Robust IMC-PID and Parameter-varying Control Strategies for Automated Blood Pressure Regulation

Abstract

The present work focuses on comparing a robust and a parameter-varying control design approach for automatically regulating blood pressure in critical hypotensive patients using vasopressor drug infusion. Mean arterial pressure (MAP) response of a patient subject to vasoactive drugs is modeled by a first-order dynamical system with time-varying parameters and a time-varying delay in the control input which limits the implementation of conventional control techniques. Two methods are examined to address the variability and the time-varying delay of the physiological response to the drug. First, a Pade approximation is used to transform the infinite-dimensional delay problem into a finite-dimensional model represented in the form of a non-minimum phase (NMP) system. A systematic parameter-varying loop-shaping control is proposed to provide the closed-loop system with stability and tracking performance in the presence of measurement noise and disturbances. Second, an internal model control (IMC) strategy is examined to design a fixed proportional-integral-derivative (PID) controller cascaded with a lag compensator by considering the time-varying model to be a perturbed uncertain system. To account for system uncertainty, the small-gain theorem is employed by which robust stability conditions are investigated. The proposed control methods are applied to critical hypotensive patient resuscitation to regulate MAP while considering the limitations posed by the time-varying parameters of the physiological response model and the large time-varying delay. Simulation results are provided and compared to evaluate the performance of the proposed control actions under various hypotensive scenarios.