Abstract: Disclosed are methods and apparatus for controlling electromagnetic field generation system to generate dynamic magnetic fields. The method can comprise: establishing a dynamic model that describes open-loop dynamics of the electromagnetic field generation system and has an unified state-space form with time delay; configuring a controller based on the dynamic model; applying, by the controller, a control signal to the electromagnetic field generation system; detecting one or more feedback signals from the electromagnetic field generation system; and updating, by the controller, the control signal for controlling the electromagnetic field generation system, according to a reference signal corresponding to a desired dynamic magnetic field, one or more compensated feedback signals, and system states. To address time delay and modeling error and to estimate system states, a Kalman filter and a Smith predictor based compensator can be incorporated.