A system's block diagram is shown below in Fig. 2. Please answer the following questions (34%)...

      

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A system's block diagram is shown below in Fig. 2. Please answer the following questions (34%) (a) Derive the transfer function of (6%) R Y (b) Derive the transfer function of - (c) Derive the transfer function of D R(s) Y N B(s) (6%) (d) If the relative degree of G,(s) is one and when the input is a step function, check the control effort u(t) and output y(t) to see whether they have impulse or step component or not. Also explain why. (8%) (e) there is a controller added from R(s) to U(s), demonstrate that the control schéme is a two-degree-of freedom controller. (8%) - Gues)! (6%) I *40 T's Kp Tø 韓 U(s) (B(s) D(s) G₂(s) Y(s) N(s) A system's block diagram is shown below in Fig. 2. Please answer the following questions (34%) (a) Derive the transfer function of (6%) R Y (b) Derive the transfer function of - (c) Derive the transfer function of D R(s) Y N B(s) (6%) (d) If the relative degree of G,(s) is one and when the input is a step function, check the control effort u(t) and output y(t) to see whether they have impulse or step component or not. Also explain why. (8%) (e) there is a controller added from R(s) to U(s), demonstrate that the control schéme is a two-degree-of freedom controller. (8%) - Gues)! (6%) I *40 T's Kp Tø 韓 U(s) (B(s) D(s) G₂(s) Y(s) N(s)