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Control in H2/Hinf space via Computer Algebra
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| Organization: | Budapest University of Technology and Economics |
| Department: | Photogrammetry and Geoinformatics |
| Organization: | Technical University Budapest, Hungary |
| Department: | Control Engineering and Information Technology |
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2006-11-14
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This article presents the H2/Hinf control (disturbance rejection LQ method) of the Bergman minimal model, [10] for Type I diabetic patients under intensive care using computer algebra. To design the optimal controller, the disturbance rejection LQ method based on the minimax differential game is applied. The critical, minimax value of the scaling parameter γcrit is determined by using the Modified Riccati Control Algebraic (MCARE) equation employing reduced Groebner basis solution on rational field. The numerical results are in good agreement with those of the Control Toolbox of MATLAB. It turned out, that in order to get positive definite solution stabilizing the closed loop, γ should be greater than γcrit. The obtained results are compared with the classical LQ technique on the original non-linear system, using a standard meal disturbance situation. It is also demonstrated that for γ >> γcrit, the gain matrix approaches the traditional LQ optimal control design solution. The symbolic and numerical computations were carried out with Mathematica 5.2, and with the CSPS Application 2, as well as with MATLAB 6.5.
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disturbance rejection LQ control, LQ control, glucose-insulin control, diabetes mellitus, symbolic computations
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| MIC_122602906.nb (470.1 KB) - Mathematica Notebook |
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