Weight parameters optimization for the weight matrices in a vehicle suspension LQR active control
ZHANG Jinqiu1, PENG Hu2, ZHANG Jian1, PENG Zhizhao1, SUN Yiquan1, WANG Hui3
1. Brigade of equipment trail and training , Academy of armored force engineering, Beijing, 100072, China;
2. Department of Technical Support Engineering, Academy of armored force engineering, Beijing, 100072, China;
3. Troop NO 66222 of PLA, Beijing, 102202, China
Abstract:Aiming at the difficulty in determining the values of weight matrices Q and R in a LQR active control algorithm, two weight parameters λ and ξ for the weight matrices Q and R of LQR were designed respectively.An optimal objective function f, was built and the influences of λ and ξ on the f were analysed.The fast searching ability of the Genetic Algorithm(GA), was utilized to obtain the optimization solution of the objective function through the dimension reduction optimization.The analysis results show that the vibration control performance of GA-LQR on the ride comfort and manipulation stability are more superior than the traditional LQR, and the value of the objective function is smaller.The proposed optimization method is simple and effective, and it is suitable for the application in the area of automobile engineering.
张进秋1,彭虎2,张建1,彭志召1,孙宜权1,王辉3. 车辆悬挂LQR主动控制权矩阵权重参数优化[J]. 振动与冲击, 2018, 37(22): 214-219.
ZHANG Jinqiu1, PENG Hu2, ZHANG Jian1, PENG Zhizhao1, SUN Yiquan1, WANG Hui3. Weight parameters optimization for the weight matrices in a vehicle suspension LQR active control. JOURNAL OF VIBRATION AND SHOCK, 2018, 37(22): 214-219.
[1] 欧进萍. 结构振动控制—主动、半主动和智能控制[M].北京:科学出版社,2003.
OU Jin-ping. Structure vibration control-active semi-active and intelligent control[M]. Beijing: Science publishing compaby,2003.
[2] 余志生. 汽车理论[M].5版,北京:机械工业出版社,2009.
YU Zhi-sheng. Vehicle theory[M].Edition 5, Beijing: Mechanical industry publishing compaby,2009.
[3] Beno J H, Worthington M T, Mock J R. Suspension Trade Studies for Hybrid Electric Combat Vehicles[J].SAE Transactions. 2005, 114(2):58-65.
[4] Okada Y, Harada H. Regenerative Contro1 of Active Vibration Damper and Suspension System[C]. Proceedings of the 35th IEEE Conference on Decision and Control. 1996, 10(11~13): 4715-4720.
[5] Babak Ebrahimi, Hamidreza Bolandhemmat, Mir Behrad Khamesee et.al. A hybrid electromagnetic shock absorber for active vehicle suspension systems [J]. Vehicle System Dynamics. 2011, 49(1):311-332.
[6] 金耀,于德介,陈中祥,等. 内分泌LQR控制策略及其主动悬挂减振研究[J]. 振动与冲击,2016,35(10):49-54.
JIN Yao, YU Jie-de, CHEN Zhong-xiang, et al. Endocrine LQR control strategy and its application in vibration suppression by active suspensions[J]. Journal of Vibration and Shock, 2016,35(10):49-54.
[7] 赵彩虹,陈士安,王骏骋. 刚度和阻尼系数对LQG控制主动悬挂控制的影响分析[J]. 农业机械学报,2015.12,46(12):301-308.
ZHAO Cai-hong, CHEN Shi-an, WANG Jun-cheng. Influences of Stiffness and Damping Parameters on Control of Active Suspension Based on LQG[J]. Transactions of the Chinese Society for Agricultural Machinery, 2015.12,46(12):301-308.
[8] 王磊,谭平,李森萍. 基于人工鱼群算法的随机结构AMD控制系统LQR权矩阵优化[J]. 振动与冲击,2016,35(8):154-158.
WANG Lei,TAN Ping, LI Sen-ping. Optimal analysis of weight matrices of LQR algorithm for stochastic structure AMD system based on artificial fish algorithm[J]. Journal of Vibration and Shock, 2016,35(8):154-158.
[9] 宋雪健,郑宾,陈哗,等. 基于多种群遗传算法的LQR振动主动控制研究[J]. 科学技术与工程,2016.10,16(29):103-109.
SONG Xue-jian,ZHENG Bin,CHEN Ye,et al. Research on Active Vibration Control of the LQR Based on Multiple Population Genetic Algorithm[J]. Science Technology and Engineering, 2016.10,16(29):103-109.
[10] 符川,屈铁军,孙世国.主动调频液柱阻尼器基于遗传算法的LQR控制优化设计[J].振动与冲击,2015;34(2) :210-214.
FU Chuan, QU Tie-jun, SUN Shi-guo. Optimal design of ATLCD with LQR control based on genetic algorithm[J]. Journal of Vibration and Shock, 2015:34 (2) :210-214.
[11] 王威,薛彦冰,宋玉玲,等. 基于GA优化控制规则的汽车主动悬挂模糊PID控制[J]. 振动与冲击,2012,31(22):157-162.
WANG lei,XUE Yan-bing,SONG Yu-ling, et al. Fuzzy-PID control strategy for an active suspension based on optimal control laws with genetic algorithm[J]. Journal of Vibration and Shock, 2012,31(22):157-162.
[12] Lal B P, Barjeev T, Hari O G. Optimal Control of Nonlinear Inverted Pendulum System Using PID Controller and L(aR: Performance Analysis Without and With Disturbance Input[J]. International Journal of Automation and Computing, 2014.12,11(6):661-670.
[13] 蓝会立,高远,范健文,等. 基于遗传算法的车辆4自由度主动悬挂最优控制研究[J]. 合肥工业大学学报(自然科学版),2014.11,37(11):1304-1310.
LAN Hui-li,GAO Yuan,FAN Jian-wen,et al. Optimal control of vehicle active suspension with four degrees of freedom based on genetic algorithm[J]. JOURNAL OF HEFEI UNIVERSITY OF TECNOLOGY, 2014.11,37(11):1304-1310.
[14] 张磊. 军用车辆复合式电磁悬挂系统振动控制及能耗研究[D]. 北京:装甲兵工程学院,2015.
ZHANG Lei. Research on Vibration Control and Power Consumption of composite Electromagnetic Suspension System for Military Vehicles[D]. Beijing: Academy of Armored Force Engineering, 2015.
[15] 郭一峰,徐赵东,涂青,等. 基于遗传算法的LQR算法中权矩阵的优化分析[J]. 振动与冲击,2010,29(11):217-220.
GUO Yi-feng, XU Zhao-dong, TU Qing, et al. Optimal analysis for weight matrices in LQR algorithm based on genetic algorithm[J]. Journal of Vibration and Shock,2010,29(11):217-220.
[16] 彭志召,张进秋,张雨,等. 车辆半主动悬挂的频域控制算法[J]. 装甲兵工程学院学报,2013.8,27(4):36-42.
PENG Zhi-zhao, ZHANG Jin-qiu, ZHANG Yu, et al. Frequency Domain Control Algorithm for Semi-active Suspension of Vehicles[J]. Journal of Academy of Armored Force Engineering, 2013.8,27(4):36-42.
[17] Poussot-Vassal C,Savaresi S, Spelta C,et al. A Methodology for Optimal Semi-active Suspension Systems Performance Evaluation [C].//Proceedings of the 49th IEEE Conference on Decision and Control. Atlanta, USA,IEEE, 2010.