基于伪谱展开的抛物型系统镇定与边界观测研究(英文)

Pseudospectral expansion-based model reduction for control and boundary observation of unstable parabolic partial differential equations

中文关键词  截断再设计  设计再截断  伪谱展开  抛物型偏微分方程

英文关键词  reduce-then-design  design-then-reduce  pseudospectral expansion  parabolic PDEs

中文摘要

      模型截断设计方法在无限维系统控制中得到广泛的应用, 但是其自身存在信息丢失的缺陷而限制了控制器对高频扰动抑制的性能. 本文研究具有内部和Neumann边界控制的抛物型系统, 其中系统采用边界测量. 内部控制采用比例反馈形式, 其中反馈增益核由Sturm-Liouville系统稳定性分析来待定; 类似地, 边界反馈的设计也采用待定反馈增益核的方式, 最终对描述系统稳定性的Sturm-Liouville系统采用伪谱方法进行求解. 数字仿真结果表明了该方法的有效性.

英文摘要

      The reduce-then-design approach is widely used for controller synthesis of infinite dimensional systems. A drawback of the reduce-then-design method is the inherent loss of information due to the truncation before control design. Moreover, the order of the model truncation is a trade-off between model accuracy and real time computation. The stabilization of an unstable linear parabolic partial differential equation (PDE) system with both Neumann boundary control and interior control is considered in this work. Point output measurement is available at one end of the physical domain. A proportional state feedback is proposed for the interior control with a symmetric kernel function, and the pseudospectral method is used to solve the stability conditions governed by the Sturm-Liouville systems. In addition, an observer is designed using the point measurement at one end of the physical domain, and used to propose an observer–based feedback controller for the PDE system. Both controller and observer gains are designed numerically to make the eigenvalues of the associated Sturm-Liouville problems stable. Simulations show the effectiveness of the proposed controller.