Robots can be used in manufacturing and assembly operations that require accurate, fast, and versatile manipulation [10, 11]. The open-loop transfer function of a direct-drive arm may be approximated by
G(s)H(s) = K(s + 10) / s(s + 3)(s2 + 4s + 8).
(a) Determine the value of gain K when the system oscillates.
(b) Calculate the roots of the closed-loop system for the K determined in part (a).