Sensitivity Analysis and Adaptive Tracking Control of Electro-hydraulic Active Suspensions

doi:10.3969/j.issn.1004-132X.2023.04.013

Abstract

Abstract: Emergency rescue vehicles carried heavy loads and travel on complex roads and the response and control accuracy of output forces of electro-hydraulic active suspensions were very important to attenuate vibrations. Firstly， the mathematical model of electro-hydraulic active suspension system was established. Secondly， the trajectory sensitivity equation of the system was established to give the sensitivity of the main parameters with the force step response， so as to provide a theoretical basis for the performance optimization. Thirdly， considering the large load characteristics of electro-hydraulic active suspensions and the sensitivity analysis results， a reference model adaptive controller was designed. Finally， the adaptive control effectiveness was verified by experiments. The results show that the proposed control method effectively improves the tracking performance and the force control accuracy of the electro-hydraulic active suspension actuator units. It will help the vehicle active suspension system to realize various advanced control algorithms.

Key words: emergency rescue vehicle, active suspension, electro hydraulic servo system, sensitivity analysis, adaptive control

摘要： 应急救援车辆载重量大、行驶路面复杂，电液主动悬架输出力的响应和控制精度对衰减振动至关重要。建立了电液主动悬架单元数学模型，给出了系统的轨迹灵敏度方程，并得到力阶跃响应对应各主要参数的灵敏度，为悬架性能优化提供理论依据；针对电液主动悬架负载质量大的特点，结合灵敏度分析结果，设计模型参考自适应控制器。最后，通过实验对自适应控制效果进行验证，结果表明所提出的控制方法可有效提高电液主动悬架单元的跟踪性能和对输出力的控制精度，助力整车主动悬架系统实现各种先进控制算法。

关键词: 应急救援车, 主动悬架, 电液伺服系统, 灵敏度分析, 自适应控制

CLC Number:

TH113

CHEN Hao, GONG Mingde, ZHAO Dingxuan, ZHANG Wei, ZHANG Yue, HAO Chunyou, . Sensitivity Analysis and Adaptive Tracking Control of Electro-hydraulic Active Suspensions[J]. China Mechanical Engineering, 2023, 34(04): 481-489.

陈浩, 巩明德, 赵丁选, 张伟, 张悦, 郝春友, . 电液主动悬架灵敏度分析与自适应跟踪控制[J]. 中国机械工程, 2023, 34(04): 481-489.

