弹性水击情况下随机非线性水轮机的概率分布控制

Probability distribution control of stochastic nonlinear hydro-turbine with elastic water column

针对随机激励下基于弹性水击的非线性水轮机系统,提出了一种新的概率分布控制方法。该方法首先采用正交分解和反馈理论的方法建立一个水轮机系统的耗散哈密顿模型。然后,利用获得耗散不可积哈密顿系统精确平稳解的技术,设计一个基于概率分布的控制方法,从而可以得到水轮机系统输出的一个预先设定的稳态概率密度函数(SPDF)值。此外,系统的稳定性分析是通过李雅普诺夫函数方法来证明受控系统的转移概率密度收敛于预先设定的稳态概率密度函数值。最后,通过系统仿真表明所提出的控制策略能够达到预期的控制效果,即系统输出量的转移概率密度能够在较短的时间里逼近到预先设定的目标稳态概率密度函数。

A novel probability distribution control method was proposed for hydro-turbine systems with e-lastic water column under stochastic disturbances. The method of orthogonal decomposition and feedback theory was used to build a dissipated Hamiltonian model for the hydro-turbine system. Furthermore,inorder to obtain a pre-sjDecified stationary probability density function （ SPDF） of hydro-turbine system out-put , a probability shaping control metliod was designed based on the technique for obtaining the exact sta-tionary solutions of tlie disi{）ated non-integrable Hamiltonian systems. In addition, the Lyapmethod was employed to prove the transient PDF of the controlled system do converge toSPDF. Finally, system simulation shows effective control results under the proposed control strategy, i. e. the output transient probability density of tiie system will approach the target SPDF in a short time.