Active Control of Energy-Regenerative Electromagnetic Suspension Based on Energy Flow Analysis

Abstract

Abstract: The mathematical model for the developed electromagnetic actuator was established and a main/inner-loop control structure was proposed for its active control. The physical constraints of control current and the energy flow states of the inner-loop system were analyzed and a two-mode controller which respectively emphasizes on vibration control and energy regeneration was designed for the main-loop. Simulations were carried out with different road inputs and the results demonstrate that the former mode can improve vehicle ride comfort by more than 30% with battery energy consumption while in the latter mode the ride comfort can be improved by up to 10% with battery charged by regenerated energy.

Key words: active suspension, electromagnetic suspension, energy regeneration, model predictive control, mixed logical dynamical system

CLC Number:

U461.1

HUANG Kun, YU Fan, ZHANG Yong-Chao. Active Control of Energy-Regenerative Electromagnetic Suspension Based on Energy Flow Analysis[J]. Journal of Shanghai Jiaotong University, 2011, 45(07): 1068-1073.

References

［1］Karnopp D. Power requirements for traversing uneven roadways［J］. Vehicle System Dynamics, 1978, 7(3): 135152.

［2］Karnopp D. Permanent magnet linear motors used as variable mechanical dampers for vehicle suspensions［J］. Vehicle System Dynamics, 1989, 18(4): 187200.

［3］Velinsky S, White R. Vehicle energy dissipation due to road roughness［J］. Vehicle System Dynamics, 1980, 9(6): 359384.

［4］Segel L, Lu X P. Vehicular resistance to motion as influenced by road roughness and highway alignment［J］. Australian Road Research, 1982, 12(4): 211222.

［5］Graves K E, Iovenitti P G, Toncich D. Electromagnetic regenerative damping in vehicle suspension systems［J］. International Journal of Vehicle Design, 2000, 24(2,3): 182197.

［6］Goldner R B, Zerigian P, Hull J. A preliminary study of energy recovery in vehicles by using regenerative magnetic shock absorbers ［C］//Government/Industry Meeting. Washington, D. C. Warrendale, PA: SAE International, 2001: 2001012071.

［7］Martins I, Esteves J, Marques G, et al. Permanentmagnets linear actuators applicability in automobile active suspensions［J］. IEEE Transactions on Vehicular Technology, 2006, 55(1): 8694.

［8］Kawamoto Y, Suda Y, Inoue H, et al. Modeling of electromagnetic damper for automobile suspension［J］. Journal of System Design and Dynamics, 2007, 1(3): 524535.

［9］Kazmierkowski M P, Malesani L. Current control techniques for threephase voltagesource PWM converters: A survey［J］. IEEE Transactions on Industrial Electronics, 1998, 45(5): 691703.

［10］黄昆,喻凡,张勇超.电磁式主动悬架模型预测控制器设计［J］. 上海交通大学学报，2010, 44(11): 16191624.

HUANG Kun, YU Fan, ZHANG Yongchao. Model predictive controller design for electromagnetic active suspension［J］. Journal of Shanghai Jiaotong University, 2010, 44(11): 16191624.

［11］Maynea D Q, Rawlingsb J B, Raob C V, et al. Constrained model predictive control: Stability and optimality［J］. Automatica, 2000, 36(6): 789814.

［12］Bemporad A, Moran M. Control of systems integrating logic, dynamics, and constraints［J］. Automatica, 1999, 35(3): 407428.

［13］Giorgetti N, Bemporad A, Tseng H E, et al. Hybrid model predictive control application towards optimal semiactive suspension［J］. International Journal of Control, 2006, 79(5): 521533.

［14］Torrisi F, Bemporad A. HYSDEL——a tool for generating computational hybrid models for analysis and synthesis problems［J］. IEEE Transactions on Control Systems Technology, 2004, 12(2): 235249.

［15］Cavalier T M, Pardalos P M, Soyster A L. Modeling and integer programming techniques applied to propositional calculus［J］. Computers & Operations Research, 1990, 17(6): 561570.

［16］余志生，汽车理论［M］. 5版.北京: 机械工业出版社，2009.

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