隨著工具機技術不斷演進，運動控制之定位精準度亦隨之提升，其中關鍵技術即在於致動器中之編碼器所提供的位置回授。而在應用層面上基於市售編碼器特殊的編碼型式，進而導致編碼器尺寸開發上往往受特定編碼和感測元件排列限制。為了整合各組編碼之特點，本篇論文以對環境耐受性高之磁性編碼器為研究主軸，提出利用De-Bruijn數列集合做為絕對列編碼的基礎，並結合單維陣列式霍爾效應感測器，使編碼器在尺寸搭配上更具適應性。而之所以能適配於任意尺寸之磁性尺和環，除了藉由該數列之子序列連續且不重複的基本特性外，亦同時調變符號數目與子序列長度以補償數列集合不足之處。最終編碼藉由電磁鐵充磁形成雙軌式磁性尺，同時結合自製陣列式感測元件與建構韌體系統。驗證此絕對式位置量測系統具有與市售編碼器相當之高定位精度。因此，這種編碼方式展現出廣泛的應用前景，並為提升感測器多樣性提供了一個有力的解決方案，進一步推動了編碼技術的發展。

As machine tool technology evolves, the precision of motion control improves significantly, largely due to the positional feedback provided by encoders within actuators. However, the development of encoder dimensions is often constrained by the specific arrangement of encoding and sensing elements due to unique encoding formats of commercially available encoders.
This research focuses on magnetically encoders with high environmental tolerance. Using De-Bruijn sequence sets as the basis for absolute column encoding and single-dimensional array-type Hall effect sensors, it enhances adaptability in encoder dimensions. The adaptability to various sizes of magnetic scales and rings is achieved through continuous and non-repeating sub-sequences, adjusting symbol numbers and sub-sequence lengths. The final encoding is realized by magnetizing electromagnets to form a dual-track magnetic scale, combined with custom array-type sensing elements and firmware system construction. Verification confirms this absolute positioning measurement system's accuracy is comparable to commercial encoders. This method demonstrates broad application prospects, providing a powerful solution for enhancing sensor diversity and driving the development of encoding technology.

[1] P. Zhang, Advanced industrial control technology. William Andrew, 2010.
[2] Statista. (2022). Leading countries for machine tool exports in 2020. Available: https://www.statista.com/statistics/264221/leading-countries-for-machine-tool-exports/
[3] PMC, "PMC Taiwanese industrial report of technology development in mechanical engineering," 2013.
[4] H. Yamaguchi and T. Ohkubo, "Development of NSK S1 SeriesTM Ball Screws and Linear Guides," vol. 11, pp. 27-34, 2001.
[5] THK. SBN series. Available: https://tech.thk.com/en/products/index.php?tar=301
[6] IKO. Beschrijving
Available: https://www.maakindustrie-hardenberg.nl/de/products/lt-linear-motor-table-2/
[7] Heidenhain. (2011). Influence of Position Measurement on Accuracy in 5-Axis Maching.
[8] 安川電機, 安川線性馬達, 安川電機, ed. [Online]. Available.
[9] RENISHAW. Enclosed optical encoders. Available: https://www.renishaw.com/en/enclosed-optical-encoders--45273
[10] P.-L. Huang, "Influence of Traveling-load on Error of Measuring Gap in a Magnetic Encoder," 2019.
[11] M. J. I. j. o. e. Benammar, "A novel amplitude-to-phase converter for sine/cosine position transducers," vol. 94, no. 4, pp. 353-365, 2007.
[12] N. L. H. Aung, C. Bi, A. Al Mamun, C. S. Soh, and Y. J. I. T. o. M. YinQuan, "A demodulation technique for spindle rotor position detection with resolver," vol. 49, no. 6, pp. 2614-2619, 2013.
[13] G. L. (GZ). TI Resolver Interface Offers Integration Benefits in Industrial Drives and HEV/EV [Online]. Available: http://e2e.ti.com/blogs_/b/analogwire/archive/2017/04/10/ti-resolver-interface-offers-integration-benefits-in-industrial-drives-and-hev-ev
[14] D. Zheng, S. Zhang, S. Wang, C. Hu, and X. Zhao, "A capacitive rotary encoder based on quadrature modulation and demodulation," vol. 64, no. 1, pp. 143-153, 2014.
