基于状态变换法的车辆悬架系统时滞反馈控制
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摘要
为了提高车辆行驶平顺性和稳定性,研究悬架系统中时滞补偿控制效果,本文以赛欧轿车悬架系统为基础,建立2自由度车辆半主动悬架系统模型,设计了时滞反馈控制器,采用理论与试验相结合的方法对系统时滞反馈控制特性进行研究。首先建立含时滞的悬架系统动力学方程,采用常微分理论和多项式判别方法分析系统稳定性,并通过时域与频域仿真对结果进行验证。研究表明:采用传统二次型最优控制律对含时滞的悬架系统进行控制,当系统控制时滞较大时,系统定性特性可能会发生改变,甚至会失稳发散。为保证系统的稳定性,采用状态变换方法设计时滞反馈最优控制律,仿真表明采用该控制律不仅可以保证系统稳定性,系统的减振特性亦有改善。最后搭建了悬架时滞反馈控制平台,基于时域辨识方法测得系统固有时滞为0.065 s,通过对相同工况下仿真结果与试验结果进行对比,发现两者具有较好的一致性,误差在15%以内,满足业内使用要求,表明研究可信,结果可为主动/半主动车辆悬架控制器实际设计应用提供参考。
Vehicle active/semi-active suspension is added with control force by actuators based on vehicle driving condition to achieve the purpose of improving vehicle ride comfort and safety. However, time delay is inevitable in control system because of the factors such as signal acquisition, transmission, controlling calculation and actuator actuation. It is found that time delay has a great influence on system control and even can lead to the system instability and divergence. In order to improve the ride comfort and stability of the vehicle, and study the effect of time delay compensation control in the suspension system, 2 degrees of freedom vehicle semi-active suspension system is established based on the suspension system of Sail sedan in this paper. And a time-delayed feedback controller is designed. Moreover, the method of combining theory and experiment is used to study the characteristics of the system with time-delayed feedback control. Firstly, a dynamic model of suspension system with time delay is established. The stability of the system is analyzed by the ordinary differential theory and polynomial discrimination method. According to this method, the time delay stable interval(0, 0.0143 s) of the system is got under the feedback gain obtained by the classic quadratic optimal control. The simulation results show that the system remains stable when the inherent time delay is 0.01 s, and when the inherent time delay is 0.0143, 0.05 or 0.065 s, the system is unstable and diverges after control. And the amplitude frequency characteristic curve of the system can also explain this phenomenon. So the results of the theoretical analysis are verified by the simulation calculation. In a word, when the time delay of the system exceeds the critical delay, the qualitative features of the suspension system with time delay may be changed and become unstable and divergent under the classic quadratic optimal control. And the structure of the system will be damaged in this time. In order to ensure the stability of the system, the state transform method and optimal control theory are applied to design the optimal time-delayed feedback controller. The controller can not only guarantee the stability of the system, but also improve the damping characteristics of the system. It can be seen that the most important evaluation index, i.e.the amplitude of the spring mass acceleration, decreases from 2.70 to less than 1.50 m/s~2 when comparing the simulation results under time-delayed feedback control with the uncontrolled results. When the inherent time delay in the system is 0.065 s, the amplitude of the spring mass acceleration is about 1.40 m/s~2. It is noted that the amplitude of the spring mass acceleration decreases by 48.15% compared with passive control. Therefore, the damping performance of the suspension system is improved effectively with time delayed feedback control, and the time-delayed feedback controller designed through integral transformation is very reasonable and effective. Finally, in order to verify the reliability of the analysis in this paper, a suspension time delay control platform is designed and assembled. Then the experimental results are compared with the simulation results under the same working conditions to verify the effectiveness of the results. In the experiment, the inherent delay of the suspension system is divided into 2 parts. One is the time lag of the signal from the acquisition to the time point before input into magneto rheological damper and it can be identified based on time domain signal. The other is the reaction delay of the actuator. Hence, the inherent time delay of the system measured is approximately equal to 0.065 s. It is found from the experiment that the experimental results and simulation results are stable, and the experimental results are slightly larger than the simulation results, but the error is less than 15%, which meets the engineering requirements. It indicates that the research is highly reliable. It provides an effective control method for suspension damping, and has a great value in engineering application.
