随机动力系统磁流变阻尼最优控制策略
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摘要
提出了基于广义密度演化方程的限界Hrovat半主动控制策略.以随机地震动作用下磁流变阻尼控制系统为研究对象,根据系统二阶统计量评价和跟踪实现目标主动最优控制力的控制准则,进行了磁流变液阻尼器的参数设计.数值结果表明在概率意义上,恰当设计的半主动控制器可以达到与主动控制器几乎相同的控制效果.同时,磁流变阻尼器表现出类似Bouc-Wen模型的动态阻尼性能,即强度退化、刚度退化和捏拢效应.
This paper presents a bounded Hrovat semi-active control strategy providing the adequate performance control of general stochastic dynamical systems.It hinges on the generalized density evolution equation recently developed to reveal the intrinsic relationship between the physical mechanism and probability density evolution of systems.An earthquake-excited system controlled by a magnetorheological (MR) damper is investigated for illustrative purpose,of which two parameters are laid down,i.e.damping coefficient and maximum Coulomb force,according to the criterion of system second-order statistics evaluation and perfectly tracing the optimal active control forces.Numerical results reveal that the appropriately designed semi-active controller can achieve almost the same effect of the active controller in the probabilistic sense.The example further proves that the advocated semi-active control strategy can prompt the dynamic damping performance of the MR damper,behaving as a type-like Bouc-Wen model with the strength deterioration,stiffness degradation and pinch effect.
This paper presents a bounded Hrovat semi-active control strategy providing the adequate performance control of general stochastic dynamical systems.It hinges on the generalized density evolution equation recently developed to reveal the intrinsic relationship between the physical mechanism and probability density evolution of systems.An earthquake-excited system controlled by a magnetorheological (MR) damper is investigated for illustrative purpose,of which two parameters are laid down,i.e.damping coefficient and maximum Coulomb force,according to the criterion of system second-order statistics evaluation and perfectly tracing the optimal active control forces.Numerical results reveal that the appropriately designed semi-active controller can achieve almost the same effect of the active controller in the probabilistic sense.The example further proves that the advocated semi-active control strategy can prompt the dynamic damping performance of the MR damper,behaving as a type-like Bouc-Wen model with the strength deterioration,stiffness degradation and pinch effect.
引文
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[5]Li J,Chen J B.The principle of preservation of probability and the generalized density evolution equation[J].Structural Safety,2008,30(1):65.
[6]Li J,Chen J B.Stochastic dynamics of structures[M].Singapore:John Wiley&Sons,2009.
[7]Hrovat D,Barak P,Rabins M.Semi-active versus passive or active tuned mass dampers for structural control[J].Journal of Engineering Mechanics,1983,109(3):691.
[8]李杰,艾晓秋.基于物理的随机地震动模型研究[J].地震工程与工程振动,2006,26(5):21.LI Jie,AI Xiaoqiu.Study on random model of earthquake ground motion based on physical process[J].Earthquake Engineering and Engineering Vibration,2006,26(5):21.
[9]彭勇波,陈建兵,刘伟庆,等.隔震结构的随机地震反应与抗震可靠度评价[J].同济大学学报:自然科学版,2008,36(11):1457.PENG Yongbo,CHEN Jianbing,LI U Weiqing,et al.Stochastic seismic response and aseismic reliability assessment of base-isolated structures[J].Journal of Tongji University:Natural Science,2008,36(11):1457.
[10]Chen J B,Li J.Strategy for selecting representative points via tangent spheres in the probability density evolution method[J].International Journal for Numerical Methods in Engineering,2008,74(13):1988.
[11]Bell man R.Dynamic programming[M].Princeton:Princeton University Press,1957.
[12]Spencer Jr B F,Sain M K,Carlson J D.Phenomenological model of magnetorheological damper[J].Journal of Engineering Mechanics,1997,123(3):230.
[2]Dyke SJ,Spencer Jr B F,Sain MK,et al.Modeling and control of magnetorheological dampers for seismic response reduction[J].Smart Materials and Structures,1996,5:565.
[3]Ying Z G,Zhu W Q,Soong T T.A stochastic opti mal semi-active control strategy for ER/MR dampers[J].Journal of Sound and Vibration,2003,259(1):45.
[4]Li J,Peng Y B,Chen J B.A physical approach to structural stochastic opti mal controls[J].Probabilistic Engineering Mechanics,2010,25:127.
[5]Li J,Chen J B.The principle of preservation of probability and the generalized density evolution equation[J].Structural Safety,2008,30(1):65.
[6]Li J,Chen J B.Stochastic dynamics of structures[M].Singapore:John Wiley&Sons,2009.
[7]Hrovat D,Barak P,Rabins M.Semi-active versus passive or active tuned mass dampers for structural control[J].Journal of Engineering Mechanics,1983,109(3):691.
[8]李杰,艾晓秋.基于物理的随机地震动模型研究[J].地震工程与工程振动,2006,26(5):21.LI Jie,AI Xiaoqiu.Study on random model of earthquake ground motion based on physical process[J].Earthquake Engineering and Engineering Vibration,2006,26(5):21.
[9]彭勇波,陈建兵,刘伟庆,等.隔震结构的随机地震反应与抗震可靠度评价[J].同济大学学报:自然科学版,2008,36(11):1457.PENG Yongbo,CHEN Jianbing,LI U Weiqing,et al.Stochastic seismic response and aseismic reliability assessment of base-isolated structures[J].Journal of Tongji University:Natural Science,2008,36(11):1457.
[10]Chen J B,Li J.Strategy for selecting representative points via tangent spheres in the probability density evolution method[J].International Journal for Numerical Methods in Engineering,2008,74(13):1988.
[11]Bell man R.Dynamic programming[M].Princeton:Princeton University Press,1957.
[12]Spencer Jr B F,Sain M K,Carlson J D.Phenomenological model of magnetorheological damper[J].Journal of Engineering Mechanics,1997,123(3):230.
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