Systems and methods for operating a linear pump system involve operating a linear motor system; reciprocating a linear pump and a motor control module that issues commands and a control logic input to the linear motor system. The linear motor system is operated to reciprocate an output shaft between first and second reversal positions. The linear pump is reciprocated with the output shaft to produce a flow of material. A pump reversal command reverses direction of the output shaft. A torque command controls speed of the output shaft. The control logic input reciprocates the output shaft at speeds to produce a constant output condition of the flow of material. The motor control module adjusts the torque command to operate the output shaft at an increased speed above what is necessary for the constant output condition for a temporary time period beginning when the reversal command is issued.