A rod pump control system includes a parameter estimator that determines from motor data parameters relating to operation of the rod pump and/or downhole dynamometer card without the need for external instrumentation, such as down hole sensors, rod load sensors, flow sensors, acoustic fluid level sensors, etc. In one embodiment, instantaneous motor current and voltage together with pump parameters are used in determining rod position and load. The rod position and load are used to control the operation of the rod pump to optimize the operation of the pump. Also disclosed in a pump stroke amplifier that is capable of increasing pump stroke without changing the overall pumping speed, or in the alternative, maintaining the well output with decreased overall pumping speed.