应用MR阻尼器的滞迟系统的非线性随机最优半主动控制

【作者】 程慧；

【导师】 朱位秋；

【作者基本信息】 浙江大学 ， 工程力学， 2006， 硕士

【摘要】 第一章中，简单介绍了随机控制理论的发展概况和研究内容及振动控制分类，并结合滞迟系统的特性简单回顾了求解滞迟系统随机响应的各种方法，提出滞迟系统的半主动控制为本文研究内容。第二章中，介绍了磁流变阻尼器的工作原理、阻尼力模型以及控制策略，提出了将磁流变阻尼器应用于滞迟系统的随机最优半主动控制。第三章中，介绍能量包线随机平均法和随机最优控制策略。第四章中，基于第三章中给出的基本原理对滞迟系统进行半主动控制。首先将滞迟系统转化为等效非线性非滞迟系统，利用能量包线随机平均法推导出系统的部分平均It(?)随机微分方程。然后基于动态规划原理建立系统的动态规划方程，求解动态规划方程得到系统的最优控制策略。将最优控制律代入系统的部分平均It(?)随机微分方程并完成平均得到系统的完全平均It(?)随机微分方程和与之对应的FPK方程。最终，通过求解FPK方程和系统的动态规划方程得到系统的响应。同时，还采用基于等效线性化的LQG控制策略对该滞迟系统进行控制。结果表明，本文提出的随机最优半主动控制策略比LQG控制策略具有更好的控制效果和控制效率。更多还原

【Abstract】 In chapter 1, the present status of the stochastic control theory is briefly reviewed, and many methods for predicting the stochastic response of the hysteretic system are introduced. In chapter 2, the working principle of the MR damper and its mathematical models are expatiated, and the control strategies for using MR dampers are enumerated. In chapter 3, the stochastic averaging method of energy envelope and stochastic optimal control strategy are introduced. In chapter 4, based on the basic principles described in chapter 3, MR damper is used to semi-actively control the hysteretic system. First, the system is converted into an equivalent non-hysteretic nonlinear stochastic system, from which a partially averaged It(?) stochastic equation is derived by using the stochastic averaging method of energy envelope. For the ergodic control problem, a dynamical programming equation is established based on the stochastic dynamical programming principle and solved to yield the optimal control law. The fully averaged It(?) equation is obtained by substituting the optimal control force into partially averaged It(?) equation and completing the average. Finally, the response of the controlled system is obtained by solving the final dynamical programming equation and the Fokker-Planck-Kolmogorov equation associated with the fully averaged It(?) equation. Simultaneously, LQG control strategy is also used to control the same system. The numerical result indicates that both the effectiveness and efficiency of the former control strategy are better than those of the latter.更多还原