Given the digital control system below where Gp(s) = 20 (s + 2)(8 + 3)' and T = 0.5 sec. r(t) e(t) X G*D(S) 1-e-T's Gp(s) c(t) S Controller ZOH Plant (a) Write the general transfer function of a PD controller using the backwards rectangular difference/integration. (b) Write the general transfer function of a Pl controller using the backwards rectangular difference/integration. (c) Find the pulse open loop transfer function of the system. (d) Find the overall) pulse close loop transfer function of the system. (e) Design a cascaded PD controller to give the system an overshoot of 10% and a settling time of 4 seconds (where necessary, assume the two zeros of the compensator are placed at the same location). (f) Draw a well labelled Simulink model that can be used to simulate the behavior of the compensated system. Remember to include a unit step function as the input and a scope as the output. Make assumptions where necessary with detailed explanations on why each assumption was made. Given the digital control system below where Gp(s) = 20 (s + 2)(8 + 3)' and T = 0.5 sec. r(t) e(t) X G*D(S) 1-e-T's Gp(s) c(t) S Controller ZOH Plant (a) Write the general transfer function of a PD controller using the backwards rectangular difference/integration. (b) Write the general transfer function of a Pl controller using the backwards rectangular difference/integration. (c) Find the pulse open loop transfer function of the system. (d) Find the overall) pulse close loop transfer function of the system. (e) Design a cascaded PD controller to give the system an overshoot of 10% and a settling time of 4 seconds (where necessary, assume the two zeros of the compensator are placed at the same location). (f) Draw a well labelled Simulink model that can be used to simulate the behavior of the compensated system. Remember to include a unit step function as the input and a scope as the output. Make assumptions where necessary with detailed explanations on why each assumption was made