[15] L. K. Baxter, "Capacitive sensors," 1997.
[16] M. Kim, W. Moon, E. Yoon, and K.-R. Lee, "A new capacitive displacement sensor with high accuracy and long-range," vol. 130, pp. 135-141, 2006.
[17] Q. Tang, D. Peng, L. Wu, and X. Chen, "An inductive angular displacement sensor based on planar coil and contrate rotor," vol. 15, no. 7, pp. 3947-3954, 2015.
[18] POSIC. (2019). Inductive Encoder Technology. Available: https://www.posicoder.com/inductive-encoder-technology
[19] J. R. J. I. t. o. i. Mayer and measurement, "High-resolution of rotary encoder analog quadrature signals," vol. 43, no. 3, pp. 494-498, 1994.
[20] L. Jogschies et al., "Recent developments of magnetoresistive sensors for industrial applications," vol. 15, no. 11, pp. 28665-28689, 2015.
[21] Alpsalpine. Alps Alpine Magnetic Sensors 2-in-1 Encoder with Variable Magnetic Pole Pitch. Available: https://tech.alpsalpine.com/e/products/faq/sensor-magnetic/magnetic-encoder/
[22] Renishaw., "Interferometric laser encoders," 2019.
[23] Z. Zhang, F. Ni, Y. Dong, C. Guo, M. Jin, and H. Liu, "A novel absolute magnetic rotary sensor," vol. 62, no. 7, pp. 4408-4419, 2015.
[24] F. Zhang, H. Zhu, K. Bian, P. Liu, and J. Zhang, "Absolute position coding method for angular sensor—Single-track Gray codes," vol. 18, no. 8, p. 2728, 2018.
[25] G. Ye, Z. Wu, Z. Xu, Y. Wang, Y. Shi, and H. Liu, "Development of a digital interpolation module for high-resolution sinusoidal encoders," vol. 285, pp. 501-510, 2019.
[26] D. J. A. m. Jiles, "Recent advances and future directions in magnetic materials," vol. 51, no. 19, pp. 5907-5939, 2003.
[27] H. Okuno, M. Ishikawa, and Y. J. I. T. J. o. M. i. J. Sakaki, "Properties of SmCo film for magnetic rotary encoder," vol. 2, no. 12, pp. 1146-1148, 1987.
[28] K.-Y. Peng and J.-Y. Chang, "Magnetization System for Spindle Axial Thermal Elongation Measurements," vol. 58, no. 2, pp. 1-5, 2021.
[29] Y.-C. Liu, H.-S. Hsiao, and J.-Y. J. Chang, "Design and validation of polarity-changeable magnetizer for encoding patterns on ring-like rotary encoders," vol. 53, no. 3, pp. 1-5, 2016.
[30] MAGNIX. ‎Magnetizing Yoke, Magnetizing Coil‎. Available: https://www.magnix.com/product/yoke_coil.htm
[31] Y. Kikuchi, T. Yoneda, Y. Kataoka, K. Shiotani, H. Wakiwaka, and H. Yamada, "Considerations of output voltage waveform on magnetic linear encoder for artificial heart using linear pulse motor," vol. 81, no. 1-3, pp. 309-312, 2000.
[32] M. Ikeda and H. Kaku, "MR sensor for magnetic encoder," vol. 7, no. 9, pp. 705-713, 1992.
[33] K.-C. Chiu, "Design and Fabrication of Multi-Pole Magnetic Components for High Precision Position System Application," 2005.
[34] Unimicron. Technology Roadmap. Available: https://www.unimicron.com/en/rd03_02.html
[35] T. Nakata and N. Takahashi, "Numerical analysis of transient magnetic field in a capacitor-discharge impulse magnetizer," vol. 22, no. 5, pp. 526-528, 1986.
[36] N. Takahashi, "3D analysis of magnetization distribution magnetized by capacitor-discharge impulse magnetizer," vol. 108, no. 2, pp. 241-245, 2001.
