Fruit flies’ flight dynamics are interesting to study because they provide a proof-of-concept framework and inspiration for the invention of man-made machines. In an experiment (Roth, 2012), flies are stimulated to follow, in flight, an oscillating vertical bar. Through frequency response measurements, the obtained open loop transfer function from stimulus stripe position to a voltage proportional to wingbeat amplitudes is

Assume a unit feedback system.

a. Make a Bode plot of the open-loop transfer function.

b. Find the gain and phase margins.

c. Use a computer program to make a plot of the corresponding Nyquist diagram.

d. Use the result in Part b to find the range of K for closed-loop stability if the open-loop transfer function becomes KG(s).

0.181s? + 1.23s +8.68 G(s) = e-0032s s3 + 20.6s2 + 277s + 1098