Adaptive PI Parameter Identification and Synchronous Control of Heat Equations Modeled Multi-Agent Systems

This paper addresses the temperature synchronization control challenge in a thermal pipeline system, which is modeled using a networked heat equation. Leveraging adaptive and PID control methodologies, an adaptive PI synchronization consensus protocol is formulated. This protocol generates a target tracking signal for the temperature output of each pipeline, thereby steering the temperature output of the pipelines accordingly. In response to the output tracking error, a synchronization controller and an infinite-dimensional observer are designed to counteract external disturbances and attain output synchronization of the system temperature. Simulation outcomes substantiate the efficacy of the proposed controller. Note to Practitioners—This study centers on the high-temperature sterilization process employed in industrial production. Throughout the heating phase, a uniform heat source supplies an identical quantity of heat. Given that the initial temperatures of individual sterilization units vary, once heating stabilizes after a certain duration, the final temperatures of these units also differ. This discrepancy results in issues such as heat wastage and suboptimal sterilization outcomes. Consequently, this study proposes the implementation of a synchronous controller based on an adaptive PI-form synchronous consensus protocol.