In the figure, fluid at a regulated pressure is supplied to a fixed-flow restriction and a variable-flow restriction connected in series.
The variable-flow restriction is varied moving the "flapper" change he distance x_i. Ideally a sudden change in x_i would cause an instantaneous change in p_o. Actually, the dynamics are approximately those of a linear, first-order system for small changes in x_i.
For mass flow rate at the operation point G_(s,0)and G_(n,0) we assume that the supplied pressure p_s and temperature T_s are constant. We can write: