Abstract
Modeling and control of diabetes mellitus (DM) are difficult due to the highly nonlinear attitude, time-delay effects, the impulse kind input signals and the lack of continuously available blood glucose (BG) level to be regulated. Regarding the mentioned problems, identification of DM model is crucial. Furthermore, due to the lack of information about the internal states (which cannot be measured in everyday life) and because the BG level is not available in every moment over time, adaptive robust control design method regardless exact model dependency would successfully handle these unfavorable effects without simplifications. The recently developed nonlinear robust fixed point transformation (RFPT)-based controller design method requires only a roughly approximate model in order to realize the controller structure. Moreover, parallel simulated approximate models—in order to provide additional internal information—can be used with the method. In this paper, the usability of the novel RFPT-based technique is demonstrated on the physiological problem of diabetes.
Highlights
The concept of modern control technology, under the name “Theory of Governors,” originates from a paper by Maxwell [25], in which, without entering into any details of the particular mechanisms that were known at that time, he directed the attention of engineers and mathematicians to a more general dynamical theory
In this great flourishment of linear control technology, the use of, and thinking on the basis of the frequency picture became prevailing. This general attitude lasted till the beginning of 1960s when, according to [19], Rudolf Kalman “...challenged the accepted approach to control theory of that period, limited to the use of Laplace transforms and the frequency domain, by showing that the basic control problems could be studied effectively through the notion of the state of the system that evolves in time according to ordinary differential equations in which control appears as parameters. ...Liberated from the confines of the frequency domain and further inspired by the development of computers, automatic control theory became the subject matter of a new science called systems theory.”
The primary goal of this study was to prove the usability of the robust fixed point transformation (RFPT)-based controller design opportunity in case of the Type 1 DM (T1DM) model created in order to ease the identification procedures
Summary
The concept of modern control technology, under the name “Theory of Governors,” originates from a paper by Maxwell [25], in which, without entering into any details of the particular mechanisms that were known at that time, he directed the attention of engineers and mathematicians to a more general dynamical theory Following his fundamental achievements in the description of the electrical and magnetic phenomena [26], by the use of the elementary circuit components as resistors, capacitors and inductances as linear timeinvariant (LTI) elements, in the field of electrical engineering rapid development was produced that intensively utilized the mathematical achievements of the nineteenth century as the analysis of complex numbers, Laplace, Z, Fourier, Mellin and other transforms [6]. The combination of nonlinearity and fractional order dynamics became an interesting research area [2,38]
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