For multiple nonlinear factors inherent in the servo-solenoid valve, an overall model of the valve was proposed, including the features of hysteresis, magnetic saturation, time-varying parameters, friction and flow force. First, a lumped-parameter model of the proportional solenoid was built based on the principle of nonlinear circuit. Step voltage dynamic tests of the solenoid under different constant air-borne gaps were conduct, so that a series of magnetization curves were obtained. Through curve fitting and data interpolation of the experimental results, nonlinear function expressions of main parameters were built, such as the inductance, electromagnetic-force gain and dissipation resistor. Second, the model of the valves mechanical motion part was built based on kinetic equation, and the values of parameters were gained by direct measurements and indirect calculation. Then, the steady-state flow force versus valve opening under constant pressure drop was measured by experiment. After curve-fitting, the expression of flow force was provided. Finally, to validate the combination model of the valve, two methods including open-loop and closed-loop tests were designed. During the open-loop test, constant voltages were exerted on/off the solenoid instantly and the step response of current and spool displacement were measured. In the closed-loop test, a PID controller was used to test the step response of the spools displacement with/without hydraulic load. The results show that, the response curves from the simulation model under the same parameters and test conditions shows good agreement with the experimental results. It validates the valves model and provides an effective tool for controller design and failure diagnosis．
FANG Jin-hui, KONG Xiao-Wu, WEI Jian-hua. Nonlinear modeling and validation of a servo-solenoid valve. JOURNAL OF ZHEJIANG UNIVERSITY (ENGINEERING SCIENCE), 2014, 48(5): 784-790.
［1］ TOPCU E, YUKSEL I, KAMIS Z. Development of electro-pneumatic fast switching valve and investigation of its characteristics［J］. Mechatronics, 2006, 16(6): 365378．
［2］ KAJIMA T, KAWAMURA Y. Development of a high-speed solenoid valve: investigation of solenoids［J］. IEEE Transactions on Industrial Electronics, 1995, 42(1): 18.
［3］ 李其朋．直动式电液伺服阀关键技术的研究［D］. 杭州：浙江大学, 2005:5155．
LI Qi-peng. Research on the key technologies of direct drive servo valve［D］. Hangzhou: Zhejiang University, 2005: 5155．
［4］ MITSUTAKE Y, HIRATA K, ISHIHARA Y. Dynamic response analysis of a linear solenoid actuator ［J］. IEEE Transactions on Magnetics, 1997, 33(2): 16341637．
［5］ SORLI M, FIGLIOLINI G, ALMONDO A. Mechatronic model and experimental validation of a pneumatic servo-solenoid valve ［J］. ASME Journal of Dynamic Systems, Measurement and Control, 2010, 132(5): 110．
［6］ CHUA L O, STROMSMOE K A. Mathematical models for dynamic hysteresis loops ［J］. International Journal of Engineering Science, 1971, 9: 435450．
［7］ BASS S C. A Generalized Hysteresis Model［D］. West Lafayette: Purdue University, 1971: 2769.
［8］ VAUGHAN N D, GAMBLE J B. The modeling and simulation of a proportional electromagnet valve［J］. ASME Journal of Dynamic Systems, Measurement and Control, 1996, 118(1): 120125．
［9］ CRISTOFORI D, VACCA A. Electrohydraulic proportional valve modeling comprehending magnetic hysteresis［C］∥ 52nd National Conference on Fluid Power. Las Vegas：Nevada, 2011: 700711．
［10］ CRISTOFORI D, VACCA A. The modeling of electrohydraulic proportional valves ［J］. ASME Journal of Dynamic Systems, Measurement and Control, 2012, 134(2): 108120．
［11］ FITCH E C, HONG I T. Hydraulic component design and selection ［M］. Stillwater, OK: BarDyne, 2008．
［12］ MANRING N D, ZHANG S S. Pressure transient flow forces for hydraulic spool valves ［J］. ASME Journal of Dynamic Systems, Measurement and Control, 2012, 134(2): 101105．
［13］ 许小庆,权龙,王旭平．伺服比例阀用动圈式直线电机［J］. 中国电机工程学报, 2010, 30(9): 9296．
XU Xiao-qing, QUAN Long, WANG Xu-ping.Moving coil linear motor used in servo proportional valve ［J］. Proceedings of the Chinese Society for Electrical Engineering, 2010, 30(9): 9296．
［14］ 周淼磊,杨志刚,高巍,等．高速精密压电型电液伺服阀及其控制方法［J］. 哈尔滨工业大学学报, 2009, 41(9): 160163．
ZHOU Miao-lei, YANG Zhi-gang, GAO Wei, et al. High-speed and precise piezoelectric electro-hydraulic servo valve and its control method ［J］. Journal of Harbin Institute of Technology, 2009, 41(9): 160163.
［15］ BOSCH REXROTH. Servo solenoid valves with electrical position feedback ［EB/OL］. (2005-10-10) ［2013-01-02］. http://www.boschrexroth.com/modules/BRMV2PDFDownload.dll/re29032_2005-01.pdf？db=brmv2&lvid=1097233&mvid=10270&clid=20&sid=E052D1E76402CE7B9FE18C711C75022E& sch=M&id=10270,20,1097233.
