Modeling and Control of a Flexible Electric Resistance Heater Coupled to a Steel Plate

Polyimide films have unique characteristics and are used to build versatile and resistant heaters that are adequate for applications in diverse areas. Their flexibility allows them to take multiple shapes but may result in intricate mathematical modeling. In this paper, a heater with flexible resistance coupled to a steel plate is modeled and compared with empirical measurements. The theoretical analysis of the system's behavior begins with determining differential equations from the energy balance. The resulting non-linear systems are submitted to a linearization process at an operating point. Transfer functions are obtained from linearized differential equations. In the experimental section, a power step is applied to the flexible resistance to plot the output temperature in a graph, where the heater's empirical parameters are identified. Theoretical and practical values are compared, proving the assertiveness of the models. Finally, a control system is projected and tested to demonstrate a practical application.