Consider the iquid-level control system shown in Fig. P12-4. The tanks are noninteract- ing. The foll wing information is known: The esistances on the tanks are linear. These resistances were tested separately, and it was found that if the steady-state flow rate q cfm is plotted against steady-state tank level h ft, the slope of the line dq/dh is 2 ft/min. The cross-sectional area of each tank is 2 ft. The control valve was tested separately, and it was found that a change of 1 psi in pressure to the valve produced a change in flow of 0.1 cfm. There is no dynamic lag in the valve or the measuring element. (a) Draw a block diagram of this control system, and in each block give the transfer func- tion, with numerical values of the parameters. (b) Determine the controller gain K, for a critically damped response. (c) If the tanks were connected so that they were interacting, what is the value of K. needed for critical damping? (d) Using 1.5 times the value of K. determined in part (c), determine the response of the level in tank 2 to a step change in set point of 1 in of level. Proportional controller Water supply R2