Diffusion systems: stability, modeling, and identification

Physical phenomena governed by diffusion (for example, mass or heat transfer) are often better described by rational transfer function models G(√s) in √s than by rational forms G(s) in the Laplace variable s. A striking difference between both models is that the impulse response of G(s) decreases exponentially to zero, while that of G(√s) decreases algebraically to zero. Hence, transient effects in diffusion phenomena may last long before they can be neglected in, for example, frequency response function measurements. This paper presents an extended transfer function model and an identification algorithm that can handle the slowly decaying transients and, as a consequence, (significantly) reduce the experiment time.