References

［1］GIYMA B， HPW A， YANG T A. Vibration Control of an Active Vehicle Suspension Systems Using Optimized Model-free Fuzzy Logic Controller Based on Time Delay Estimation［J］. Advances in Engineering Software， 2019， 127：141-149.
［2］许力，曹青松，张定军. 基于量子粒子群算法的主动悬架分数阶控制策略［J］. 振动与冲击， 2021， 40（16）：227-233.
XU Li， CAO Qingsong， ZHANG Dingjun. Fractional Order Control Strategy of Active Suspension Based on QPSO［J］. Journal of Vibration and Shock， 2021， 40（16）：227-233.
［3］PRASAD V， PAWASKAR D N， SESHU P. Controller Design and Multi-objective Optimization of Heavy Goods Vehicle Suspension System by Geometry-inspired GA［J］. Structural and Multidisciplinary Optimization， 2021， 64（1）：89-111.
［4］DU M， ZHAO D， YANG M， et al. Nonlinear Extended State Observer-based Output Feedback Stabilization Control for Uncertain Nonlinear Half-car active Suspension Systems［J］. Nonlinear Dynamics， 2020， 100（1）：2483-2503.
［5］WANG G A， MC B， CHEN H A， 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.
［6］寇发荣，方宗德. 汽车可控悬挂系统的研究进展［J］. 汽车工程， 2007， 29（5）：426-432.
KOU Farong， FANG Zongde. The Research Trend in Controlled Suspension System of Vehicle［J］. Automotive Engineering， 2007， 29（5）：426-432.
［7］RATH J J， KARIMI H R， DEFOORT M， et al. Output Feedback Active Suspension Control with Higher Order Terminal Sliding Mode［J］. IEEE Transactions on Industrial Electronics， 2017， 64（2）：1392-1402.
［8］安晨亮，马金玉，王嘉维，等. 磁流变阻尼器输出阻尼力灵敏度分析［J］. 机电工程， 2018， 35（11）：1137-1144.
AN Chenliang， MA Jinyu， WANG Jiawei， et al. Sensitivity Analysis of Output Damping Force Based on Magnetorheological Damper［J］. Journal of Mechanical and Electrical Engineering， 2018， 35（11）：1137-1144.
［9］张农，王少华，张邦基，等. 液压互联悬架参数全局灵敏度分析与多目标优化［J］. 湖南大学学报（自然科学版）， 2020， 47（10）：1-9.
ZHANG Nong， WANG Shaohua， ZHANG Bangji， et al. Global Sensitivity Analysis and Multi-objective Optimization of Hydraulically Interconnected Suspension Parameters［J］. Journal of Hunan University（Natural Sciences）， 2020， 47（10）：1-9.
［10］周创辉，文桂林. 液电馈能式悬架的液压参数灵敏度分析与优化［J］. 湖南大学学报（自然科学版）， 2017， 44（10）：1-8.
ZHOU Chuanghui， WEN Guilin. Sensitivity Analysis and Optimization of Hydraulic Parameters to a Hydraulic-electrical Regenerative Suspensions Performance［J］. Journal of Hunan University（Natural Sciences）， 2017， 44（10）：1-8.
［11］FARASAT S， AJAM H. Sensitivity Analysis of Parameter Changes in Nonlinear Hydraulic Control Systems［J］. International Journal of Engineering， 2005， 18（3）：239-252.
［12］KONG X D， YU B， QUAN L X， et al. Nonlinear Mathematical Modeling and Sensitivity Analysis of Hydraulic Drive Unit［J］. Chinese Journal of Mechanical Engineering， 2015， 28（5）：999-111.
［13］KONG X D， BA K X， YU B， et al. Trajectory Sensitivity Analysis of First Order and Second Order on Position Control System of Highly Integrated Valve Controlled Cylinder［J］. Journal of Mechanical Science and Technology， 2015， 29（10）：4445-4464.
［14］BREZAS P， SMITH M C. Linear Quadratic Optimal and Risk-sensitive Control for Vehicle Active Suspensions［J］. IEEE Transactions on Control Systems Technology， 2014， 22（2）：543-556.
［15］HU M J， PARK J H， CHENG J. Robust Fuzzy Delayed Sampled-data Control for Nonlinear Active Suspension Systems with Varying Vehicle Load and Frequency-domain Constraint［J］. Nonlinear Dynamics， 2021， 105：2265-2281.
［16］陈保帆，李云勇. 基于混合滑模控制的电液主动悬架抖振研究［J］. 中国工程机械学报， 2020， 18（5）：465-470.
CHEN Baofan， LI Yunyong. Research on Buffeting of Electrohydraulic Active Suspension Based on Hybrid Sliding Mode Control［J］. Chinese Journal of Construction Machinery， 2020， 18（5）：465-470.
［17］ESKI I， YILDIRIM S. Vibration Control of Vehicle Active Suspension System Using a New Robust Neural Network Control System［J］. Simulation Modelling Practice and Theory， 2009， 17（5）：778-793.
［18］ZHANG Y， LIU Y， WANG Z， et al. Neural Networks Based Adaptive Dynamic Surface Control for Vehicle Active Suspension Systemswith Time-varying Displacement Constraints［J］. Neurocomputing， 2020， 408：176-187.

