Problem 2 [25 marks] R(s) + E(s) U(s) Y(s) C(s) P(s) Figure 2: A closed-loop control system. Consider the closed-loop control system shown in Figure 2. Let the plant be given by P(s) and the controller be given by C(s) = k(2+), where the gain k is non-negative, k 0. a) State what kind of controller C(s) is and briefly state one simple advantage of such a controller. [5 Marks] b) Determine the characteristic equation of the control system in terms of k. [5 Marks] c) Find the damping ratio (5) of the closed-loop system if k is 1. [5 Marks] d) Find the range of k such that the poles of the closed-loop system are both real. [10 Marks]