Petrus Bryan, Chen Zhelin, El-Kebir Hamza, Bentsman Joseph, Thomas Brian G
University of Illinois Urbana-Champaign, Champaign, IL 61801 USA. He is now with Nucor Steel Decatur, Decatur, AL 35673 USA.
University of Illinois Urbana-Champaign, Champaign, IL 61801 USA.
IEEE Trans Automat Contr. 2023 Jun;68(6):3485-3500. doi: 10.1109/tac.2022.3197704. Epub 2022 Aug 9.
By taking enthalpy-an internal energy of a diffusion-type system-as the system state and expressing it in terms of the temperature profile and the phase-change interface position, the output feedback boundary control laws for a fundamentally nonlinear single-phase one-dimensional (1-D) PDE process model with moving boundaries, referred to as the Stefan problem, are developed. The control objective is tracking of the spatiotemporal temperature and temporal interface (solidification front) trajectory generated by the reference model. The external boundaries through which temperature sensing and heat flux actuation are performed are assumed to be solid. First, a full-state single-sided tracking feedback controller is presented. Then, an observer is proposed and proven to provide a stable full-state reconstruction. Finally, by combining a full-state controller with an observer, the output feedback trajectory tracking control laws are presented and the closed-loop convergence of the temperature and the interface errors proven for the single-sided and the two-sided Stefan problems. Simulation shows the exponential-like trajectory convergence attained by the implementable smooth bounded control signals.
通过将扩散型系统的焓（一种内能）作为系统状态，并根据温度分布和相变界面位置来表示它，针对具有移动边界的基本非线性单相一维（1 - D）偏微分方程过程模型（称为斯蒂芬问题），开发了输出反馈边界控制律。控制目标是跟踪参考模型生成的时空温度和时间界面（凝固前沿）轨迹。假设进行温度传感和热通量驱动的外部边界是固体。首先，提出了一种全状态单边跟踪反馈控制器。然后，提出并证明了一个观测器可提供稳定的全状态重构。最后，通过将全状态控制器与观测器相结合，给出了输出反馈轨迹跟踪控制律，并证明了单边和双边斯蒂芬问题中温度和界面误差的闭环收敛性。仿真表明，可实现的平滑有界控制信号实现了指数型轨迹收敛。
