基于T-S模糊模型的车辆电液悬架系统H_∞控制
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摘要
为了进一步降低主动悬架作动器输出力并优化控制系统鲁棒性,建立车辆7自由度整车模型,采用Takagi-Sugeno(T-S)模糊建模技术,设计主动悬架外环H_∞控制器,从而根据路面输入调节主动悬架性能,提升作动器能效。通过构建一个包括控制器稳定性分析、悬架运动空间及力的限值问题的线性矩阵不等式组,将控制器的优化问题转换为此线性不等式组的求解问题,并结合并行分配补偿控制技术,得到此控制器状态反馈系数。针对系统不确定性参数,内环采用自适应鲁棒控制方法,提升控制力的跟踪性能。通过对不同路面轮廓激励工况、交叉轴双轮激励工况以及控制力跟踪性能进行仿真试验,分析被动悬架和主动悬架性能评价指标,并对其作动器输出力进行对比研究。研究结果表明:在小激励下,基于T-S模糊模型的H_∞控制主动悬架相比被动悬架,各车轮处加速度均方根值可降低80%以上,与最优控制相比可降低47%以上;而在大激励时,虽然其加速度均方根值有所上升,但其悬架动挠度峰值较被动悬架有所下降;通过路面交叉轴激励对比可以看出,针对整车平顺性参数,该方法可在路面小激励时较被动悬架降低质心、俯仰以及侧倾加速度均方根值达55%、83%以及90%以上;与反演作动器输出力及最优控制作动器输出力对比结果表明,该控制方法可有效降低主动悬架控制力峰值20%以上,并提升控制力的跟踪性能;基于T-S模糊模型的H_∞控制可以在保证车辆悬架性能的基础上有效降低系统能耗。
To reduce the output force of active actuator and improve the robustness of a control system,an H_∞-outer-loop controller was built based on a 7-degree-of-freedom full car model of the Takagi-Sugeno(T-S)fuzzy modeling technique to adapt its strategy to different road disturbances and improve system efficiency.The resulting optimizing problem was transformed into a solution issue of linear matrix inequalities associated with system stability analysis,suspension stroke limit,and force constraints.By integrating these via parallel distributed compensation method,the controller gain was obtained.In response to the uncertain parameters,the adaptive robust control was employed in the inner loop to improve the force-tracking performance.Based on the simulation test under the condition of different road profiles,crossaxle double-road input,and control force tracking,the suspension performance indexes were analyzed and the control force was compared to backstepping and optimal control.The results show that the T-S fuzzy model based on the H_∞ control can reduce the root mean square(RMS)value of acceleration by more than 80% and 47% compared to passive suspension and optimal control,respectively.The RMS value of acceleration increases when under intensive disturbance with suspension dynamic deflection suppression.In cross-axle double-road input tests,the mean values of mass,pitch,and roll accelerations were reduced by more than 55%,83%,and 90%,respectively,compared to those of passive suspension under a small road disturbance.The peak control force was observed to reduce by more than 20%than that of the backstepping control and optimal control method,and the tracking accuracy was improved.These results show that the combination of the H_∞ control and adaptive robust control based on the T-S fuzzy model can reduce the system energy consumption with a guaranteed suspension performance.
To reduce the output force of active actuator and improve the robustness of a control system,an H_∞-outer-loop controller was built based on a 7-degree-of-freedom full car model of the Takagi-Sugeno(T-S)fuzzy modeling technique to adapt its strategy to different road disturbances and improve system efficiency.The resulting optimizing problem was transformed into a solution issue of linear matrix inequalities associated with system stability analysis,suspension stroke limit,and force constraints.By integrating these via parallel distributed compensation method,the controller gain was obtained.In response to the uncertain parameters,the adaptive robust control was employed in the inner loop to improve the force-tracking performance.Based on the simulation test under the condition of different road profiles,crossaxle double-road input,and control force tracking,the suspension performance indexes were analyzed and the control force was compared to backstepping and optimal control.The results show that the T-S fuzzy model based on the H_∞ control can reduce the root mean square(RMS)value of acceleration by more than 80% and 47% compared to passive suspension and optimal control,respectively.The RMS value of acceleration increases when under intensive disturbance with suspension dynamic deflection suppression.In cross-axle double-road input tests,the mean values of mass,pitch,and roll accelerations were reduced by more than 55%,83%,and 90%,respectively,compared to those of passive suspension under a small road disturbance.The peak control force was observed to reduce by more than 20%than that of the backstepping control and optimal control method,and the tracking accuracy was improved.These results show that the combination of the H_∞ control and adaptive robust control based on the T-S fuzzy model can reduce the system energy consumption with a guaranteed suspension performance.
引文
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[15] LU L,YAO B.Energy-saving Adaptive Robust Control of a Hydraulic Manipulator Using Five Cartridge Valves with an Accumulator[J].IEEE Transactions on Industrial Electronics,2014,61(12):7046-7054.
[16] SUN W,GAO H,YAO B.Adaptive Robust Vibration Control of Full-car Active Suspensions With Electrohydraulic Actuators[J].IEEE Transactions on Control Systems and Technology,2013,21(6):2417-2422.