[37] Y.-J. Luo, E.-T. Hwang, and S.-M. Huang, "Multi-pole magnetization of high resolution magnetic encoder," in Proceedings of Electrical/Electronics Insulation Conference, 1993, pp. 237-242: IEEE.
[38] Y. Kikuchi, F. Nakamura, H. Wakiwaka, H. Yamada, and J. J. I. T. o. M. Yamamoto, "Consideration of magnetization and detection on magnetic rotary encoder using finite element method," vol. 33, no. 2, pp. 2159-2162, 1997.
[39] Y. Kikuchi, F. Nakamura, H. Wakiwaka, and H. Yamada, "Index phase output characteristics of magnetic rotary encoder using a magneto-resistive element," vol. 33, no. 5, pp. 3370-3372, 1997.
[40] C.-K. Chang, "Feasibility Study of High Resolution and High Precision Magnetic Scale Fabricated by Multi-Pole Magnetizing Head," 2020.
[41] L. Ney Hwu Magnetism Material Co. Industrial magnetic charger, discharger, flux-reduce equipment & automatic equipment. Available: http://www.magnetizer.com.tw/
[42] 林政逸, "發展一兩列錯位式編碼之線性精密絶對位置量測系統," 國立清華大學, 2016.
[43] H.-S. Hsiao and J.-Y. J. J. I. T. o. M. Chang, "Characterization of signal integrity due to pitch–roll–yaw rotation tolerance in magnetic position sensing systems," vol. 53, no. 3, pp. 1-7, 2016.
[44] K.-Y. Peng and J.-Y. J. I. T. o. M. Chang, "Magnetization System for Spindle Axial Thermal Elongation Measurements," vol. 58, no. 2, pp. 1-5, 2021.
[45] 史碩五, "應用於轉軸軸向位移即時量測之新型磁性編碼器開發," 國立清華大學, 2017.
[46] NeoMag. Magnetization direction of magnet (magnetization direction). Available: https://www.neomag.jp/mag_navi/mames/mame_magdir.html
[47] J.-F. Charpentier, G. J. C.-T. i. j. f. c. Lemarquand, m. i. electrical, and e. engineering, "Calculation of ironless permanent magnet couplings using semi‐numerical magnetic pole theory method," vol. 20, no. 1, pp. 72-89, 2001.
[48] E. N. J. T. b. s. t. j. Gilbert, "Gray codes and paths on the n-cube," vol. 37, no. 3, pp. 815-826, 1958.
[49] J. R. Bitner, G. Ehrlich, and E. M. J. C. o. t. A. Reingold, "Efficient generation of the binary reflected Gray code and its applications," vol. 19, no. 9, pp. 517-521, 1976.
[50] A. P. Hiltgen, K. G. Paterson, and M. J. I. T. o. i. t. Brandestini, "Single-track Gray codes," vol. 42, no. 5, pp. 1555-1561, 1996.
[51] M. Schwartz and T. J. I. T. o. i. t. Etzion, "The structure of single-track Gray codes," vol. 45, no. 7, pp. 2383-2396, 1999.
[52] W. Messtechnik. Magnetic sensors. Available: https://www.willtec.de/en/measure/magnetic-length-and-angle-measuring-systems/magnetic-sensors/
[53] W. Qiu-Hua, W. Yuan-Yuan, S. Ying, and Y. Shou-Wang, "A novel miniature absolute metal rotary encoder based on single-track periodic Gray code," in 2012 Second International Conference on Instrumentation, Measurement, Computer, Communication and Control, 2012, pp. 399-402: IEEE.
[54] R. W. Doran, "The gray code," Citeseer2007.
[55] S. Paul, J. J. J. o. E. E. Chang, and Technology, "Design and Development of a Novel High Resolution Absolute Rotary Encoder System Based on Affine n-digit N-ary Gray Code," vol. 13, no. 2, pp. 943-952, 2018.
[56] AsahiLASEI. Invremental type and absolute type. Available: https://www.akm.com/kr/ko/products/rotation-angle-sensor/tutorial/type-mechanism-2/
[57] F. J. MacWilliams and N. J. Sloane, "Pseudo-random sequences and arrays," vol. 64, no. 12, pp. 1715-1729, 1976.
