Please answer all step by step (from C to G)

Given a plant with the transfer function G(s) Kg (s + 2)(s + a) (c) Having in mind the PID controller and its variants, if the damping of the closed-loop system needs to be improved, please suggest which variant should be applied to this system. [2 marks] (d) Draw the block diagram of the closed-loop system with the plant G(s) and the controller you choose in (c). [2 marks] (e) For Kg = 1 and a = 1, transforming the transfer function G(s) into a state-space model gives the state equation X Check the controllability of this state-space model. [3 marks) (1) In order to reduce the settling time of the system (e) in closed-loop, design a state feedback controller u = -Kx (find the feedback gain K), such that the closed-loop poles are at $1,2 = -4 [5 marks) (g) Draw the block diagram of the closed-loop system with the plant (e) and the feedback controller (f). [3 marks