邻接高耸结构的随机最优控制
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摘要
本文基于随机动态规划原理与随机平均法,提出耦合相邻高耸结构的随机最优控制方法。先建立任意层数并在任意层高处控制联接的耦合结构的缩聚模型,再运用随机平均法导出关于模态能量的Ito随机微分方程,应用随机动态规划原理建立动态规划方程,由此可确定最优控制律。将结构的响应控制化为模态能量控制,缩减控制系统的维数。用高斯随机过程模拟地震激励,可计及其功率谱特性。数值结果表明该耦合结构控制方法的有效性。
In this paper, a stochastic optimal control-method for coupled adjacent high-rise structures is proposed based on the stochastic dynamical programming principle and the stochastic averaging method. A reduced-order model of coupled structures with an arbitrary number of stories and with connecting control devices at any floors in formulated. Then the stochastic averaging method is applied to the coupled structures to yield Ito stochastic differential equations for modal energies. The stochastic dynamical programming principle is applied to the energy processes to establish a dynamical programming equation, from which an optimal control law is determined. The structural response control is performed by the modal energy control and the dimension of control system is reduced. The seismic excitation is modeled as a Gaussian random process and the power spectrum can be taken into account. Numerical results illustrate the control efficacy of the proposed method for coupled structures.
In this paper, a stochastic optimal control-method for coupled adjacent high-rise structures is proposed based on the stochastic dynamical programming principle and the stochastic averaging method. A reduced-order model of coupled structures with an arbitrary number of stories and with connecting control devices at any floors in formulated. Then the stochastic averaging method is applied to the coupled structures to yield Ito stochastic differential equations for modal energies. The stochastic dynamical programming principle is applied to the energy processes to establish a dynamical programming equation, from which an optimal control law is determined. The structural response control is performed by the modal energy control and the dimension of control system is reduced. The seismic excitation is modeled as a Gaussian random process and the power spectrum can be taken into account. Numerical results illustrate the control efficacy of the proposed method for coupled structures.
引文
[1] T. T. Soong. Active Structural Control: Theory and Practice [M]. John Wiley & Sons, New York, 1990．
[2] G. W. Housner, L. A. Bergman, et al. Structural Control: past, present, and future[J] ASCE J. En-grg. Mech. , 1997, 123 (1) :897-971．
[3] K. Seto. Vibration control method for flexible structures arranged in parallel[C]. Proc. 1st World Conf. on Struct. Control, 1994, Los Angeles, California, 62-71．
[4] R. E. christenson, B. F. Spencer and E. A. Johnson. Coupled building control using active and smart damping strategies [C]. Optimization & Control in Civil & Struct. Engrg. , 1999, Civil-Comp Press, Edinburgh, 187-195．
[5] W. Q. Zhu, Z. G. Ying and T. T. Soong. Optimal nonlinear feedback control of structures under random loading[C]. Stochastic Struct. Dyn. , 1999, Balkema, Rotterdam, 141-148．
[2] G. W. Housner, L. A. Bergman, et al. Structural Control: past, present, and future[J] ASCE J. En-grg. Mech. , 1997, 123 (1) :897-971．
[3] K. Seto. Vibration control method for flexible structures arranged in parallel[C]. Proc. 1st World Conf. on Struct. Control, 1994, Los Angeles, California, 62-71．
[4] R. E. christenson, B. F. Spencer and E. A. Johnson. Coupled building control using active and smart damping strategies [C]. Optimization & Control in Civil & Struct. Engrg. , 1999, Civil-Comp Press, Edinburgh, 187-195．
[5] W. Q. Zhu, Z. G. Ying and T. T. Soong. Optimal nonlinear feedback control of structures under random loading[C]. Stochastic Struct. Dyn. , 1999, Balkema, Rotterdam, 141-148．
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