前馈反馈控制对保持系统稳定性的研究

Feedforward and feedback control approach to the stabilization of system

为了证明前馈反馈控制策略在保持带扰动系统稳定性的可行性,以带有扰动的Euler-Bernoulli方程为例,通过设计同时带有前馈控制和反馈控制的控制策略,使系统保持稳定。首先,设置了一个高增益评估器来估计扰动。然后使用前馈控制u1(t)=-r(t)来减弱扰动对欧拉梁系统稳定性的影响。其次,使用反馈控制u_2(t)=kw_t(1,t)使系统保持稳定,并使用乘子法证明系统的稳定性。

In order to study the effective of the feedback and feedforward strategy, we consider the stabilization of a one-dimension Euler-Bernoulli beam with unknown disturbance at the control end. Firstly, one high-gain estimator is designed to detect the disturbance. The feedforward control u（t） = -r（t） is given based on the estimator. Secondly, we utilize the feedback control u（t） = - kw, （l, t） to make the system stable. The Lyapunov function method is used to prove the stability of the system.