斜拉索随机最优主动/半主动控制
摘要
本文首先研究动拉索面内振动的最优边界控制问题。将拉索面内振动方程通过Galerkin方法离散为两个自由度的运动,应用拟不可积Hamilton系统随机平均法和随机动态规划原理,建立动态规划方程。由性能指标最小,得到随机最优控制策略,并与双线性控制进行了对比,结果表明随机最优控制策略有较好的控制效果和较高的控制效率。然后研究了拉索面内面外的耦合振动,用类似方法得到最优控制策略,结果表明随机控制策略对面内-面外耦合的振动也有很好的控制性能。而线性化面内振动,通过拟可积Hamilton系统随机平均法和动态规划原理的结合,得到了关于面内多模态振动的随机最优主动控制,与双线性控制进行对比,并研究了系统参数对控制效果和控制效率的影响。最后,研究应用MR阻尼器实现对拉索的振动控制,MR阻尼器采用Bingham模型,将控制力分为被动力和主动力。被动力并入到系统的阻尼中,应用拟可积Hamilton随机平均法与随机动态规划原理,得到随机最优控制策略,说明MR能始终执行最优控制,比Bang-bang控制具有更好控制性能。
A stochastic optimal control strategy for a slightly sagged cable using support motion in the cable axial direction is first proposed. The nonlinear equation of cable motion in plane is derived and reduced to the equations for the first two modes of the cable vibration by using the Galerkin method. The partially averaged Ito equation for controlled system energy is further derived by applying the stochastic averaging method for quasi non-integrable Hamiltonian systems. The dynamical programming equation for the controlled system energy with a performance index is established by applying the stochastic dynamical programming principle and a stochastic optimal control law is obtained through solving the dynamical programming equation. A bilinear controller by using the direct method of Lyapunov is also introduced and a comparison between the two controllers shows that the proposed stochastic optimal control strategy is superior to the bilinear control strategy in the sense of higher control effectiveness and efficiency. The same procedure is carried out for the controlled motion in-plane and out-of-plane to show the superiority of the stochastic optimal control strategy. The motions in plane can be further reduced to linear equations with active motion control at the boundary. By applying the stochastic averaging method for quasi integrable Hamiltonian systems and the stochastic dynamical programming principle, a stochastic optimal control law is obtained through solving the dynamical programming equation. Extensive parameter studies are carried out for indicating the features of the proposed control strategy. Finally, the stochastic optimal semi-active control for stay cable multi-mode vibration attenuation by using magneto-reheological (MR) damper is developed. The Bingham model for MR damper is used. The force produced by an MR damper is split into passive and active parts. The passive part is combined with structural damping forces into effective damping forces. The stochastic averaging method for quasi integrable Hamiltonian systems and the stochastic dynamic principle are applied and a stochastic optimal semi-active control law is obtained through solving the dynamical programming equation. For controlled modal energies with an index not involving control force, bang-bang control law is obtained without solving dynamical programming equation. A comparison between the two control laws shows that the stochastic optimal semi-active control strategy is superior to the bang-bang control strategy in the sense of higher control effectiveness and efficiency and less chattering.
A stochastic optimal control strategy for a slightly sagged cable using support motion in the cable axial direction is first proposed. The nonlinear equation of cable motion in plane is derived and reduced to the equations for the first two modes of the cable vibration by using the Galerkin method. The partially averaged Ito equation for controlled system energy is further derived by applying the stochastic averaging method for quasi non-integrable Hamiltonian systems. The dynamical programming equation for the controlled system energy with a performance index is established by applying the stochastic dynamical programming principle and a stochastic optimal control law is obtained through solving the dynamical programming equation. A bilinear controller by using the direct method of Lyapunov is also introduced and a comparison between the two controllers shows that the proposed stochastic optimal control strategy is superior to the bilinear control strategy in the sense of higher control effectiveness and efficiency. The same procedure is carried out for the controlled motion in-plane and out-of-plane to show the superiority of the stochastic optimal control strategy. The motions in plane can be further reduced to linear equations with active motion control at the boundary. By applying the stochastic averaging method for quasi integrable Hamiltonian systems and the stochastic dynamical programming principle, a stochastic optimal control law is obtained through solving the dynamical programming equation. Extensive parameter studies are carried out for indicating the features of the proposed control strategy. Finally, the stochastic optimal semi-active control for stay cable multi-mode vibration attenuation by using magneto-reheological (MR) damper is developed. The Bingham model for MR damper is used. The force produced by an MR damper is split into passive and active parts. The passive part is combined with structural damping forces into effective damping forces. The stochastic averaging method for quasi integrable Hamiltonian systems and the stochastic dynamic principle are applied and a stochastic optimal semi-active control law is obtained through solving the dynamical programming equation. For controlled modal energies with an index not involving control force, bang-bang control law is obtained without solving dynamical programming equation. A comparison between the two control laws shows that the stochastic optimal semi-active control strategy is superior to the bang-bang control strategy in the sense of higher control effectiveness and efficiency and less chattering.
引文
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