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

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.