Discrete-time realization of transcendental impedance models, with application to modeling spherical solid diffusion

This paper introduces the “discrete-time realization algorithm” (DRA) as a method to find a reduced-order, discrete-time realization of an infinite-order distributed-parameter system such as a transcendental impedance function. In contrast to other methods, the DRA is a bounded-time deterministic method that produces globally optimal reduced-order models. In the DRA we use the sample and hold framework along with the inverse discrete Fourier transform to closely approximate the discrete-time impulse response. Next, the Ho–Kalman algorithm is used to produce a state-space realization from this discrete-time impulse response. Two examples are presented to demonstrate the DRA using low-order rational-polynomial transfer functions, where the DRA solution can be compared to known solutions. A third example demonstrates the DRA with a transcendental impedance function model of lithium diffusion in the solid phase of a lithium-ion battery, showing that a third-order discrete-time model can closely approximate this infinite-order model behavior.

► In this paper, we present the discrete-time realization algorithm (DRA).
► The DRA can find a reduced-order realization of a transcendental impedance function.
► It is based on estimating the impulse response and then using the Ho–Kalman algorithm.
► Three examples are given, including that of lithium diffusion in a solid particle.
► The third-order DRA-produced model closely approximates these infinite-order phenomena.