System/method for real-time monitoring and control of pump operations at a well provide a pump control system that uses pump fillage with a proportional-integral-differential (PID) based algorithm to control positive displacement pump operations. The pump control system/method obtains measured or inferred pump speed from available pump speed data and, using certain pump characteristics provided by the well operator, calculates a theoretical fluid flow rate based on the pump speed. The pump control system/method thereafter compares the calculated theoretical fluid flow rate to a measured or observed fluid flow rate to calculate a pump fillage. The calculated pump fillage is then provided as a process input to the PID based algorithm along with a desired pump fillage from the well operator. The PID based algorithm processes the calculated pump fillage and the desired pump fillage using tuning parameters to determine an optimum pump speed based on the desired pump fillage.