organization in the brain,” Psychological review, vol. 65, no. 6, pp. 386. 1958.
[23] K. Fukushima, and S. Miyake, “Neocognitron: A new algorithm for pattern recognition tolerant of deformations and shifts in position,” Pattern recognition, vol. 15, no. 6, pp. 455-469. 1982.
[24] Y. LeCun, B. Boser, J. Denker, D. Henderson, R. Howard, W. Hubbard, and L. Jackel, “Handwritten digit recognition with a back-propagation network,” Advances in neural information processing systems, vol. 2. 1989.
[25] A. Krizhevsky, I. Sutskever, and G. E. Hinton, “Imagenet classification with deep convolutional neural networks,” Advances in neural information processing systems, vol. 25. 2012.
[26] L. Alzubaidi, J. Zhang, A. J. Humaidi, A. Al-Dujaili, Y. Duan, O. Al-Shamma, J. Santamaría, M. A. Fadhel, M. Al-Amidie, and L. Farhan, “Review of deep learning: Concepts, CNN architectures, challenges, applications, future directions,” Journal of big Data, vol. 8, pp. 1-74. 2021.
[27] C. Tian, Y. Xu, Z. Li, W. Zuo, L. Fei, and H. Liu, “Attention-guided CNN for image denoising,” Neural Networks, vol. 124, pp. 117-129. 2020.
[28] M. Yousefi, and J. H. Hansen, “Block-based high performance CNN architectures for frame-level overlapping speech detection,” IEEE/ACM Transactions on Audio, Speech, and Language Processing, vol. 29, pp. 28-40. 2020.
[29] S. Montaha, S. Azam, A. R. H. Rafid, M. Z. Hasan, A. Karim, and A. Islam, “Timedistributed-cnn-lstm: A hybrid approach combining cnn and lstm to classify brain tumor on 3d mri scans performing ablation study,” IEEE Access, vol. 10, pp. 60039-60059. 2022.
[30] N. Jin, J. Wu, X. Ma, K. Yan, and Y. Mo, “Multi-task learning model based on multi-scale CNN and LSTM for sentiment classification,” IEEE Access, vol. 8, pp. 77060-77072. 2020.
[31] S. Kiranyaz, T. Ince, R. Hamila, and M. Gabbouj, “Convolutional neural networks for patient-specific ECG classification,” in Proc. 2015 37th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), 2015, pp. 2608-2611.
[32] L. Eren, T. Ince, and S. Kiranyaz, “A generic intelligent bearing fault diagnosis system using compact adaptive 1D CNN classifier,” Journal of Signal Processing Systems, vol. 91, pp. 179-189. 2019.
[33] J. Zhao, X. Mao, and L. Chen, “Speech emotion recognition using deep 1D & 2D CNN LSTM networks,” Biomedical signal processing and control, vol. 47, pp. 312-323. 2019.
[34] C. Lang, F. Steinborn, O. Steffens, and E. W. Lang, “Applying a 1D-CNN network to electricity load forecasting,” in Proc. Theory and Applications of Time Series Analysis: Selected Contributions from ITISE 2019 6, 2020, pp. 205-218.
[35] N. Sabor, G. Gendy, H. Mohammed, G. Wang, and Y. Lian, “Robust arrhythmia classification based on qrs detection and a compact 1d-cnn for wearable ecg devices,” IEEE Journal of Biomedical and Health Informatics, vol. 26, no. 12, pp. 5918-5929. 2022.
[36] 楊孟晨，基於最佳化分數階模糊PID控制之X-Y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，台北市， 2019。
[37] J.J. E. Slotine, and W. Li, Applied nonlinear control: Prentice hall Englewood Cliffs, NJ, 1991.
[38] L. Yang, and J. Yang, “Nonsingular fast terminal sliding‐mode control for nonlinear dynamical systems,” International Journal of Robust and Nonlinear Control, vol. 21, no. 16, pp. 1865-1879. 2011.
[39] J. Liu, Sliding mode control using MATLAB: Academic Press, 2017.
[40] "Akribis AVM Series User Manual," https://static-data2.manualslib.com/product-images/185/18401/1840096/raw.jpg.
[41] "AVM SERIES," https://www.acepillar.com/files/akribis_avm-series_brochure_en.pdf.
[42] "馬唯科技有限公司-easyDSP-F28377xDAQ參考使用手冊," http://www.mcudsp.com.tw/C2000/easyDSP-F28377xDAQ.html.
[43] "Elmo Motion Control," https://www.elmomc.com/product/cello/.
[44] "INTELLIGENT MOTION CONTROL LIMITED," https://inmoco.co.uk/product/legacy-products/mercury-ii-1600-encoders/.