A control system has G_v = G_m = 1 and a second-order process G_p with K_p = 2, τ₁ = 4 min, and τ₂ = 1 min, which is to be controlled by a PI controller with K_c = 2 and τ_I = τ₁ = 4 min (i.e., the integral time of the controller is set equal to the dominant time constant). For a set-point change

(a) Determine the closed-loop transfer function.
(b) Derive the characteristic equation, which is a quadratic polynomial ins. Is it over damped or under damped?
(c) Can a large value of K_c make the closed-loop process unstable?