Vehicle active/semi-active suspension is added with control force by actuators based on vehicle driving condition to achieve the purpose of improving vehicle ride comfort and safety. However, time delay is inevitable in control system because of the factors such as signal acquisition, transmission, controlling calculation and actuator actuation. It is found that time delay has a great influence on system control and even can lead to the system instability and divergence. In order to improve the ride comfort and stability of the vehicle, and study the effect of time delay compensation control in the suspension system, 2 degrees of freedom vehicle semi-active suspension system is established based on the suspension system of Sail sedan in this paper. And a time-delayed feedback controller is designed. Moreover, the method of combining theory and experiment is used to study the characteristics of the system with time-delayed feedback control. Firstly, a dynamic model of suspension system with time delay is established. The stability of the system is analyzed by the ordinary differential theory and polynomial discrimination method. According to this method, the time delay stable interval(0, 0.0143 s) of the system is got under the feedback gain obtained by the classic quadratic optimal control. The simulation results show that the system remains stable when the inherent time delay is 0.01 s, and when the inherent time delay is 0.0143, 0.05 or 0.065 s, the system is unstable and diverges after control. And the amplitude frequency characteristic curve of the system can also explain this phenomenon. So the results of the theoretical analysis are verified by the simulation calculation. In a word, when the time delay of the system exceeds the critical delay, the qualitative features of the suspension system with time delay may be changed and become unstable and divergent under the classic quadratic optimal control. And the structure of the system will be damaged in this time. In order to ensure the stability of the system, the state transform method and optimal control theory are applied to design the optimal time-delayed feedback controller. The controller can not only guarantee the stability of the system, but also improve the damping characteristics of the system. It can be seen that the most important evaluation index, i.e.the amplitude of the spring mass acceleration, decreases from 2.70 to less than 1.50 m/s~2 when comparing the simulation results under time-delayed feedback control with the uncontrolled results. When the inherent time delay in the system is 0.065 s, the amplitude of the spring mass acceleration is about 1.40 m/s~2. It is noted that the amplitude of the spring mass acceleration decreases by 48.15% compared with passive control. Therefore, the damping performance of the suspension system is improved effectively with time delayed feedback control, and the time-delayed feedback controller designed through integral transformation is very reasonable and effective. Finally, in order to verify the reliability of the analysis in this paper, a suspension time delay control platform is designed and assembled. Then the experimental results are compared with the simulation results under the same working conditions to verify the effectiveness of the results. In the experiment, the inherent delay of the suspension system is divided into 2 parts. One is the time lag of the signal from the acquisition to the time point before input into magneto rheological damper and it can be identified based on time domain signal. The other is the reaction delay of the actuator. Hence, the inherent time delay of the system measured is approximately equal to 0.065 s. It is found from the experiment that the experimental results and simulation results are stable, and the experimental results are slightly larger than the simulation results, but the error is less than 15%, which meets the engineering requirements. It indicates that the research is highly reliable. It provides an effective control method for suspension damping, and has a great value in engineering application.
引文
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[2]陆建辉,周孔亢,侯永涛,等.基于遗传算法的厢式货车平顺性优化[J].机械工程学报,2017,53(20):121-130.Lu Jianhui,Zhou Kongkang,Hou Yongtao,et al.Ride optimization of van truck based on genetic algorithm[J].Journal of Mechanical Engineering,2017,53(20):121-130.(in Chinese with English abstract)
[3]周长城,潘礼军,于曰伟,等.车辆钢板弹簧悬架系统减振器最佳阻尼匹配[J].农业工程学报,2016,32(07):106-113.Zhou Changcheng,Pan Lijun,Yu Yuewei,et al.Optimal damping matching for shock absorber of vehicle leaf spring suspension system[J].Transactions of the Chinese Society of Agricultural Engineering(Transactions of the CSAE),2016,32(7):106-113.(in Chinese with English abstract)
[4]聂佳梅,张孝良.车辆被动天棚阻尼悬架系统台架试验[J].农业工程学报,2015,31(07):66-71.Nie Jiamei,Zhang Xiaoliang.Experiment of vehicle passive skyhook damping suspension system[J].Transactions of the Chinese Society of Agricultural Engineering(Transactions of the CSAE),2015,31(07):66-71.(in Chinese with English abstract)
[5]易晨阳,张瑞亮,陈澔利,等.重型商用车钢板弹簧悬架硬点优化设计[J].汽车技术,2017(03):33-37.Yi Chenyang,Zhang Ruiliang,Chen Haoli,et al.Optimal design of leaf-spring suspension hard-points for a heavy commercial vehicle[J].Automobile Technology,2017(03):33-37.(in Chinese with English abstract)
[6]Crolla D,喻凡.车辆动力学及其控制[M].北京:人民交通出版社,2004.
