Large welding robots are used in today's auto plants. The welding head is moved to different positions on the auto body, and a rapid, accurate response is required. A block diagram of a welding head positioning system is shown in Figure for Q.3. Determine the range of K and a for which the system is stable using the Routh-Hurwitz criterion. A system has a characteristic equation K(s + a) s (s + 1)(s + 2)(s + 3) 1+ G(s) = 1+ Controller Head dynamics Rts) Y(s) K(s + a) s+ 1 Desired Data head s(s + 2)(s + 3) position position Figure for Q. 3