Design of Event Trigger-based Vibration Control for Active Suspension System

doi:10.12382/bgxb.2023.0590

Abstract

Abstract:

To improve the ride smoothness and safety of vehicles, an intelligent vibration controller based on event trigger (ET) and long short-term memory (LSTM) neural network is devised for automotive active suspension systems characterized by input dead zone and saturation. On the basis of building a quarter-car active suspension model, an appropriate ET controller is proposed, which effectively mitigates the communication bottlenecks and avoids the inherent Zeno phenomenon of controllers, thus enhancing their stability and reliability. A LSTM neural network is introduced to further improve the intelligence and adaptability of controller. A radial basis function neural network is utilized to simulate and generate the required response data for training LSTM neural network and compensate for input dead zone and saturation, making the vertical acceleration of the active suspension system get closer to 0m/s² and thus improve the vehicle ride comfort. The applicability and effectiveness of the designed controller are verified by numerical simulation. The research findings indicate that the controller can effectively enhance the dynamic performance of active suspension system under diverse operating conditions.

Key words: active suspension system, event trigger, long short-term memory network, radial basis function neural network

CLC Number:

U461.4

PANG Hui, WANG Mingxiang, WANG Lei, ZHENG Lizhe. Design of Event Trigger-based Vibration Control for Active Suspension System[J]. Acta Armamentarii, 2024, 45(8): 2698-2711.

Figures/Tables 21

Fig.1 Active suspension system dynamic model

Table 1 Parameter values of active suspension model

参数	数值
m_s/kg	492
m_u/kg	40
k_s/(N·m^-1)	46021
k_t/(N·m^-1)	238145
c/(N·s·m^-1)	2040

Fig.2 Input dead zone and saturation characteristics

Fig.3 Suspension system control scheme

Fig.4 LSTM neural network structure

Fig.5 The structure of RBFNN

Fig.6 Construction process of LSTM controller

Fig.7 Comparison of predicted results

Table 2 Parameter values of active suspension model

符号	数值	符号	数值
q₁	7.792×10⁴	n_in, n_im,n_out	3,5,1
q₂	9.1831×10⁴	I_gc	0.05
q₃	9.6057×10⁴	n_lstm, n_Fcln	200,50
r_lBP	0.2	r_lLSTM	0.01
N_max	200	G_gt	1
N_min	20	r_AR	0.5

Fig.8 Response curves of suspension system on bump road

Table 3 Comparison of RMSs of active suspension performance on bump road

控制器	$z · · s$ RMS	y_uRMS	F RMS
Passive	0.3827	0.002340	243.9
ET-BPNN	0.3637	0.001871	225.6
ET-LSTM	0.3060	0.001821	207.3

Table 3 Comparison of RMSs of active suspension performance on bump road

控制器	$z · · s$ RMS	y_uRMS	F RMS
Passive	0.3827	0.002340	243.9
ET-BPNN	0.3637	0.001871	225.6
ET-LSTM	0.3060	0.001821	207.3

Fig.9 The output of controller

Fig.10 Release instants of ET controller

Fig.11 Response curves of suspension system on random road

Table 4 Comparison of RMSs of active suspension performance on random road

控制器	$z · · s$ RMS	y_uRMS	F RMS
Passive	0.938	0.01092	567.1
ET-BPNN	0.791	0.008958	399.1
ET-LSTM	0.494	0.008127	263.7

Table 4 Comparison of RMSs of active suspension performance on random road

控制器	$z · · s$ RMS	y_uRMS	F RMS
Passive	0.938	0.01092	567.1
ET-BPNN	0.791	0.008958	399.1
ET-LSTM	0.494	0.008127	263.7

Fig.12 The output of controller

Fig.13 Release instants of ET controller

Fig.14 Response curves of suspension system on random road at a speed of 5m/s

Fig.15 Response curves of suspension system on random road at a speed of 10m/s

Fig.16 Response curves of suspension system on random road at a speed of 15m/s

Table 5 Comparison of RMSs of active suspension performance on random road at different speeds