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[18] CHEN H,GUO K H.Constrained Control of Active Suspensions:An LMI Approach[J].IEEE Transaction on Control System Technology,2005,13(3):412-421.
[19] DAMATO F J,VIASSOLO D E.Fuzzy Control for Active Suspensions[J]. Mechatronics,2000,10(8):897-920.
[20] JIANG Y,JIANG Z P.Computational Adaptive Optimal Control for Continuous-time Linear Systems with Completely Unknown Dynamics[J].Automatica,2012,48(10):2699-2704.
[21]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):301-354.ZHAO Cai-hong, CHEN Shi-an, WANG Juncheng.Influence of Stiffness and Damping Parameters on Control of Active Suspension Based on LQG[J].Transactions of Chinese Society for Agriculture Machinery,2015,46(12):301-354.
[22]唐诗晨,陈龙,汪若尘,等.基于阻尼多模式切换的主动悬架最优控制研究[J].广西大学学报:自然科学版,2014,39(2):300-307.TANG Shi-chen,CHEN Long,WANG Ruo-chen,et al.Research on Optimal Control of Active Suspension Based on Damping Multi-modal Switching[J].Journal of Guangxi University:Nature Science Edition,2014,39(2):300-307.
[23] LI H,YU J,HILTON C,et al.Adaptive Slidingmode Control for Nonlinear Active Suspension Vehicle Systems Using T-S Fuzzy Approach[J].IEEE Transaction on Industrial Electronics,2013,60(8):3328-3338.
[24] DU H,ZHANG N.Fuzzy Control for Nonlinear Uncertain Electrohydraulic Active Suspensions with Input Constraint[J].IEEE Transaction on Fuzzy System,2009,17(2):343-356.
[25] DU H,ZHANG N.Static Output Feedback Control for Electrohydraulic Active Suspension via T-S Fuzzy Model Approach[J].Journal of Dynamic Systems,Measurement,and Control,2009,131(5):4-15.
[26] WANG H,TANAKA K,GRIFFIN M F.An Approach to Fuzzy Control of Nonlinear Systems:Stability and Design Issues[J].IEEE Transactions on Fuzzy Systems,1996,4(1):14-23.
[27]马建,冯镇,宋宏勋.基于非线性系统结构稳定性理论的车辆转向动力学研究[J].中国公路学报,2015,28(3):110-116.MA Jian,FENG Zhen,SONG Hong-xun.Study on Vehicle Steering Dynamics Based on Structural Stability Theory of Nonlinear System[J].China Journal of Highway and Transport,2015,28(3):110-116.
[28] YAO B,TOMIZUKA M.Adaptive Robust Control of MIMO Nonlinear Systems in Semi-strict Feedback Forms[J].Automatica,2001,37(9):1305-1321.
[29] CHANTRANUWATHANA S,PENG H.Adaptive Robust Force Control for Vehicle Active Suspensions[J].International Journal of Adaptive Control and Signal Processing,2004,18(2):83-102.
[30]周辰雨,张硕,武丽颖.基于Backstepping和LQG算法的车辆主动悬架控制研究[J].西南大学学报:自然科学版,2015,37(4):138-146.ZHOU Chen-yu, ZHANG Shuo, WU Li-ying.Research on Automobile Active Suspension Based on Backstepping and LQG Control[J].Journal of Southwest University:Natural Science Edition,2015,37(4):138-146.
[2] LI Z,ZUO L,LUHRS G,et al.Electromagnetic Energy-harvesting Shock Absorbers:Design,Modeling,and Road Tests[J].IEEE Transactions on Vehicle Technology,2013,62(3):1065-1074.
[3] SU X,YANG X,SHI P,et al.Fuzzy Control of Nonlinear Electromagnetic Suspension Systems[J].Mechatronics,2014,24(4):328-335.
[4] KUMAR M S,VIJAYANGAN S.Analytical and Experimental Studies on Active Suspension System of Light Passenger Vehicle to Improve Ride Comfort[J].Mechanics,2016,65(3):34-41.
[5] YAGIZ N,HACIOGLU Y.Backstepping Control of a Vehicle with Active Suspensions[J].Control Engineer Practice,2008,16(12):1457-1467.
[6] SUN W,PAN H,ZHANG Y,et al.Multi-objective Control for Uncertain Nonlinear Active Suspension Systems[J]. Mechatronics,2014,24(4):318-327.
[7] ALLEYNE A,LIU R.On the Limitations of Force Tracking Control for Hydraulic Servo-systems[J].Journal of Dynamics,Measurement,and Control,1999,121(2):184-190.
[8] WANG Y,CAO L,ZHANG S,et al.Command Filtered Adaptive Fuzzy Backstepping Control Method of Uncertain Non-linear Systems[J].IET Control Theory and Applications,2016,10(10):1134-1141.
[9] GOVAL A,KUMAR J,KUMAR V.Comparative Study of BLF and QLF Based Backstepping Controllers for Active Suspension System[C]//IEEE.2015 National Systems Conference. New York:IEEE,2015:1-6.
