Consider a 250-liter tank used for liquid storage is configured as in Figure 2.5 where the outflow passes through a valve. The cross-sectional area of the tank is 0.25 m2, and it may be assumed to be uniform. Assume that the valve discharge rate is related to the square root of the liquid level: q = C√h where Cv depends on the fixed opening of the valve. Cross-sectional area = A Figure 1: Level Control The entire system was initially at steady state with the inlet flowrate of 0.037 m³/min. Dynamic system behavior 1. Describe the system (give background) 2. Derive the model equations (chapter 2) 3. Steady state and dynamic behavior. Using the information shown below, derive transfer function for the process. (Chapter 3) 4. Response of the system to a step change (+100%) to the disturbance (ql). (Chapter 4) 5. Discuss the stability of the process. Control Scheme 1. Draw a block diagram of a classical feedback control system. (Chapter 7) 2. Using the information shown below, derive a transfer function for each block. (Chapter 4-8) 3. Using proportional only controller, carry out the closed-loop time domain Simulation to find the ultimate gain (Kcu) for the process 4. Compare this value with the value resulted from the Routh Stability analysis. 5. Simulate the closed-loop response for the PI controller setting given below and a +100% step disturbance. (Chapter 10) 6. Simulate the closed-loop response for the PI controller setting given below and a - 50% step disturbance. (Chapter 10) 7. Perform the controller tuning to get the best controller parameters for PI controller. (Chapter 11) G