Stiffness-damping matching method of an ECAS system based on LQG control

Abstract

A novel method of matching stiffness and continuous variable damping of an ECAS (electronically controlled air suspension) based on LQG (linear quadratic Gaussian) control was proposed to simultaneously improve the road-friendliness and ride comfort of a two-axle school bus. Taking account of the suspension nonlinearities and target-height-dependent variation in suspension characteristics, a stiffness model of the ECAS mounted on the drive axle of the bus was developed based on thermodynamics and the key parameters were obtained through field tests. By determining the proper range of the target height for the ECAS of the fully-loaded bus based on the design requirements of vehicle body bounce frequency, the control algorithm of the target suspension height (i.e., stiffness) was derived according to driving speed and road roughness. Taking account of the nonlinearities of a continuous variable semi-active damper, the damping force was obtained through the subtraction of the air spring force from the optimum integrated suspension force, which was calculated based on LQG control. Finally, a GA (genetic algorithm)-based matching method between stepped variable damping and stiffness was employed as a benchmark to evaluate the effectiveness of the LQG-based matching method. Simulation results indicate that compared with the GA-based matching method, both dynamic tire force and vehicle body vertical acceleration responses are markedly reduced around the vehicle body bounce frequency employing the LQG-based matching method, with peak values of the dynamic tire force PSD (power spectral density) decreased by 73.6%, 60.8% and 71.9% in the three cases, and corresponding reduction are 71.3%, 59.4% and 68.2% for the vehicle body vertical acceleration. A strong robustness to variation of driving speed and road roughness is also observed for the LQG-based matching method.

Keywords

matching method / electronically controlled air suspension / linear quadratic Gaussian / genetic algorithm

References

[1] JangI, KimH, LeeH, HanS. Height control and failsafe algorithm for closed loop air suspension control system [C]. Proceeding of International Conference on Control, Automation and Systems. Seoul, South Korea, 2007373-378

[2] Kia MotorCompanyInstruction manual for MOHAVE [R], 2009, 5: 37-38

[3] Hyundai Motor Company.Instruction manual for GENESIS [R], 20095-35

[4] KimH, LeeH. Fault-tolerant control algorithm for a four-corner closed-loop air suspension system [J]. IEEE Transactions on Industrial Electronic, 2011, 58(10): 4866-4879

[5] RoebuckR L, CebonD, DaleS G. Optimal control of a semi-active tri-axle lorry suspension [J]. Vehicle System Dynamics, 2009, 44(s): 892-903

[6] XiaoJ, KulakowskiB T, CaoMing. Active air-suspension design for transit buses [J]. International Journal of Heavy Vehicle Systems, 2007, 14(4): 421-440

[7] KimH, LeeH. Development and analysis of an air spring model [J]. International Journal of Automotive Technology, 2010, 11(4): 471-479

[8] KimH, LeeH. Height and leveling control of automotive air suspension system using sliding mode approach [J]. IEEE Transactions on Vehicular Technology, 2011, 60(5): 2027-2041

[9] KimH, LeeH. Model-based fault-tolerant control for an automotive air suspension control system [J]. Journal of Automobile Engineering, 2011, 225(11): 1462-1480

[10] BalloI. Comparison of the properties of active and semi-active suspension [J]. Vehicle System Dynamics, 2007, 45(11): 1065-1073

[11] JiangH, LiK, ZhouW-t, ZhouK-kang. Control mode and control strategy in ECAS system [J]. Chinese Journal of Mechanical Engineering, 2009, 45(12): 224-231

[12] JiangH, LiZ-x, ZhouW-t, ZhouK-kang. Optimum match design of tri-grade adjustable damper in ECAS system based on genetic algorithm [J]. Chinese Journal of Mechanical Engineering, 2009, 45(10): 278-283

[13] LuqueP, MántarasD A. Pneumatic suspensions in semi-trailers: Part I general considerations and simplified models [J]. International Journal of Heavy Vehicle Systems, 2003, 10(4): 295-308

[14] LuqueP, MántarasD A. Pneumatic suspensions in semi-trailers: Part II computer simulation [J]. International Journal of Heavy Vehicle Systems, 2003, 10(4): 309-320

[15] GuagliaG, SorliM. Air suspension dimensionless analysis and design procedure [J]. Vehicle System Dynamics, 2001, 35(6): 443-475

[16] LeeS J. Development and analysis of an air spring model [J]. International Journal of Automotive Technology, 2010, 11(4): 471-479

[17] MarlinPDerivation of air spring model parameters for train simulation [D], 2002, Lulea, Lulea University of Technology

[18] ClausB, RichardE SFundamentals of thermodynamics [M], 20087th editionHoboken, John Wiley & Sons: 36-69

[19] LloydD, JonathanB. Altering heavy vehicle air suspension dynamic forces by modifying air lines [J]. International Journal of Heavy Vehicle Systems, 2011, 18: 1-17

[20] ZengY-h, LiuS-j, EJ-qiang. Neuron PI control for semi-active suspension system of tracked vehicle [J]. Journal of Central South University of Technology, 2011, 18(2): 444-450

[21] HiroseM. Toyota electronic modulated air suspension system for the 1986 soarer [J]. IEEE Transactions on Industrial Electronics, 1988, 35(2): 193-200

[22] YuZ-shengAutomotive theory [M], 2009, Beijing, China Machine Press: 203-251

[23] AshoryM R, NajafiM, JamshidiE. Optimal design of a damped vibration absorber using genetic algorithm [J]. Advances in Vibration Engineering, 2012, 11(1): 47-58

[24] ChiouJ S, LiuM T. Using fuzzy logic controller and evolutionary genetic algorithm for automotive active suspension system [J]. International Journal of Automotive Technology, 2009, 10(6): 703-710

[25] CrewsJ H, MattsonM G, BucknerG D. Multi-objective control optimization for semi-active vehicle suspensions [J]. Journal of Sound and Vibration, 2011, 330(23): 5502-5516.