A micro robot with a high-performance manipulator has been designed for testing very small particles, such as simple living cells [6]. The single-loop unity negative feedback system has a loop transfer function

(a) Sketch the root locus for K > 0.
(b) Find the gain and roots when the characteristic equation has two imaginary roots.
(c) Determine the characteristic roots when K = 20 and K = 100.
(d) For K = 20, estimate the percent overshoot to a step input, and compare the estimate to the actual overshoot determined from a computer program.

LG)- GASGs)- Ks +)+20s + 3) s(s - 1)