[58] BOGEN. Absolute and incremental measurement. Available: http://bogenstage.bpanet.de/en/magnetic-measurement-solutions/technology/absolute-and-incremental-measurement.html
[59] T. Ueda, F. Kohsaka, T. Iino, and H. Nakayama, "Absolute encoder for linear or angular position measurements," ed: Google Patents, 1988.
[60] C.-Y. Lin, H.-S. Hsiao, and J.-Y. J. J. I. T. o. M. Chang, "Novel method for determining absolute position information from magnetic patterns," vol. 52, no. 7, pp. 1-4, 2016.
[61] A. ASIC. Nonius interpolation circuit GC-NIP. Available: http://www.amac-chemnitz.de/
[62] S. H. H. MANFRED, "ntegrated circuit arrangement for sampling magnetic scale, has auxiliary group of Hall-effect sensors for sensing secondary track, which is arranged on two arcuate scanning paths with different curvatures," DE Patent DE102011050834A, 2012. Available: https://worldwide.espacenet.com/patent/search/family/047173108/publication/DE102011050834A1?q=Hartmut%20Scherner.
[63] iC-Haus. Magnetic Off-Axis Absolute Position Encoder. Available: https://www.ichaus.de/product/iC-MU150
[64] K.-Y. Peng and J.-Y. J. I. S. L. Chang, "Generation of Absolute Patterns for Magnetic Encoders of Arbitrary Size with De-Bruijn Sequences," 2024.
[65] N. G. De Bruijn, "A combinatorial problem," vol. 49, no. 7, pp. 758-764, 1946.
[66] T. Etzion and A. Lempel, "Algorithms for the generation of full-length shift-register sequences," vol. 30, no. 3, pp. 480-484, 1984.
[67] Y.-J. Yan, C.-C. Liao, T.-F. Wang, and M. Ou-Yang, "Optimizing the De-Bruijn code of rotary optical encoders preventing from the photocurrent blooming," vol. 21, no. 2, pp. 1493-1503, 2020.
[68] T.-C. W. C.-K. Sung, "Analysis and Reduction of the Harmonic Noise Acquired from the Magnetic Encoder," 2021.
[69] J. D. Jackson, "Classical electrodynamics," ed: American Association of Physics Teachers, 1999.
[70] C.-W. L. C.-K. Sung, "Study on Adaptive Calibration of Magnetic Encoder," 2022.
[71] E. H. J. A. J. o. M. Hall, "On a new action of the magnet on electric currents," vol. 2, no. 3, pp. 287-292, 1879.
[72] W. J. P. o. t. R. S. o. L. Thomson, "XIX. On the electro-dynamic qualities of metals:—Effects of magnetization on the electric conductivity of nickel and of iron," no. 8, pp. 546-550, 1857.
[73] K.-Y. Peng and J.-Y. Chang, "Effects of assembly errors on axial positioning accuracy for rotating machinery with magnetoresistance-based magnetic encoders," Microsystem Technologies, vol. 27, no. 6, pp. 2507-2514, 2021.
[74] T. McGuire and R. J. I. T. o. M. Potter, "Anisotropic magnetoresistance in ferromagnetic 3d alloys," vol. 11, no. 4, pp. 1018-1038, 1975.
[75] K. Hoffmann, Applying the wheatstone bridge circuit. HBM Darmstadt, Germany, 1974.
[76] M. N. Baibich et al., "Giant magnetoresistance of (001) Fe/(001) Cr magnetic superlattices," vol. 61, no. 21, p. 2472, 1988.
[77] S. GmbH. (2023). AL798 MagnetoResistive FixPitch Sensor (1mm). Available: https://www.sensitec.com/fileadmin/sensitec/Service_and_Support/Downloads/Data_Sheets/AL700/AL798_DSE_13.pdf
[78] Winson. (2020). Hall Effect Switch IC. Available: https://www.winson.com.tw/Product/83
[79] K.-Y. Peng and J.-Y. Chang, "Polarity Influence of Poles on Positional Accuracy in Absolute Encoders," in 2024 IEEE International Magnetic Conference-Short papers (INTERMAG Short papers), 2024, pp. 1-2: IEEE.