P7.36 A microrobot with a high-performance manipula

tor has been designed for testing very small particles, such as simple living cells [6]. The unity feedback sys

tem 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 = 50 and K = 100.

(d) For K = 50, esti

mate the percent overshoot to a step input, and com

pare the estimate to the actual percent overshoot.

L(s) =G(s)G(s) = K(s+5)(s+10) s (s+2)(8-8)