Introduction. The study is devoted to the development of the functionality of a railway track switch by introducing a switched-inductor electric drive. This solution justifies simplifying the mechanical part of the switches by changing the gearbox to a ball-screw and locating the all kinematic line of the switches on the mono-sleeper type. Goal. A study of the mono-sleeper turnout type behaviour to meet modern traffic safety requirements and improve operational reliability factors. Methodology. Based on electric drive theory, a kinematic line of a mono-switch turnout type with nonlinear friction characteristic is presented. Using differential equation theory and Laplace transformation, a mathematic description of a four-phase switched-inductor motor with ball-screw in a mechanical line of a single-mass electromechanical system has been made. A simulation mathematical model of the electric drive of mono-sleeper turnout type as the control system with a switched-inductor motor and nonlinear friction characteristic was built in MATLAB. Results. Simulation modelling of a mathematical model of a mono-sleeper turnout type with a switched-inductor motor and ball-screw gear has been developed and implemented. Studies of dynamics of turnout point movement have shown that, in contrast to the motors used today, the switched-inductor motor makes it possible to simplify the mechanical part of the drive, which leads to reduced time spent on laying and maintenance of turnout points, and therefore makes the design more reliable. The application of PID controller and fuzzy speed controller has shown improved dynamics of turnout point, while the fuzzy PID controller provides better performance of the set values and turnout point movements. Originality. First developed a mathematical model of the electric drive of the mono-sleeper turnout type, taking into account nonlinear friction characteristic, as an object of speed control of turnout point movement, is developed. Practical value. The developed mathematical model of a railway track turnout of the mono-sleeper type with a switched-inductor motor and ball-screw gear enables more efficient use of a microprocessor control system, creation of promising electric motor protection means and control of a turnout point.