车速/ (m·s^-1)	控制算法	RMS( $z · · s$ )	RMS (y_u)	RMS (F)
	Passive	0.469	0.005458	233.5
5	ET-BPNN	0.4354 (↓7.16%)	0.004479 (↓17.9%)	220.9 (↓5.4%)
	ET-LSTM	0.3955 (↓15.67%)	0.003478 (↓36.28%)	199.5 (↓14.56%)
	Passive	0.6633	0.007716	330.3
10	ET-BPNN	0.6157 (↓7.17%)	0.006334 (↓17.9%)	312.5 (↓5.4%)
	ET-LSTM	0.5593 (↓15.68%)	0.004919 (↓36.25%)	282.2 (↓14.56%)
	Passive	0.8124	0.009453	402.5
15	ET-BPNN	0.7641 (↓5.9%)	0.007758 (↓17.93%)	382.7 (↓4.92%)
	ET-LSTM	0.685 (↓15.68%)	0.006024 (↓36.27%)	345.6 (↓14.14%)

Table 5 Comparison of RMSs of active suspension performance on random road at different speeds

车速/ (m·s^-1)	控制算法	RMS( $z · · s$ )	RMS (y_u)	RMS (F)
	Passive	0.469	0.005458	233.5
5	ET-BPNN	0.4354 (↓7.16%)	0.004479 (↓17.9%)	220.9 (↓5.4%)
	ET-LSTM	0.3955 (↓15.67%)	0.003478 (↓36.28%)	199.5 (↓14.56%)
	Passive	0.6633	0.007716	330.3
10	ET-BPNN	0.6157 (↓7.17%)	0.006334 (↓17.9%)	312.5 (↓5.4%)
	ET-LSTM	0.5593 (↓15.68%)	0.004919 (↓36.25%)	282.2 (↓14.56%)
	Passive	0.8124	0.009453	402.5
15	ET-BPNN	0.7641 (↓5.9%)	0.007758 (↓17.93%)	382.7 (↓4.92%)
	ET-LSTM	0.685 (↓15.68%)	0.006024 (↓36.27%)	345.6 (↓14.14%)

