The properties of linear induction motor and areas of its application are analyzed; frequency converters and their control methods are discussed in this final work. Methods to realize a pulse width modulation are analyzed, scalar and vector control principles as well as perspectives of perfection of semiconductor commutating elements and control systems are discussed. The principle of operation of control systems applied in frequency converters is analyzed On the base of analysis mathematical and Simulink model of linear induction motor in α-β reference frame is developed, mathematical and Simulink models of frequency controlled linear induction drives are carried out. Two models of linear frequency controlled induction drive: scalar and vector control are investigated, transient characteristics of inverter output voltage, currents of linear motor, developed force and linear speed are analyzed and results of different control principles are compared.