A simplified block diagram of a human pupil servomechanism is shown in Figure P8.16. The term e -0.18s represents a time delay. This function can be approximated by what is known as a Padé approximation. This approximation can take on many increasingly complicated forms, depending upon the degree of accuracy required. If we use the Padé approximation
then
Since the retinal light flux is a function of the opening of the iris, oscillations in the amount of retinal light flux imply oscillations of the iris (Guy, 1976). Find the following:
a. The value of K that will yield oscillations
b. The frequency of these oscillations
c. The settling time for the iris if K is such that the eye is operating with 20% overshoot
