The sketch in Figure P7.56 shows a half-sectional view of a flow control valve, which is intended to keep the flow to a hydraulic load constant regardless of the variations of the load pressure P3 (disturbance input).
(a) Briefly discuss the physical operation of the valve, noting that the flow will be constant if the pressure drop across the fixed area orifice is constant.
(b) Write the equations that govern the dynamics of the unit. The mass, the damping constant, and the spring constant of the valve are denoted by m, b, and k, respectively. The volume of oil under pressure P2 is V, and the bulk modulus of the oil is β. Make the usual linearizing assumptions.
(c) Set up a block diagram for the system from which the dynamics and stability of the valve could be studied.
FIGURE P7.56
