In this paper, the speed control of a permanent magnet synchronous motor is performed in a desired finite time. Due to the nonlinearity of the dynamics of this type of motors and the form of the state equations, a back-stepping strategy has been chosen to design the control system. In the proposed method, in each design step, the finite time stability condition is used, so the nonlinear controller has the ability to guarantee finite time convergence of output tracking error. The finite time stability of the proposed control method is proved based on Lyapunov theory. Adjusting the convergence time of system outputs can be done by changing the gain of the controllers. Furthermore, the proposed controller generates smooth control signal that can be implemented. The simulation results show that the proposed method is able to control the speed and current of a permanent magnet synchronous motor in desired finite time. تفاصيل المقالة