Frequency domain hammerstein model of glucose-insulin process in IDDM patient

Abstract

This paper deals with a frequency domain kernel estimation problem for modeling a nonlinear dynamic system of multivariable glucose-insulin process in an insulin dependent diabetes mellitus (IDDM) patient. For such a process with uncertainties and parameter variations, the nonparametric models are most useful for closed loop model predictive control. The present work proposes a frequency domain kernel estimation of a Hammerstein model using the harmonic excitation input by taking FFT on the input data sequence from the glucose-insulin process of IDDM patient model. For the multivariable system, the first block is a two-input single output nonlinear block followed by a SISO linear filter. The adaptive recursive least square (ARLS) algorithm is used to solve up to second order kernels of Volterra equations with extended input vector consisting of self and cross components. Twice the length of the extended input vector for the MISO system was considered for finding the kernels and the output in frequency domain. The input-output data taken from the first principle model of nonlinear process, have been used to identify the system with a short filter memory length of M=2 and the validation results have shown good fit both in frequency and time domain responses.

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“…Thus, frequency domain kernels have been computed by taking fast Fourier transforms (FFTs) on the time domain kernels for a specific length of extended input vector. The set of kernels G (1) ( f ), G (2) ( f 1 , f 2 ) obtained from the frequency domain Volterra model describes the nonlinear transfer function or the VTF [36].…”