Summary form only given. A pacemaker-cardiovascular system sets a reference venous oxygen saturation level as the input and cardiovascular venous oxygen saturation as the output. The error drives the pacemaker with gain to regulate the heart rate. Cardiac output is obtained as a function of heart rate and the work load (using the Frank-Starling mechanism). The oxygen supplied by the blood is consumed due to normal activity and performance of the work load. The net oxygen saturation in the venous blood gives the system output. In the forward-loop of the model, the term (1/cardiac output) was linearized using a Taylor-series expansion, about the steady-state level. An average time delay (=82.5/cardiac output) was also calculated on the basis of the steady-state heart rate. The closed-loop pole locations can be obtained from the open-loop transfer function using the root-locus technique. A root locus program which allows for a time delay in the forward loop was used to plot the closed-loop pole locations of the linearized pacemaker-cardiovascular system as a function of controller gain.
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