open-loop digital controller for the glucoregulatory system by insulin therapy

ABSTRACT

Based on a fourth order digital model of the experimentally validated gluccregulatory system derived from the state differential equations which represent the system metabolism, a proportional-integral- derivative controller was achieved, that restores and maintains the normal glucose concentration in the human subject. The controller uses as a reference, a ramp function followed by step input, to overcome the large peak undershoot of the conditionally stable metabolic system. The control strategy was to optimize the controller parameters and the switching time [time at which the reference switches] simultaneously, such that, dynamics which are comparatively fast with small undamped terms are achieved. The controller parameters are determined from the solution of a set of linear simultaneous equations, based on a partial pole placement technique. Three sets of well behaved responses and internal states were obtained with variable peak undershoot. The robustness property of the controller was measured using the bounding polynomials suggested by Kharitonov's stability criterion