References 33

[1]	马硕, 李永明, 伊曙东. 汽车主动悬架系统的控制方法综述[J]. 控制工程, 2024, 31(4):695-702.
	MA S, LI Y M, YI S D. A Survey of control methods of automobile active suspension systems[J]. Control Engineering of China, 2024, 31(4):695-702. (in Chinese)
[2]	曹青松, 许力, 易星. 轮毂电机驱动的电动汽车主动悬架构型与控制[J]. 机械设计, 2020, 37(10): 85-92. doi: 10.13841/j.cnki.jxsj.2020.10.012
	CAO Q S, XU L, YI X. Active suspension's architecture and control for electric vehicles driven by hub motors[J]. Journal of Machine Design, 2020, 37(10): 85-92. (in Chinese)
[3]	殷珺, 罗建南, 喻凡. 汽车电磁式主动悬架技术综述[J]. 机械设计与研究, 2020, 36(1): 161-168.
	YIN J, LUO J N, YU F. The-state-of-art review on automotive electromagnetic active suspension technology[J]. Machine Design & Research, 2020, 36(1): 161-168. (in Chinese)
[4]	SUN X, GU Z, YANG F, et al. Memory-event-trigger-based secure control of cloud-aided active suspension systems against deception attacks[J]. Information Sciences, 2021, 543: 1-17.
[5]	李金辉, 张柯柯, 徐立友. 重型汽车主动悬架次优控制策略设计与分析[J]. 振动与冲击, 2020, 39(13): 141-147.
	LI J H, ZHANG K K, XU L Y. Design and analysis of sub-optimal control strategy for heavy vehicle active suspension[J]. Journal of Vibration and Shock, 2020, 39(13): 141-147. (in Chinese)
[6]	LIU L, LI X S, LIU Y J, et al. Neural network based adaptive event trigger control for a class of electromagnetic suspension systems[J]. Control Engineering Practice, 2021, 106: 104675.
[7]	FANG F, DING H T, LIU Y J, et al. Fault tolerant sampled-data H_∞ control for networked control systems with probabilistic time-varying delay[J]. Information Sciences, 2021, 544: 395-414.
[8]	PANG H, LIU F, XU Z R. Variable universe fuzzy control for vehicle semi-active suspension system with MR damper combining fuzzy neural network and particle swarm optimization[J]. Neurocomputing, 2018, 306: 130-140.
[9]	李韶华, 张培强, 杨建森. 轮毂电机驱动电动汽车主动悬架T-S变论域模糊控制研究[J]. 振动与冲击, 2022, 41(24): 201-209.
	LI S H, ZHANG P Q, YANG J S. Research on T-S variable domain fuzzy control of active suspension on the electric vehicle driven by an in-wheel motor[J]. Journal of Vibration and Shock, 2022, 41(24): 201-209. (in Chinese)
[10]	张云, 孙劭泽, 金贤建, 等. 轮毂式电机驱动电动汽车主动悬架滑模控制研究[J]. 动力学与控制学报, 2021, 19(3): 89-94.
	ZHANG Y, SUN S Z, JIN X J, et al. Sliding mode control for active suspension of in-wheel-drive electric vehicles[J]. Journal of Dynamics and Control, 2021, 19(3): 89-94. (in Chinese)
[11]	秦武, 朱钢, 上官文斌, 等. 具有扰动观测器的汽车主动悬架滑模控制[J]. 振动工程学报, 2020, 33(1): 158-167.
	QIN W, ZHU G, SHANGGUAN W B, et al. Sliding model control with disturbance observer for active suspension[J]. Journal of Vibration Engineering, 2020, 33(1): 158-167. (in Chinese)
[12]	李娜. 基于模糊神经网络的二自由度主动悬架滑模控制系统设计[J]. 计算机测量与控制, 2021, 29(9): 101-104, 120.
	LI N. Design of sliding model control system for 2-DOF active suspension based on fuzzy neural network[J]. Computer Measurement & Control, 2021, 29(9): 101-104, 120. (in Chinese)
[13]	ZHANG Y Q, LIU Y J, WANG Z F, et al. Neural networks-based adaptive dynamic surface control for vehicle active suspension systems with time-varying displacement constraints[J]. Neurocomputing, 2020, 408: 176-187.
[14]	吕科, 杨正才, 赵宝. 递归对角神经网络算法在汽车主动悬架控制系统中的研究[J]. 燕山大学学报, 2017, 41(1): 27-31.
	LÜ K, YANG Z C, ZHAO B. Recurrent diagonal neural network algorithm study on vehicle active suspension control system[J]. Journal of Yanshan University, 2017, 41(1): 27-31. (in Chinese)
[15]	XING Y, LÜ C. Dynamic state estimation for the advanced brake system of electric vehicles by using deep recurrent neural networks[J]. IEEE Transactions on Industrial Electronics, 2019, 67(11): 9536-9547.
[16]	WANG S, ZHAO X, YU Q, et al. Identification of driver braking intention based on long short-term memory (LSTM) network[J]. IEEE Access, 2020, 8: 180422-180432.
[17]	刘秋, 孙晋伟, 张华, 等. 基于卷积神经网络的路面识别及半主动悬架控制[J]. 兵工学报, 2020, 41(8): 1483-1493. doi: 10.3969/j.issn.1000-1093.2020.08.002