[10] DESHPANDE V S,MOHAN B,SHENDGE P,et al.Disturbance Observer Based Sliding Mode Control of Active Suspension Systems[J].Journal of Sound and Vibration,2014,333(11):2281-2296.
[11] FENG Y,HAN F,YU X.Chattering Free Full-order Sliding-mode Control[J].Automatica,2014,50(4):1310-1314.
[12] YAO B,TOMIZUKA M.Adaptive Robust Control of SISO Nonlinear Systems in a Semi-strict Feedback Form[J].Automatica,1997,33(5):893-900.
[13] YAO J,JIAO Z,YAO B.Nonlinear Adaptive Robust Backstepping Force Control of Hydraulic Load Simulator:Theory and Experiments[J].Journal of Mechanical Science and Technology,2014,28(4):1499-1507.
[14] MOHANTY A,GAYAKA S,YAO B.An Adaptive Robust Observer for Velocity Estimation in an Electro-hydraulic System[J].International Journal of Adaptive Control and Signal Processing,2012,26(12):1076-1089.
[15] LU L,YAO B.Energy-saving Adaptive Robust Control of a Hydraulic Manipulator Using Five Cartridge Valves with an Accumulator[J].IEEE Transactions on Industrial Electronics,2014,61(12):7046-7054.
[16] SUN W,GAO H,YAO B.Adaptive Robust Vibration Control of Full-car Active Suspensions With Electrohydraulic Actuators[J].IEEE Transactions on Control Systems and Technology,2013,21(6):2417-2422.
[17] MENG J,CHEN Q,HE R.Research on Optimal Control for the Vehicle Suspension Based on the Simulated Annealing Algorithm[J].Journal of Applied Mathematics,2014(5):1-5.
[18] CHEN H,GUO K H.Constrained Control of Active Suspensions:An LMI Approach[J].IEEE Transaction on Control System Technology,2005,13(3):412-421.
[19] DAMATO F J,VIASSOLO D E.Fuzzy Control for Active Suspensions[J]. Mechatronics,2000,10(8):897-920.
[20] JIANG Y,JIANG Z P.Computational Adaptive Optimal Control for Continuous-time Linear Systems with Completely Unknown Dynamics[J].Automatica,2012,48(10):2699-2704.
[21]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):301-354.ZHAO Cai-hong, CHEN Shi-an, WANG Juncheng.Influence of Stiffness and Damping Parameters on Control of Active Suspension Based on LQG[J].Transactions of Chinese Society for Agriculture Machinery,2015,46(12):301-354.
[22]唐诗晨,陈龙,汪若尘,等.基于阻尼多模式切换的主动悬架最优控制研究[J].广西大学学报:自然科学版,2014,39(2):300-307.TANG Shi-chen,CHEN Long,WANG Ruo-chen,et al.Research on Optimal Control of Active Suspension Based on Damping Multi-modal Switching[J].Journal of Guangxi University:Nature Science Edition,2014,39(2):300-307.
[23] LI H,YU J,HILTON C,et al.Adaptive Slidingmode Control for Nonlinear Active Suspension Vehicle Systems Using T-S Fuzzy Approach[J].IEEE Transaction on Industrial Electronics,2013,60(8):3328-3338.
[24] DU H,ZHANG N.Fuzzy Control for Nonlinear Uncertain Electrohydraulic Active Suspensions with Input Constraint[J].IEEE Transaction on Fuzzy System,2009,17(2):343-356.
[25] DU H,ZHANG N.Static Output Feedback Control for Electrohydraulic Active Suspension via T-S Fuzzy Model Approach[J].Journal of Dynamic Systems,Measurement,and Control,2009,131(5):4-15.
[26] WANG H,TANAKA K,GRIFFIN M F.An Approach to Fuzzy Control of Nonlinear Systems:Stability and Design Issues[J].IEEE Transactions on Fuzzy Systems,1996,4(1):14-23.
[27]马建,冯镇,宋宏勋.基于非线性系统结构稳定性理论的车辆转向动力学研究[J].中国公路学报,2015,28(3):110-116.MA Jian,FENG Zhen,SONG Hong-xun.Study on Vehicle Steering Dynamics Based on Structural Stability Theory of Nonlinear System[J].China Journal of Highway and Transport,2015,28(3):110-116.
[28] YAO B,TOMIZUKA M.Adaptive Robust Control of MIMO Nonlinear Systems in Semi-strict Feedback Forms[J].Automatica,2001,37(9):1305-1321.
[29] CHANTRANUWATHANA S,PENG H.Adaptive Robust Force Control for Vehicle Active Suspensions[J].International Journal of Adaptive Control and Signal Processing,2004,18(2):83-102.
[30]周辰雨,张硕,武丽颖.基于Backstepping和LQG算法的车辆主动悬架控制研究[J].西南大学学报:自然科学版,2015,37(4):138-146.ZHOU Chen-yu, ZHANG Shuo, WU Li-ying.Research on Automobile Active Suspension Based on Backstepping and LQG Control[J].Journal of Southwest University:Natural Science Edition,2015,37(4):138-146.