[7]汪若尘,陈龙,张孝良,等.车辆半主动空气悬架系统设计与试验[J].农业机械学报,2012,43(4):6-9.Wang Ruochen,Chen Long,Zhang Xiaoliang,et al.Design and test of semi-active air suspension system of vehicle[J].Transactions of the Chinese Society for Agricultural Machinery,2012,43(4):6-9.(in Chinese with English abstract)
[8]Spentzas K,Kanarachos S A.Design of a non-linear hybrid car suspension system using neural networks[J].Mathematics and Computers in Simulation,2002,60(3-5):369-378.
[9]Song X B,Ahmadian M,Southward S,et al.An adaptive semi-active control algorithm for magneto rheological suspension systems[J].Journal of Vibration and Acoustics,2005,127(5):493-502.
[10]张晗,过学迅,胡三宝,等.液电式馈能半主动悬架控制特性仿真分析与能量回收验证[J].农业工程学报,2017,33(16):64-71.Zhang Han,Guo Xuexun,Hu Sanbao,et al.Simulation analysis on hydraulic-electrical energy regenerative semiactive suspension control characteristic and energy recovery validation test[J].Transactions of the Chinese Society of Agricultural Engineering(Transactions of the CSAE),2017,33(16):64-71.(in Chinese with English abstract)
[11]陈杰平,冯武堂,郭万山,等.整车磁流变减振器半主动悬架变论域模糊控制策略[J].农业机械学报,2011,42(5):8-13.Chen Jieping,Feng Wutang,Guo Wanshan,et al.Whole vehicle magneto rheological fluid damper semi-active suspension variable universe fuzzy control simulation and test[J].Transactions of the Chinese Society for Agricultural Machinery,2011,42(5):8-13.(in Chinese with English abstract)
[12]Yoshimura T,Kume A,Kurimoto M,et al.Construction of an active suspension system of a quarter car model using the concept of sliding mode control[J].Journal of Sound and Vibration,2001,239(2):187-199.
[13]孙会来,金纯,张文明,等.考虑驱动电机激振的电动车油气悬架系统振动分析[J].农业工程学报,2014,30(12):41-49.Sun Huilai,Jin Chun,Zhang Wenming,et al.Vibration analysis of hydro-pneumatic suspension system based on drive motor excitation force[J].Transactions of the Chinese Society of Agricultural Engineering(Transactions of the CSAE),2014,30(12):41-49.(in Chinese with English abstract)
[14]赵彩虹,陈士安,王骏骋.刚度和阻尼系数对LQG控制主动悬架控制的影响分析[J].农业机械学报,2015,46(12):301-308+354.Zhao Caihong,Chen Shian,Wang Juncheng.Influences of stiffness and damping parameters on control of active suspension based on LQG[J].Transactions of the Chinese Society for Agricultural Machinery,2015,46(12):301-308+354.(in Chinese with English abstract)
[15]I Mihai,F Andronic.Behavior of a semi-active suspension system versus a passive suspension system on an uneven road surface[J].Mechanics,2014,20(1):64-69.
[16]王刚,陈长征,于慎波.含路面预瞄信息的车辆主动悬架有限频域多目标控制[J].农业机械学报,2015,46(12):294-300.Wang Gang,Chen Changzheng,Yu Shenbo.Finite frequency multi-objective control of vehicle active suspension with road preview information[J].Transactions of the Chinese Society for Agricultural Machinery,2015,46(12):294-300.(in Chinese with English abstract)
[17]宋刚,许长城.考虑控制时滞的车辆主动悬架随机预瞄控制[J].农业机械学报,2013,44(6):1-7.Song Gang,Xu Changcheng.Stochastic optimal preview control of active vehicle suspension with time-delay consideration[J].Transactions of the Chinese Society for Agricultural Machinery,2013,44(6):1-7.(in Chinese with English abstract)
[18]申永军,祁玉玲,杨绍普,等.含时滞的单自由度半主动悬架系统的动力学分析[J].振动与冲击,2012,31(24):38-40.Shen Yongjun,Qi Yuling,Yang Shaopu,et al.Dynamic analysis of a SDOF semi-active suspension system with time-delay[J].Journal of Vibration and Shock,2012,31(24):38-40.(in Chinese with English abstract)
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