Application of the root locus technique to the closed-loop SO2 pacemaker-cardiovascular system.

Abstract

A previously developed nonlinear model of the pacemaker-cardiovascular system contained a term of the form 1/CO in the forward loop. CO, the cardiac output, is a linear function of heart rate and exercise level. To evaluate the dynamic behavior of the system over a range of pacemaker controller gains, a piecewise linear model was developed. The model was linearized by taking the first two terms of the Taylor's series expansion of 1/CO about the steady state heart rate. A root locus algorithm, with the unique feature of a time delay element in the forward loop, was used to calculate the linear model closed-loop poles as a function of pacemaker controller gain for exercise levels of 25, 50, and 100 W. Step response simulation of the complete nonlinear model showed dynamics close to that predicted from the pole location in the root locus plot. Thus, the root locus technique can be used to quantify systematically the dynamics of the pacemaker-cardiovascular system for different exercise levels and over a wide range of controller gain values.