Hybrid Control of Electromagnetic Active Suspensions Based on Nonlinear Actuators#br#

doi:10.3969/j.issn.1004-132X.2022.02.002

Abstract

Abstract: In response to the problems that the nonlinear characteristics of the electromagnetic active suspension linear actuators affected the performance of the control system， a nonlinear mathematical model of input current and electromagnetic actuation force was established based on the theory of magnetic field harmonics. A nonlinear dynamics model of electromagnetic active suspension was established by combining with the suspension systems， and the influences of nonlinear characteristics on active suspension performance were analyzed. In order to eliminate the influences of nonlinear characteristics， a MOPSOH2/H∞ robust controller was designed based on filter-x recursive least squares adaptive filter compensation. Simulation results show that the proposed hybrid controller may restrain the control force in the unsaturated interval and compensate the fluctuations of the control force effectively， which improves the vehicle dynamics performance and the control efficiency of the active suspensions， and significantly eliminates the influences of the nonlinear characteristics of the actuator on the active suspensions.

Key words: electromagnetic active suspension, nonlinear characteristics, adaptive filter, multi-objective particle swarm optimization（MOPSO）H2/H∞ control

摘要： 针对电磁主动悬架直线作动器的非线性特性对控制系统性能的影响问题，基于磁场谐波理论建立了输入电流与电磁作动力的非线性数学模型。结合作动力输出模型与悬架系统，建立了电磁主动悬架非线性动力学模型，分析作动器非线性特性对主动悬架性能的影响。为了消除影响，设计了基于滤波递归最小二乘法（FxRLS）自适应滤波补偿的多目标粒子群H2/H∞鲁棒混合控制器。仿真结果表明，混合控制器能将控制力约束在非饱和区间内并能对控制力的波动进行有效的补偿，提高了车辆动力学性能及主动悬架的控制效率，显著地消除了作动器非线性特性对主动悬架的影响。

关键词: 电磁主动悬架, 非线性特性, 自适应滤波器, 多目标粒子群优化H2/H∞控制

CLC Number:

U463.33

HU Yiming, LI Yinong, ZHENG Ling. Hybrid Control of Electromagnetic Active Suspensions Based on Nonlinear Actuators#br#[J]. China Mechanical Engineering, 2022, 33(02): 134-142.

胡一明, 李以农, 郑玲. 基于作动器非线性特性的电磁主动悬架混合控制[J]. 中国机械工程, 2022, 33(02): 134-142.

