Problem 1: Routh-Hurwitz stability criterion 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 below. R(s) Desired Position K(s+a) s+1 1 s(s+2)(s+3) C(s) Data head Position Controller Head dynamics Determine 1) the range of K and 2) the relationship between K and a for which the system is stable.