Tunable progressive cavity pump

A well pump assembly includes a progressive cavity pump having a stator with an elastomeric inner portion. The stator has an axial cavity with internal lobes; a rotor with external lobes positioned within the axial cavity. An effector selectively increases and decreases a stiffness of the stator by changing a cross sectional area of the axial cavity in the stator. The effector may include a reservoir within the stator containing a fluid. A reservoir pump selectively increases and decreases a pressure of the fluid in the reservoir in response to sensing the flow rate from the progressive cavity pump and the torque of the motor. Alternately, the reservoir may contain a magneto-rheological fluid (MR fluid). A coil generates an electromagnetic field within the MR fluid to selectrively increase and decrease a viscosity of the MR fluid.