边界控制输入含外部干扰的Euler-Bernoulli梁方程的输出反馈镇定研究

In order to make the closed-loop system stable, this project is to design a boundary output feedback controller, based on observer, to Euler-Bernoulli beam which has general external disturbance in boundary input. The output signals are boundary point ones, that is, the system we considered is point measured/point controlled. In infinite-dimensional system, observer itself is an independent research area. When there are disturbances in such systems and only finite point signals are measureble, the observers have significant meanings in both theory and practice. Because of disturbance, proportional output feedback controller based on passive principal is not effective, new one must be redesigned. To deal with disturbance, roughly speaking, there are two methods: estimate/cancel and high gain. Active disturbance redjection control(ADRC) and sliding mode control(SMC) are typical representatives respectively. ADRC has many successful applications in finite-dimensional systems and is an economic control strategy in that we suffer from energy shortage nowadays. SMC has high gain which make the disturbance relative small. In this project, we will design output feedback controller to stabilize the Euler-Bernoulli beam equation via both methods.

本项目旨在对边界控制输入含有一般外部干扰的Euler-Bernoullii梁设计基于观测器的边界输出反馈控制器，使得闭环系统稳定。量测信号同样是边界点信号，即此系统是点观测点控制。对于无穷维系统，观测器本身就是一个研究方向。尤其对于含有干扰的无穷维系统，用有限个边界点信号来估计出原系统的全部状态，使得观测器不论在理论上还是实际应用中都有着重要的意义。由于干扰的存在，以前的基于无源性原理的比例输出反馈控制器一般情况下不再适用，新的控制器必须重新设计。对付干扰的方法大致可以分为两种：估计抵消和高增益压制。自抗扰控制和滑模控制就分别是两种策略的典型代表。自抗扰控制方法在有限维系统中取得大量的成功的工程应用，尤其是在现今要求节能减排的大环境下，是一种非常经济的控制方法。而滑模控制要求控制增益特别大，从而使得扰动对于增益来说相对小来达到压制的效果。本项目分别用这两种方法设计输出反馈控制器镇定系统。

对于边界含有一般外界干扰的Euler-Bernoulli梁，我们直接设计了输出反馈控制器，并没有用到观测器，从而成功完成本项目。相关的结果已经发表在国际杂志上:.F.F.Jin and B.Z.Guo, Lyapunov approach to output feedback stabilization for Euler-Bernoulli beam equation with boundary input disturbance, Automatica, 52(2015), 95-102.