农业工程学报2017，Vol.33Issue(17)：91-97,7.DOI:10.11975/j.issn.1002-6819.2017.17.012
基于Padé模型降阶法的车辆侧倾动力学研究
Research on vehicle roll dynamics based on Padé techniques for model reduction
摘要
Abstract
With the continuous development of agricultural engineering, architectural engineering and transportation, more and more technical vehicles for agriculture and architecture, heavy trucks, buses, vans, and so on have run on the road. However, the vehicle rollover accidents caused by high center of gravity have also increased in recent years. In order to study the vehicle roll dynamics and prevent rollover accidents by effective control, it is necessary to calculate the roll angle of vehicle body accurately. In this paper, a linear 3-DOF (degree of freedom) vehicle model was built firstly, then the transfer function of the vehicle body roll angle was deduced from it and the steady-state gain of the roll angle was also obtained. The denominator of the roll angle transfer function is a fourth order expression, and the numerator is a second order expression. High order system is difficult to be calculated and controlled for transient-state, so this paper proposes main effort to reduce the order of the vehicle roll model inspired by the thought of reducing system order from some researchers. Considering that the frequency of the roll dynamics is low generally, and the Padé technique for model reduction has good approximation in low frequency domain, the Padé reduction technique was adopted in this paper. After reducing the order of the roll model, the denominator and numerator of the transfer function came to be a second order expression and a first order expression respectively. Subsequently, the validity of this reduction method was illustrated from 3 aspects, i.e. time domain, frequency domain and complex domain respectively. In the time domain, the original model was simulated by Trucksim, and was also simulated by Matlab. Then, the roll angle of reduced model was compared with that of the original model in the vehicle driving conditions of angle step and sine wave. Simulation results show that, the steady-state gain and the changing tendency both fit well. With the vehicle velocity increasing, the approximation result will get a little bad. It also confirms that the approximation result is good in low frequency and this method is suitable for vehicle roll dynamics. In the frequency domain, the frequency characteristics of amplitude and phase were expatiated. As the Bode diagram shows, the frequency characteristics of the reduced system and the original system coincide almost completely when the angular frequency is not exceeding 6 rad/s. Lastly, the open loop stability and closed loop stability were also analyzed. The root locus diagram and the Nyquist stability criterion were used to elaborate the open loop stability and closed loop stability respectively. The results reveal that, the open loop stability and closed loop stability of the reduced system are consistent with that of the original system, and the relative consistency of the 2 systems also fits well. So the conclusion is that: This reduction method is suitable for calculating the vehicle roll angle and this reduction model approximates to the original model very well in low frequency domain which is the frequently-used working condition of vehicle. Additionally, in order to study the steady-state characteristics of the roll dynamics, the steady-state roll angle expression was also deduced and the roll influence coefficient was proposed in this paper. This coefficient is relative with the distance between front axle and mass center, the distance between rear axle and mass center, the distance from vehicle body mass center to roll axle, vehicle body mass, front axle mass, rear axle mass, front tire sideslip stiffness and rear tire sideslip stiffness. The special case was also analyzed when the roll influence coefficient is equal to 0. This provides a theoretical basis for studying the steady-state characteristics of the roll dynamics.关键词
车辆/模型/动力学/侧倾角/Padé降阶法/时域/频域/稳定性Key words
vehicles/models/kinetics/roll angle/Padé reduction techniques/time domain/frequency domain/stability分类
交通工程引用本文复制引用
陈翔,许男,郭孔辉..基于Padé模型降阶法的车辆侧倾动力学研究[J].农业工程学报,2017,33(17):91-97,7.基金项目
中国汽车产业创新发展联合基金资助(U1564213) （U1564213）
