A PM DC motor with torque constant kPM is used to power a hydraulic pump; the pump is a positive displacement type and generates a flow proportional to the pump velocity: qp = kpω. The fluid travels through a conduit of negligible resistance; an accumulator is included to smooth out the pulsations of the pump. A hydraulic load (modeled by a fluid resistance R) is connected between the pipe and a reservoir (assumed at zero pressure). Sketch the motor-pump circuit. Derive the dynamic equations for the system, and determine the transfer function between motor voltage and the pressure across the load.