For permanent magnet synchronous motor (PMSM) driving system, the challenge is that the PMSM model parameters are too complex to be determined precisely along with they can vary while the motor in use. As a result, controller performance is significantly decreased. Therefore, it is necessary to use algorithms to determine accurately unknown parameters, via observers for online parameter identification. This paper aims to build an identification PMSM model for an advanced controller using the back-stepping technique that requires motor model information. At the same time, to ensure the maximum torque per ampere condition, the d-axis current must also be controlled stably at zero. Based on the above requests, this paper proposes an equivalent model back-stepping controller (EMBSC) for a permanent magnet synchronous motor (PMSM) driving system. Specifically, EMBSC control law is utilized to generate the control signal to guide the motor toward the given current reference based on the equivalent mathematical model that is determined by the metaheuristic algorithm. Finally, an experiment is carried out to validate the theoretical conclusions, which confirms the high performance and accuracy of the designed speed and current control scheme.