References

［1］来飞，胡博. 汽车主动悬架技术的研究现状［J］. 南京理工大学学报， 2019， 43（4）：518-526.
LAI Fei， HU Bo. Research Status of Automotive Active Suspension Technology［J］. Journal of Nanjing University of Science and Technology， 2019， 43（4）：518-526.
［2］GYSEN B L J， PAULIDES J J H， JANSSEN J L G， et al. Active Electromagnetic Suspension System for Improved Vehicle Dynamics［J］. IEEE Transactions on Vehicular Technology， 2009， 59（3）：1156-1163.
［3］MARTINS I， ESTEVES J， MARQUES G D， et al. Permanent-magnets Linear Actuators Applicability in Automobile Active Suspensions［J］. IEEE Transactions on Vehicular Technology， 2006， 55（1）：86-94.
［4］HIROSE M， MATSUSHIGE S， BUMA S， et al. Toyota Electronic Modulated Air Suspension System for the 1986 Soarer［J］. IEEE Transactions on Industrial Electronics， 1988， 35（2）：193-200.
［5］LIU Y J， ZENG Q， LIU L， et al. An Adaptive Neural Network Controller for Active Suspension Systems with Hydraulic Actuator［J］. IEEE Transactions on Systems， Man， and Cybernetics：Systems， 2018， 50（12）：5351-5360.
［6］KAWAMOTO Y， SUDA Y， INOUE H， et al. Modeling of Electromagnetic Damper for Automobile Suspension［J］. Journal of System Design and Dynamics， 2007， 1（3）：524-535.
［7］曹民，刘为，喻凡. 车辆主动悬架用电机作动器的研制［J］. 机械工程学报， 2008， 44（11）：224-228.
CAO Min， LIU Wei， YU Fan. Developmenton Electromotor Actuatorfor Active Suspension of Vehicle［J］. Journal of Mechanical Engineering， 2008， 44（11）：224-228.
［8］LIN J， CHENG K W E， ZHANG Z， et al. Active Suspension System Based on Linear Switched Reluctance Actuator and Control Schemes［J］. IEEE Transactions on Vehicular Technology， 2013， 62（2）：562-572.
［9］杨超，李以农，钟银辉，等. 主动悬架用直线作动器结构设计及性能分析［J］. 汽车工程， 2015， 37（9）：1040-1046.
YANG Chao， LI Yinong， ZHONG Yinhui， et al. Structure Design and Performance Analysis of Linear Actuator for Active Suspension［J］. Automotive Engineering， 2015， 37（9）：1040-1046.
［10］GYSEN B L J， JANSSEN J L G， PAULIDES J J H， et al. Design Aspects of an Active Electromagnetic Suspension System for Automotive Applications［J］. IEEE Transactions on Industry Applications， 2009， 45（5）：1589-1597.
［11］裴金顺，李以农，王艳阳，等. 采用电磁直线电机的主动悬架控制系统的设计与能量分析［J］. 汽车工程， 2014， 36（11）：1386-1391.
PEI Jinshun， LI Yinong， WANG Yanyang， et al. Design and Energy Analysis of an Active Suspension Control System with Electromagnetic Linear Motor［J］. Automotive Engineering， 2014， 36（11）：1386-1391.
［12］WANG J， HOWE D. Tubular Modular Permanent-magnet Machines Equipped with Quasi-halbach Magnetized Magnets—Part Ⅱ：Armature Reaction and Design Optimization［J］. IEEE Transactions on Magnetics， 2005， 41（9）：2479-2489.
［13］POLINDER H， SLOOTWEG J G， HOEIJMAKERS M J， et al. Modelling of a Linear PM Machine Including Magnetic Saturation and End Effects：Maximum Force to Current Ratio［C］∥IEEE International Electric Machines and Drives Conference. Madison， WI， 2003：805-811.
［14］杨超，李以农，郑玲，等. 基于多目标粒子群算法的电磁主动悬架作动器优化［J］. 机械工程学报， 2019， 55（19）：154-166.
YANG Chao， LI Yinong， ZHENG Ling， et al. Optimum of Electromagnetic Active Suspension Actuator Using Multi-objective Particle Swarm Optimization Algorithm［J］. Journal of Mechanical Engineering， 2019， 55（19）：154-166.
［15］WANG J B， GERAINT W J， DAVID H. A General Framework for the Analysis and Design of Tubular Liear Permanent Magnet Machines［J］. IEEE Transactions on Magnetics， 1999， 35（3）：1986-2000.
［16］GYSEN B L J， van der SANDE T P J， PAULIDES J JH， et al. Efficiency of a Regenerative Direct-drive Electromagnetic Active Suspension［J］. IEEE Transactions on Vehicular Technology， 2011， 60（4）：1384-1393.
［17］HUANG Y A， BENESTY J. Adaptive Multi-channel Least Mean Square and Newton Algorithms for Blind Channel Identification［J］. Signal Processing， 2002， 82（8）：1127-1138.
［18］SUN W， LI Y N， ZHANG F， et al. Active Gear Pair Vibration Control Based on Filtered-x RLS Algorithm［J］. Applied Mechanics & Materials， 2011， 86：166-169.
［19］俞立. 鲁棒控制-线性矩阵不等式处理方法［M］. 北京：清华大学出版社， 2002.
YU Li. Robust Control-linear Matrix Inequality ProcessingMethod［M］. Beijing：Tsinghua University Press， 2002.
［20］CHEN H， LIU Z Y， SUN P Y. Application of Constrained H∞ Control to Active Suspension Systems on Half-car Models［J］. Journal of Dynamic Systems， Measurement， and Control， 2005， 127（3）：345-354.
［21］CHEN H， GUO K H. Constrained H/sub/splin-fin∥Control of Active Suspensions：an LMI Approach［J］. IEEE Transactions on Control Systems Technology， 2005， 13（3）：412-421.
［22］彭冲，郑玲，李以农. 基于粒子群优化算法主动悬架作动器多目标优化设计［J］. 中南大学学报：自然科学版， 2017， 48（4）：968-976.
PENG Chong， ZHENG Ling， LI Yinong， et al， Optimum Design of Active Suspension Actuator Using Multi-objective Stochastic Particle Swarm Optimization［J］. Journal of Central South University of Technology， 2017， 48（4）：968-976.

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