G(s)=(2s+1)(5s+1)2(14s)e2r change in setpoint, what will the steady-state offset in the procets of the 2. When the system 3. Design a direct synthesis controller for the systern using re=2, what is K6,z1 ted re Show all your steps and derivations. Do not simulate ( 10 marks) Question (2) (20 Marks) In a series of experiments aimed at studying the characteristics of blood pressure control in mammals when extemal intervention is required, the drug Nitroprusside was infused into in though the observed responses were nonlinear, the approximate linear model: Y(s)=(5s+1)2(2.9s+1)2.5U(s) was found to be adequate. Here, Y is the deviation if the MAP (in mmHg ) from the average value observed prior to the administration of the drug; U is the Nitroprusside infusion rate (in ml/min ); tume is in minutes. Since it could be fatal to deviate significantly from the prescribed value of the MAP in either direction, it is desired to design a feedback control system which will exhibit little or no oscillatory behavior. (a) Use Ziegler-Nichols tuning rules in Table to design P, PI, and PID controllers for this "process. "[4 marks] (b) Evaluate all three controllers by obtaining a simulation of the closed-loop systern response to a demand for a 20mmHg step change in the dog's MAP. Plot both Y and U for each of the three controllers. [8 Marks] (c) Considering the requirement stipulated above, are any of the three controllers acceptable? If not, how would you modify the controller parameters to make them acceptable? [8 Marks]