Differential geared amplification of auxiliary power unit

An auxiliary power unit assembly for a gas turbine engine comprising:

• an auxiliary power unit coupled to drive a first drive shaft, the auxiliary power unit including an APU compressor, an APU combustor and an APU turbine disposed along an APU rotational axis;
• a first electric motor coupled to drive a second drive shaft;
• a differential gear system including a ring gear driven by the second drive shaft, a carrier attached to the ring gear, wherein the carrier supports a plurality of planet gears and the plurality of planet gears are meshed with a first pinion gear coupled to the first drive shaft and a second pinion gear coupled to an output shaft;
• a second clutch disposed on the second drive shaft configured to selectively decouple the second drive shaft from the differential gear system for preventing back driving of the first electric motor;
• a generator driven by the output shaft, wherein the electric motor and the auxiliary power unit combine to drive the output shaft;
• and
• a controller configured to control operation of the first electric motor, the auxiliary power unit and the generator,
• where the controller is configured to 1) determine an increase in a demand for power on the generator, 2) increase a speed of the electric motor to increase a power output from the generator to meet the demand while maintaining the APU at a constant speed and 3) determine the demand for power is beyond what can be provided by only adjusting the speed of the electric motor and in response increase the speed of the APU to increase the power output from the generator to meet the demand for power.