Question 4 The block diagram of a feedback control system shown in Figure 2 has been suggested to control a system modelled by a first order plus dead-fime transfer function, Figure 2. A proposed feedback control strategy, incorporating an additional feedback loop and the transfer function (1ex)G(s). The process transfer function is given by, ap(s)=ps+11ex=G(s)ez In addition, Gc(a) is the fransfer function of the feedback controller, R(s), the set-point, u(s), the manipulated variable and y(s) the output that is to be controlled. a) Derive the closed loop equation for the feedback system shown in Figure 2, i.e. the mathematical relationship between y(s) and R(s). [50 marks] [CME3008] Question Continues Overleaf b) Analyse and critically discuss the benefits of the block containing the transfer function (1ets)a(s) when compared to a conventional feedback control system. In both cases you may assume that Gc(s) is the transfer function of a proportional - integral (PI) control law. [50 marks]