	LIU Q, SUN J W, ZHANG H, et al. Road identification and semi-active suspension control based on convolutional neural network[J]. Acta Armamentarii, 2020, 41(8): 1483-1493. (in Chinese) doi: 10.3969/j.issn.1000-1093.2020.08.002
[18]	寇发荣, 胡凯仑, 陈若晨, 等. 基于ResNeSt网络路面状态识别的主动悬架模型预测控制[J]. 控制与决策, 2024, 39(6): 1849-1858.
	KOU F R, HU K L, CHEN R C, et al. Model predictive control of active Suspension based on Road surface condition recognition by ResNeSt[J]. Control and Decision, 2024, 39(6): 1849-1858. (in Chinese)
[19]	梁冠群, 赵通, 王岩, 等. 基于LSTM网络的路面不平度辨识方法[J]. 汽车工程, 2021, 43(4): 509-517, 628.
	LIANG G Q, ZHAO T, WANG Y, et al. Road unevenness identification based on LSTM network[J]. Automotive Engineering, 2021, 43(4): 509-517, 628. (in Chinese)
[20]	ZHU G B, MA Y, LI Z X, et al. Event-triggered adaptive neural fault-tolerant control of underactuated MSVs with input saturation[J]. IEEE Transactions on Intelligent Transportation Systems, 2021, 23(7): 7045-7057.
[21]	范利蓉, 王芳, 周超, 等. 状态时延和全状态约束下的多智能体系统自适应事件触发控制[J]. 控制与决策, 2022, 37(4): 892-902.
	FAN L R, WANG F, ZHOU C, et al. Adaptive event-triggered control for multi-agent systems with state time-delays and full state constraints[J]. Control and Decision, 2022, 37(4): 892-902. (in Chinese)
[22]	张栋, 马苏慧, 吕石, 等. 多智能体系统事件触发一致性研究综述[J]. 北京理工大学学报, 2022, 42(10): 1059-1072.
	ZHANG D, MA S H, LÜ S, et al. Overview on event-triggered consensus of multi-agent systems[J]. Transactions of Beijing Institute of Technology, 2022, 42(10): 1059-1072. (in Chinese)
[23]	WANG G, CHADLI M, CHEN H H, et al. Event-triggered control for active vehicle suspension systems with network-induced delays[J]. Journal of the Franklin Institute, 2019, 356(1): 147-172.
[24]	ZHANG H, ZHENG X Y, LI H Y, et al. Active suspension system control with decentralized event-triggered scheme[J]. IEEE Transactions on Industrial Electronics, 2019, 67(12): 10798-10808.
[25]	SHAH D, SANTOS M M D, CHAOUI H, et al. Event-triggered non-switching networked sliding mode control for active suspension system with random actuation network delay[J]. IEEE Transactions on Intelligent Transportation Systems, 2021, 23(7): 7521-7534.
[26]	PAN H H, SUN W C, JING X J, et al. Adaptive tracking control for active suspension systems with non-ideal actuators[J]. Journal of Sound and Vibration, 2017, 399: 2-20.
[27]	PEDRO J O, DANGOR M, DAHUNSI O A, et al. Intelligent feedback linearization control of nonlinear electrohydraulic suspension systems using particle swarm optimization[J]. Applied Soft Computing, 2014, 24: 50-62.
[28]	ZHANG M H, JING X J. A bioinspired dynamics-based adaptive fuzzy SMC method for half-car active suspension systems with input dead zones and saturations[J]. IEEE Transactions on Cybernetics, 2020, 51(4): 1743-1755.
[29]	庞辉, 王延, 刘凡. 考虑参数不确定性的主动悬架H₂/H_∞保性能控制[J]. 控制与决策, 2019, 34(3): 470-478.
	PANG H, WANG Y, LIU F. H₂/H_∞ guaranteed cost control for active suspensions considering parameter uncertainty[J]. Control and Decision, 2019, 34(3): 470-478. (in Chinese)
[30]	DING F, LI Q L, JIANG C, et al. Event-triggered control for nonlinear leaf spring hydraulic actuator suspension system with valve predictive management[J]. Information Sciences, 2021, 551: 184-204.
[31]	陈浩浩, 樊渊. 基于动态事件触发机制的线性系统最优控制[J]. 控制工程, 2020, 27(10): 1820-1827.
	CHEN H H, FAN Y. Optimal control for linear systems based on dynamic event-triggered mechanism[J]. Control Engineering of China, 2020, 27(10): 1820-1827. (in Chinese)
[32]	XUE M, YAN H C, WANG M, et al. LSTM-based intelligent fault detection for fuzzy markov jump systems and its application to tunnel diode circuits[J]. IEEE Transactions on Circuits and Systems II: Express Briefs, 2022, 69(3):1099-1103.
[33]	WANG M X, PANG H, LUO J B, et al. On an enhanced back propagation neural network control of vehicle semi-active suspension with a magnetorheological damper[J]. Transactions of the Institute of Measurement and Control, 2023, 45(3): 512-523.