The system shown in Fig. P16-4 is controlled by a proportional controller. The concentration of salt in the solution leaving the tank is controlled by adding a concentrated solution through a control valve. C=25 lb/ft 1 ft/min of water Holdup volume 3 ft Controller FIGURE P16-4 The following data apply: 1. Concentration of concentrated salt solution C1 = 25 lb salt/ft3 solution. 2. Controlled concentration C = 0.1 lb salt/ft3 solution. 3. Control valve: The flow through the control valve varies from 0.002 to 0.0006 ft3/min with a change of valve-top pressure from 3 to 15 psi. This relationship is linear. 4. Distance velocity lag: It takes 1 min for the solution leaving the tank to reach the concentration-measuring element at the end of the pipe. 5. Neglect lags in the valve. (a) Draw a block diagram of the control system. Place in each block the appropriate transfer function. Calculate all the constants and give the units. (b) Using a frequency-response diagram and the Ziegler-Nichols rules, determine the settings of the controller. (c). Using the controller settings of part (b), calculate the offset when the set point is changed by 0.02 unit of concentration.