The actuator based on a single-phase thyristor current inverter (CI) for fast plasma position control systems in tokamaks is described. It has been successfully applied in the operating Globus-M/M2 (Ioffe Institute, SPetersburg, Russia) and T-11M (TRINITI, Troitsk, Russia) tokamaks for plasma position control. The mode of operation for the CI, allowing to control the current value in an inductive load, is described. The control algorithm for the CI, forming the average (on a period of self-oscillations) output voltage, proportional to the value of the input control signal at minimal amplitude of the voltage self-oscillations, is designed. The initial phase of the CI operation (current increasing through the inductive energy storage and the CI starting up into the selfoscillating mode of operation) is described. The autonomous protection elements for the CI are presented. The application results from the present tokamaks have demonstrated the reliability of the designed control algorithm and the declared quality of the CI operation reaching. The linear identification performed defines the linear CI's model for linear control system synthesis showing the dynamical properties of the CI in terms of the linear system analysis.