Abstract State estimation is an important problem in distributed parameter system especially with nonlinear dynamics in industrial process. An extended Luenberger observer based on the eigen-spectrum of the system operator is developed in this paper to handle this problem. The distributed parameter system is projected into a finite-dimensional subspace where a low-order ordinary differential equation describing the dominant dynamics of the system is derived. A Luenberger observer extended with a nonlinear part is developed based on that dominant dynamics. A sufficient condition is given in this paper for the convergence of the estimated error. Finally, by applying the developed design method to the temperature estimation of a catalytic rod, the achieved simulation results show the effectiveness of the proposed observer.

中文翻译：

---

一类分布式参数系统的基于特征谱的扩展 Luenberger 观测器

摘要 状态估计是分布式参数系统中的一个重要问题，尤其是工业过程中的非线性动力学问题。本文开发了一种基于系统算子本征谱的扩展 Luenberger 观测器来处理这个问题。分布参数系统被投影到一个有限维子空间中，在该空间中可以导出描述系统主要动力学的低阶常微分方程。基于该主要动力学开发了带有非线性部分的 Luenberger 观测器。本文给出了估计误差收敛的充分条件。最后，通过将开发的设计方法应用于催化棒的温度估计，所获得的模拟结果表明了所提出的观测器的有效性。