考虑控制器拓扑的随机动力系统最优控制
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摘要
在简要回顾几类结构控制模式的基础上,本文提出考虑控制装置最优布设与控制器参数优化的随机最优控制方法,将它们统一为物理随机最优控制的广义最优控制律。为有效地寻找每个序列工况的控制器最优拓扑和控制器参数,分别定义基于超越概率的层可控指标梯度最小准则和能量均衡最优准则。数值算例分析表明,采用广义最优控制律可以以最小的投资获得最大的控制效益。同时表明,按层可控指标梯度最小准则寻优,比先前按层可控指标最大准则寻优能更有效地收敛到目标性态。
A Generalized Optimal Control Policy(GOCP),including the optimal placement and optimization of parameters of controllers,is proposed for the physical stochastic optimal control of structural systems.It extends the classical forms of structural optimal control policy inherent in passively controlled modalities,active control modalities,semi-active control modalities and hybrid control modalities.A control criterion of minimum storey controllability index gradient related to the exceedance probability is defined so as to search for the optimal structural topology efficiently,which characterizes system safety(indicated as inter-story drift),system serviceability(indicated as inter-story velocity),system comfort(indicated as story acceleration),controller workability(indicated as control force) and their trade-offs.Another exceedance probability based control criterion associated with the optimal trade-off of system energy is also constructed to define the optimized parameters of controllers.Numerical results reveal that the proposed GOCP may achieve the maximum controlled effectiveness with minimum cost.Meanwhile,the utilization of the design criterion of the minimum controllability index gradient achieves the objective performance more efficiently than that of the currently used maximum controllability index.
A Generalized Optimal Control Policy(GOCP),including the optimal placement and optimization of parameters of controllers,is proposed for the physical stochastic optimal control of structural systems.It extends the classical forms of structural optimal control policy inherent in passively controlled modalities,active control modalities,semi-active control modalities and hybrid control modalities.A control criterion of minimum storey controllability index gradient related to the exceedance probability is defined so as to search for the optimal structural topology efficiently,which characterizes system safety(indicated as inter-story drift),system serviceability(indicated as inter-story velocity),system comfort(indicated as story acceleration),controller workability(indicated as control force) and their trade-offs.Another exceedance probability based control criterion associated with the optimal trade-off of system energy is also constructed to define the optimized parameters of controllers.Numerical results reveal that the proposed GOCP may achieve the maximum controlled effectiveness with minimum cost.Meanwhile,the utilization of the design criterion of the minimum controllability index gradient achieves the objective performance more efficiently than that of the currently used maximum controllability index.
引文
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[2]Yang J N.Application of optimal control theory to civilengineering structures[J].Journal of the EngineeringMechanics Division,ASCE,19751,01(6):819-838
[3]Li J,Peng Y B,Chen J B.A physical approach tostructural stochastic optimal controls[J].ProbabilisticEngineering Mechanics,2009,25(1):127-141
[4]Li J,Peng Y B,Chen J B.Probabilistic criteria of structuralstochastic optimal controls[J.]Probabilistic EngineeringMechanics,20112,6(2):240-253
[5]Amini F,Tavassoli M R.Optimal structural active controlforce,number and placement of controllers[J].Engineering Structures,2005,27(9):1306-1316
[6]Chen G S,Bruno R J,Salama M.Optimal placement ofactive/passive members in truss structures using simulatedannealing[J].AIAA Journal,19912,9(8):1327-1334
[7]Chang M I J,Soong T T.Optimal controller placement inmodal control of complex systems[J].Journal ofMathematical Analysis and Applications,1980,75(2):340-358
[8]Ibidapo-Obe O.Optimal actuators placements for the activecontrol of flexible structures[J].Journal of MathematicalAnalysis and Applications,19851,05(1):12-25
[9]Zhang R H,Soong T T.Seismic design of viscoelasticdampers for structural applications[J].Journal ofStructural Engineering,ASCE,1992,118(5):1375-1392
[10]Li J,Chen J B.Probability density evolution method fordynamic response analysis of structures with uncertainparameters[J].Computational Mechanics,2004,34(5):400-409
[11]Hrovat D,Barak P,Rabins M.Semi-active versus passive oractive tuned mass dampers for structural control[J.]Journalof Engineering Mechanics,1983,109(3):691-705
[12]Chu S Y,Soong T T,Reinhorn A M.Active,hybrid andsemi-active structural control[M].West Sussex:JohnWiley&Sons,2005
[13]Yang J N,Akbarpour A,Ghaemmaghami P.New optimalcontrol algorithms for structural control[J].Journal ofEngineering Mechanics,ASCE,1987,113(9):1369-1386
[14]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):21-26(Li Jie,AiXiaoqiu.Study on random model of earthquake groundmotion based on physical process[J].EarthquakeEngineering and Engineering Vibration,2006,26(5):21-26(in Chinese))
[15]Chen J B,Li J.Strategy for selecting representative pointsvia tangent spheres in the probability density evolutionmethod[J].International Journal for Numerical Methods inEngineering,2008,74(13):1988-2014
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