Robust control techniques and its graphical representation in case of Type I diabetes using Mathematica

Abstract

The case study presents modern robust control methods of the Bergman minimal model of Type I diabetic patients under intensive care using computer algebra: the disturbance rejection LQ control or minimax control (as extension of the classical LQ control) and the robust H¿ control. It is shown the minimax control has limitations in practice, but employing reduced Gro¿bner basis on rational field, it is possible to approximate the theoretical solution and so getting a better solution than LQ does. The symbolic and numeric computations were carried out with Mathematica 5.2 and with its CSPS Application, as well as with MATLAB 6.5. In case of H¿ control, the graphical method in frequency domain- implemented under Mathematica by-is extended with a disturbance rejection constraint and the robustness of the resulted highorder linear controller is demonstrated by nonlinear closed loop simulation in state-space, in case of standard meal disturbances.