Abstract：In magnetically suspended rotor systems, harmonic currents are inevitably produced by the mass unbalance of the rotor and sensor runout, which will cause harmonic vibrations.The repetitive control (RC) is an effective method to eliminate periodic disturbances in a control system.The conventional RC (CRC) attempts to compensate all frequency components equivalently.However, in most practical applications, such as in magnetically suspended rotor (MSR) systems, low-order harmonics usually dominate the harmonic current.A universal selective fractional repetitive control (USFRC) scheme for harmonic current suppression was proposed, and the internal model for arbitrary-order discrete periodic time sequence was established.The proposed scheme can achieve the acceleration of the transient response of the system.By introducing fractional delay filters to approximate the ideal RC at fixed sampling rate, the proposed USFRC can provide frequency adaptability to eliminate low-order dominant harmonics.A stability criterion with the rigorous proof for USFRC system was addressed as well.The application example of a baseline pre-stable MSR system was given to demonstrate the effectiveness of the proposed approach.
崔培玲，张国玺，刘志远，许涵，韩邦成. 基于通用选择性分数重复控制的磁悬浮转子谐波电流抑制[J]. 振动与冲击, 2019, 38(18): 165-172.
CUI Peiling,ZHANG Guoxi,LIU Zhiyuan,XU Han,HAN Bangcheng. Universal fractional repetitive control for the selective harmonic current suppression in magnetically suspended rotor systems. JOURNAL OF VIBRATION AND SHOCK, 2019, 38(18): 165-172.
[1] Fang J, Ren Y. High-precision control for a single-gimbal magnetically suspended control moment gyro based on inverse system method[J], IEEE Transactions on Industry Electronics., 2011, 58(9), pp. 4331–4342.
[2] Zheng S, Li H, and Han B, et al, Power consumption reduction for magnetic bearing systems during torque output of control moment gyros[J], IEEE Transactions on Power Electronics., 2017, 32(7), pp. 5752–5759.
[3] Han B, Zheng S, and Wang Z, et al. Design, modelling, fabrication, and test of a large-scale single-gimbal magnetically suspended control moment gyro[J], IEEE Transactions on Industry Electronics., 2015, 62(12), pp. 7424-7435.
[4] Tung P, Tsai M, and Chen K, et al. Design of model-based unbalance compensator with fuzzy gain tuning mechanism for an active magnetic bearing system, Expert System with Applications., 2011, 38, pp. 12861-12868.
[5] Kim C, Lee C. In situ runout identification in active magnetic bearing system by extended influence coefficient method[J], IEEE/ASME Transactions on Mechatronics, 1997, 2(1), pp. 51-57.
[6] Fang J, Zheng S, and Han B, AMB vibration control for structural resonance of double-gimbal control moment gyro with high-speed magnetically suspended rotor[J], IEEE/ASME Transactions on Mechatronics., 2013, 18(1), pp. 32–43.
[7] Chen Y, Zhu C. Active vibration control based on linear matrix inequality for rotor system under seismic excitation[J], Journal of Sound Vibration., 2008, 314, pp. 53-69.
[8] Wacker T, Weimer L, Eckert K. GOCE platform micro-vibration verification by test and analysis. Proceedings of the European Conference Spacecraft Structures[C], Materials and Mechanical Testing, Noordwijk, Netherlands, 2015, pp.1-8.
[9] Francis B, Wonham W. The internal model principle of control theory[J], Automatica, 1976, 12(5), pp. 457-465.
[10] Sun J, Gong J, and Chen B, et al. Analysis and design of repetitive controller based on regeneration spectrum and sensitivity function in active power filter system[J], IET Power Electronics, 2014, 7(8), pp. 2133-2140.
[11] Hara S, Yamammoto Y, and Omata T, et al. Repetitive control system: A new type servo system for periodic exogenous signals[J], IEEE Trans. Automatic Control., 1988, 33(7), pp.659-666.
[12] Xu X, Fang J, Liu G, et al. Model development and harmonic current reduction in active magnetic bearing systems with rotor imbalance and sensor runout[J]. Journal of Vibration & Control, 2015, 21(13), pp. 2520–2535.
[13] Cui P, Li S, and Zhao G, et al. Suppression of harmonic current in active-passive magnetically suspended CMG using improved repetitive controller[J], IEEE/ASME Transactions on Mechatronics, 2016, 21(4), pp. 2132-2141.
[14] Zhang X, Shinshi T, Li L, et al. A combined repetitive control for precision rotation of magnetic bearing[J]. Precision Engineering, 2003, 27(3):273-282.
[15] Ye Y, Zhou K, and Zhang B, et al. High performance repetitive control of PWM DC-AC converters with real-time phase-lead FIR filter[J], IEEE Transactions on Circuits and Systems II: Express Briefs., 2006, 53(8), pp.768-772.
[16] Kimura K, Mukai R, Kobayashi R. Interpolative variable-speed repetitive control and its application to a deburring robot with cutting load control[J], Advanced Robotics., 1993, 7(1), pp. 25–39.
[17] Zou Z, Zhou K, and Wang Z, et al. Fractional-order repetitive control of programmable AC power sources[J], IET Power Electronics, 2014, 7(2), pp. 431–438.
[18] Cui P, Wang Q, and Zhang G, et al. Hybrid fractional repetitive control for magnetically suspended rotor systems[J], IEEE Transactions on Industrial Electronics, 2018, 65(4), pp. 3491-3498.
[19] Loh C, Tang Y, and Blaabjerg F, et al. Mixed-frame and stationary-frame repetitive control schemes for compensating typical load and grid harmonics[J], IET Power Electronics, 2011, 4(2), pp. 218-226.
[20] Ni R, Li Y, and Zhang Y, et al. Virtual impedance-based selective harmonic compensation (VI-SHC) PWM for current source rectifiers[J], IEEE Transactions on Power Electronics., 2014, 29(7), pp. 3346-3356.
[21] Lu W, Zhou K, and Wang D, et al. A general parallel structure repetitive control scheme for multiphase dc-ac PWM converters[J], IEEE Transactions on Power Electronics., 2013, 28(8), pp. 3980–3987.
[22] Liu T, Wang D, and Zhou K. High-performance grid simulator using parallel structure fractional repetitive control[J], IEEE Transactions on Power Electronics, 2016, 31(3), pp. 2669–2679.
[23] Li C, Gu G, and Zhu L, et al. Odd-harmonic repetitive control for high-speed raster scanning of piezo-actuated nanopositioning stages with hysteresis nonlinearity, Sensors and Actuators A: Physical., 2016, 244, pp. 95-105.
[24] Yang S, Wang P, and Li T, et al. Circulating current suppression in modular multilevel converters with even-harmonic repetitive control[J], IEEE Transactions on Industry Applications., 2017, 54(1), pp. 298-309.
[25] Wu X, Panda S, and Xu J. Design of a plug-in repetitive control scheme for eliminating supply-side current harmonics of three-phase PWM boost rectifiers under generalized supply voltage conditions[J], IEEE Transactions on Power Electronics, 2010, 25(7), pp. 1800-1810.
