论文标题
1-D半线性波方程的PI调节控制
PI regulation control of a 1-D semilinear wave equation
论文作者
论文摘要
本文涉及一维半线性波方程的左NEU-MANN轨迹的比例积分（PI）调节。对控件输入选择为右Neumann Trace。控制设计如下。首先，采用初步（经典）速度反馈，以将基础无界操作员的所有eIvenValues除了所有有限数量的左侧半平面。然后，我们将系统轨迹的投影投影到足够的riesz基础上，以获得捕获其余不稳定模式的系统的截断模型。由半线性波方程，初步速度反馈和PI控制器组成的所得闭环无限二维系统的局部稳定性是通过研究适当的Lyapunov函数获得的。最后，得出了评估左Neumann Trace的设定点跟踪性能的估计值。
This paper is concerned with the Proportional Integral (PI) regulation control of the left Neu-mann trace of a one-dimensional semilinear wave equation. The control input is selected as the right Neumann trace. The control design goes as follows. First, a preliminary (classical) velocity feedback is applied in order to shift all but a finite number of the eivenvalues of the underlying unbounded operator into the open left half-plane. We then leverage on the projection of the system trajectories into an adequate Riesz basis to obtain a truncated model of the system capturing the remaining unstable modes. Local stability of the resulting closed-loop infinite-dimensional system composed of the semilinear wave equation, the preliminary velocity feedback, and the PI controller, is obtained through the study of an adequate Lyapunov function. Finally, an estimate assessing the set point tracking performance of the left Neumann trace is derived.
