Fuel flow control system and method for controlling two positive displacement pumps

A fuel flow system (10) for a gas turbine engine includes a first pump (20), a second pump (38), a bypass loop (12e), an integrating bypass valve (28) and a pilot valve (30). The first pump (20) connects to an actuator (48) and a metering valve (24). The second pump (38) connects to the metering valve (24) and is arranged in parallel with the first pump (20). The bypass loop (12c) recycles fuel flow from the first pump (20) and the second pump (38) to inlets of the first pump (20) and second pump (38). Integrating bypass valve (28) includes first and second windows (28a,28b). The first window (28a) regulates fuel from the first pump (20) through the bypass loop (12e) and the second window (28b) regulates fuel from the second pump (38) through the bypass loop (12e). The pilot valve (30) controls the size of the first and second windows (28a,28b).