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1 2 . 4 . Consider the liquid - level control system shown in Fig. P 1 2 - 4 . The tanks are noninteract

12.4. Consider the liquid-level control system shown in Fig. P12-4. The tanks are noninteract-
ing. The following information is known:
The resistances on the tanks are linear. These resistances were tested separately, and
it was found that if the steady-state flow rate qcfm is plotted against steady-state tank
level hft, the slope of the line dqdh is 2ft2min.
The cross-sectional area of each tank is 2ft2.
The control valve was tested separately, and it was found that a change of 1 in pressure
to the valve produced a change in flow of 0.1cfm.
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 Kc for a critically damped response.
(c) If the tanks were connected so that they were interacting, what is the value of Kc needed
for critical damping?
(d) Using 1.5 times the value of Kc 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.
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