An artificial heart works in closed loop by varying its pumping rate according to changes in signals from the recipient's nervous system. For feedback compensation design it is important to know the heart's open-loop transfer function.
To identify this transfer function, an artificial heart is implanted in a calf while the main parts of the original heart are left in place.
Then the atrial pumping rate in the original heart is measured while step input changes are effected on the artificial heart.
It has been found that, in general, the obtained response closely resembles that of a second-order system.
In one such experiment it was found that the step response has a %OS=30% and a time of first peak Tp = 127 sec (Nakamura, 2002).
Find the corresponding transfer function.