[1]	LI Xiao-Li, CHEN Wei, YAN Rong. Adaptive Compensation of Contour Errors Based on BP Neural Networks [J]. J4, 201016, 21(16): 1902-1906.
[2]	DAI Xin, LIU Huanlao, WANG Yulin, LI Xiang. A Key Geometric Error Identification Method for CNC Machine Tools Based on Machining Trajectory Sensitivity Indicators [J]. China Mechanical Engineering, 2025, 36(12): 2862-2869.
[3]	GUO Feiyan1, ZHANG Hui2, SONG Changjie1, ZHANG Shuo1. Identification and Evaluation of Key Error Elements in Complex Composite Aviation Componts Assembly Driven by Mechanism and Data Model Fusion [J]. China Mechanical Engineering, 2025, 36(07): 1530-1543.
[4]	JI Li, CHEN Meihao. Adaptive Control Method of AMB Based on Characteristic Model and Tracking Differentiator [J]. China Mechanical Engineering, 2025, 36(06): 1363-1370.
[5]	LIU Chunchao1, ZHU Yaguang1, 2, ZHOU Yating1, HAN Zhigang1. Adaptive Impedance Control of Hexapod Robots Based on Virtual Motoneuron System [J]. China Mechanical Engineering, 2025, 36(02): 315-324,332.
[6]	SHEN Yehu1, LI Huan1, ZHANG Daqing1, MIAO Yang1, ZHAO Chong2, JIANG Quansheng1. Visual Loop Detection Method with Sensitivity Analysis of Network Weight Parameters [J]. China Mechanical Engineering, 2024, 35(07): 1212-1221.
[7]	NI Tao1, 2, ZHANG Panhong1, 2 , ZHAO Zeren1, 2. Adaptive Variable Impedance Control for Force Sensor-less Joysticks [J]. China Mechanical Engineering, 2024, 35(06): 1034-1043，1051.
[8]	NI Tao1, LYU Bo1, ZHANG Panhong1, ZHAO Zeren1, SUN Xu1, ZHANG Hongyan2. Research on Control Strategy of Electro-hydraulic Servo Actuators Based on Strict Feedback Model#br# #br# [J]. China Mechanical Engineering, 2024, 35(05): 928-937,949.
[9]	CHEN Junxiang, KONG Xiangdong, XU Kelong, AI Chao, . Comprehensive Performance Optimization of High Pressure Threaded Plug-in Relief Valves [J]. China Mechanical Engineering, 2023, 34(24): 2909-2919,2926.
[10]	QU Xiaozhang, ZHANG Jiabei, ZHAI Fangzhi. Sensitivity Analysis and Optimization of High Speed Train Cooling Centrifugal Fan Performance [J]. China Mechanical Engineering, 2023, 34(20): 2504-2512.
[11]	ZHAO Ximei, WANG Chao, JIN Hongyan. Adaptive Fractional Order Sliding Mode Control for PMSMs Based on NDO [J]. China Mechanical Engineering, 2023, 34(09): 1093-1099,1119.
[12]	LI Meng, WANG Shilong, MA Chi, XIA Changjiu. Identification of Key Errors for Large-sized Gear Hobbing Machines Based on Tooth Surface Posture-geometric Error Model [J]. China Mechanical Engineering, 2023, 34(05): 533-542.
[13]	ZHU An, AI Haiping, CHEN Li. Compliance Control of Dual-arm Space Robot Capture Satellite Based on Barrier Lyapunov Functions [J]. China Mechanical Engineering, 2022, 33(24): 2997-3006.
[14]	LU Chengwei, QIAN Bozeng, WANG Huimin, XIANG Sitong. Key Geometric Error Analysis and Compensation Method of Five-axis CNC Machine Tools under Workpiece Feature Decomposition [J]. China Mechanical Engineering, 2022, 33(14): 1646-1653.
[15]	ZHU Jianxu, ZHAO Dingxuan, , GONG Mingde, CHEN Hao, , YANG Mengke, . Active Suspension System Energy Consumption and Engine Power Matching Control for Emergency Rescue Vehicles [J]. China Mechanical Engineering, 2022, 33(11): 1361-1368.