Permanent Magnet Linear Synchronous Motor drives have excellent performance features such as no backlash and less friction, high speed and high precision in long distance location, in addition it has imple mechanical structure which is resulted in higher reliability and frame stiffness and high thrust. Because of these advantages, the PMLSM drive has been used widely in industry, machine tools, and robotics and traortation applications. The driving principles of PMLSM are similar to the traditional Rotary type Permanent Magnet Synchronous Motors (RPMSM), but its control characteristics are more complicated, that is because of the motor parameters are time-varying due to changes in operating conditions, such as speed mover, temperature, and configuration of the rail. In this research, using feedback linearization, adaptive backstepping method and Artificial Neural Network (ANN), the speed (position) and flux tracking control of this drive is studied. At first, the controllers are proposed when the armature slides in the magnet array region and the computer simulation results are shown. Because of complex structure of PMLSM and in addition due to existence of considerable uncertainties that exist in its parameters, the controllers can not guarantee a proper performance for the drive system when the armature goes out from the PM array. So, considering the operation motor in the extended region, the sliding mode flux and speed controllers are proposed for the LIM drive. Finally, using adaptive backstepping controller and neural networks, the position and flux of the motor, considering the extended region are controlled.