This article proposes a novel control algorithm of a thermal phase-change process and shows its experimental verification using paraffin as a phase-change material (PCM). The core problem is to design a boundary feedback control for the “Stefan system” that describes the time evolution of the temperature profile in the liquid phase, which is associated with the time evolution of a position of liquid–solid phase interface, for the sake of stabilizing the interface position at a chosen set point. First, we design the continuous-time full-state feedback control law by means of the PDE backstepping method, which, in the absence of a demand for accelerated convergence, can also be arrived at by the energy-shaping method, and rigorously prove the stability of the closed-loop system under sufficiently small heat loss. Next, the control law is refined via observer-based output feedback under sampled-data measurements of the surface temperature and the phase interface position so that the control algorithm is practically implementable. Then, we conducted an experiment under a constant input to calibrate unknown parameters involved with the heat loss. Finally, the proposed model-based boundary feedback control algorithm is implemented in the experiment of melting paraffin. The experiment was successful: the convergence of the phase interface to the set point was achieved.

中文翻译：

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石蜡中的能量存储：PDE 反推实验

本文提出了一种新的热相变过程控制算法，并展示了使用石蜡作为相变材料 (PCM) 的实验验证。核心问题是为“Stefan 系统”设计一个边界反馈控制，该系统描述液相中温度分布的时间演化，这与液固相界面位置的时间演化相关联，以便将界面位置稳定在选定的设定点。首先，我们通过 PDE 反步法设计了连续时间全状态反馈控制律，在没有加速收敛要求的情况下，也可以通过能量整形方法来达到，并严格证明在足够小的热损失下闭环系统的稳定性。下一个，在表面温度和相界面位置的采样数据测量下，通过基于观测器的输出反馈来改进控制律，从而使控制算法具有实际可实现性。然后，我们在恒定输入下进行了实验，以校准与热损失有关的未知参数。最后，将所提出的基于模型的边界反馈控制算法用于熔炼石蜡的实验。实验成功：实现了相位界面与设定点的收敛。最后，将所提出的基于模型的边界反馈控制算法用于熔炼石蜡的实验。实验成功：实现了相位界面与设定点的收敛。最后，将所提出的基于模型的边界反馈控制算法用于熔炼石蜡的实验。实验成功：实现了相位界面与设定点的收敛。