Robust Blood-Glucose Control of Type I Diabetes Patients Under Intensive Care Using Mathematica

This article presents a robust control design method on frequency domain using Mathematica for regularization of glucose level in Type I diabetes persons under intensive care. The method originally proposed under Mathematica by Helton and Merino (1998) is now improved with a disturbance rejection constraint inequality, and is tested on the three-state minimal model. Nonlinear closed loop simulation in state-space, in case of standard meal disturbances, demonstrates the robustness of the resulted high-order linear controller. The obtained results are compared with H∞ design implemented with Matlab, proving that the controller (for the considered model parameters) can operate properly, even in case of parameter values of the worst-case scenario. The blood-glucose control is one of the most difficult control problems to be solved in biomedical engineering. The main reason is that patients are extremely diverse in their dynamics and, in addition, their characteristics are time-varying. The investigations of Hernjak and Doyle (2005) discourage the use of a low complexity control such as PID, if high level of performance is desired. To design an optimal, high-quality control, one needs a relevant model of the process, as well as a proper control technique. There are several studies in both areas (Parker, Doyle, & Peppas, 2001). The mostly used model, and also the simplest one, proved to be the minimal model of Bergman, Philips, and Cobelli (1981), but its shortcoming is its big sensitivity to variance in the parameters. Henceforward, the plasma insulin concentration must be known as a function of time. Therefore, extensions of this minimal model have been proposed (e.g., de Gaetano and Arino (2000) analyzed the different models of glucose-insulin interactions in human body). Also, more general models have been used in the literature, like the model developed by Hovorka, Shojaee-Moradie, Carroll, Chassin, Gowrie, Jackson, Tudor, Umpleby, and Jones (2002), or the 21st order nonlinear model of Sorensen (1985). However, probably the best way to approach the problem of blood-glucose control is to consider the system model and the applied control technique together (Makroglou, Li, & Kuang, 2006; Parker et al., 2001). As models of diabetic systems are imprecise by nature, some research works are concentrated on adaptive control techniques using online parameter estimation (e.g., Lin, Chase, Shaw, Doran, Hann, Robertson, Browne, Lotz, Wake, & Broughton, 2004), others like Ruiz-Velazquez, Femat, and Campos-Delgado (2004) or Parker, Doyle, Ward, and Peppas (2000) suggest robust control design. This study focuses on robust control design, for regulating glucose level in Type I diabetes patients under intensive care. The investigations were done using the minimal patient model of Bergman et al. (1981). The method applied using Mathematica lays on a different approach by that under Matlab. The corresponding Mathematica program package OPTDesign was originally developed by Helton and Merino (1998). The technique of the computations and closed loop simulations, employing the Mathematica Application, Control System Professional Suite (CSPS), together with OPTDesign, has been already demonstrated by Palancz (2006). Béla Paláncz Budapest University of Technology and Economics, Hungary