具有边界扰动的不确定Euler-Bernoulli梁方程输出反馈控制

针对带有边界扰动、内部不确定扰动和外部扰动的Euler-Bernoulli梁方程,为克服传统扰动观测器引入的高增益及未知扰动导数难以准确求解问题,本文将主动干扰抑制控制(ADRC)技术应用到Euler-Bernoulli梁方程这个偏微分方程(PDE)系统上,提出并设计了一种新的在线扰动观测器,可实时估计扰动值.依据估计扰动值,设计了一个边界输出反馈控制器.仿真结果表明,本文所提出的方法可很好地实现对内部不确定扰动和外部扰动的估计,配合输出反馈控制器,可对边界扰动进行有效抑制,进而实现系统的指数稳定.

Output feedback control for an uncertain Euler-Bernoulli beam equation with boundary disturbances

For the Euler-Bernoulli beam equation which involves boundary disturbances, internal uncertainties, and external disturbances, the high gain and difficult-to-accurately-solve unknown disturbance derivative problems introduced by traditional perturbation observers need to be overcome. In this paper, active disturbance rejection control (ADRC) technology is applied to the Euler-Bernoulli beam equation, a partial differential equation (PDE) system. A new online disturbance observer is proposed and designed, which can estimate the disturbance values in real-time. Based on the estimated disturbance values, a boundary output feedback controller is designed. The simulation results show that the proposed method can achieve the estimation of internal uncertainty and external disturbance well, and the effective rejection of the boundary disturbance can be achieved with the output feedback controller, and then the exponential stability of the system can be achieved.