Complex-order PID controller design for enhanced blood-glucose regulation in Type-I diabetes patients

Abstract

Type-I Diabetes (TID) is a chronic autoimmune disease that elevates the glucose levels in the patient’s bloodstream. This paper formulates a fractional complex-order Proportional-Integral-Derivative (PID) control strategy for robust Blood Glucose (BG) regulation in TID patients. The glucose-insulin dynamics in blood plasma are modeled via the Bergman-Minimal-Model. The proposed control procedure employs the ubiquitous fractional order PID controller as the baseline BG regulator. The design flexibility of the baseline regulator to effectively normalize the BG levels is enhanced by assigning complex orders to the integral and differential operators instead. The resulting Complex Order PID (CO-PID) regulator strengthens the controller’s robustness against abrupt variations in the patient’s BG levels caused by meal disturbances or sensor noise. The controller parameters are numerically optimized offline. The aforesaid propositions are justified by performing credible simulations in which the proposed controller is tasked to effectively track a set point value of 80 mg/dL from an initial state of hyperglycemia under various disturbance factors. As compared to the FO-PID controller, the CO-PID controller improves the reference tracking-error, transient recovery-time, and control expenditure by 13.1%, 33.4%, and 28.1%, respectively. The simulation results validate the superior reference-tracking accuracy of the proposed CO-PID controller for BG regulation.