The open-loop transfer function of a fluid-flow system can be written as

(5) 1 G(s): = 1 (5) TS + 1' where RC, R is a constant equivalent to the resis- tance offered by the orifice so that 1/R = 1/2kH, and C = the cross-sectional area of the tank. Since AH=RAQ2, we have the following for the transfer function relating the head to the input change: G(s) = AH(s) R 1 (5) RCS + 1' For a closed-loop feedback system, a float-level sen- sor and valve may be used as shown in Figure P4.1. Assuming the float is a negligible mass, the valve is controlled so that a reduction in the flow rate, AQ, is proportional to an increase in head, AH, or AQKAH. Draw a signal flow graph or block diagram. Determine and compare the open-loop and closed-loop systems for (a) sensitivity to changes in the equivalent coefficient R and the feedback coefficient K, (b) the ability to reduce the effects of a disturbance in the level AH(s), and (c) the steady-state error of the level (head) for a step change of the input AQ(s).