The Implementation of Optimal Control for Thermal Regulation in Finite Volume Spaces Described by Second-Order Dynamics

Abstract

Temperature control systems have various applications, from cooling to casting, and are crucial for ensuring quality in production. Although essential, their usage entails a significant energy consumption. This project focuses on implementing optimal control synthesized from the calculus of variations applied to the Hamilton-Jacobi-Bellman equation to regulate temperature within a finite volume space. The objective is to enhance thermal efficiency without compromising product quality. The approach not only aims to optimize energy consumption but also to ensure uniformity and quality in products and processes affected by temperature. This can be achieved by maintaining thermal stability at desired values and responsible resource management. In general, the article proposes improving efficiency and quality in temperature regulation, contributing to sustainable and effective industrial practices.