Closed-loop Proportional-Integral Control of Physiological Systems

This work presents a general methodology to de sign Proportional-Integral (PI) controllers for negative feedback physiological control systems (NFPCS). It is shown that the resulting closed-loop system preserves the NFPCS structure and admits a unique equilibrium point. A local linearization around the equilibrium is then employed to derive general gains selection criteria guaranteeing closed-loop stability and convergence to the healthy physiological state. The proposed methodology is validated on the insulin-glucose regulatory system, where the proposed PI controller is able to drive the system back to the desired physiological equilibrium after a perturbation, achieving zero steady-state error.