The effect of continuum model on the stability of feedback control of thermal systems

In this paper, we study the stability of a thermal system with feedback control in which the sensor is modeled by a partial differential equation. The problem is motivated by the thermal management requirement in energy systems such as lithium ion batteries where the heating information must pass through a finite distance through conduction. The focus of this paper is to examine the stability issue of the feedback control system when different modeling methods are used for the heat conduction process. Two models are investigated: the commonly used lumped-parameter model and a more realistic distributed-parameter model. It is shown that the lumped-parameter model is stable with arbitrary feedback gains, whereas the distributed-parameter model exhibits instability when the feedback gains exceed the critical values. The instabilities exhibit as Hopf bifurcations. The closed-loop system is simulated using a finite difference method. We conclude that care must be taken in modeling the sensor to avoid controller instability.