An active magnetic bearing (AMB) is a frictionless bearing used in high-speed motors and other electromechanical products. Due to its open loop instability, utilization of controller is essential to stabilize the system. In this paper, a comparative study between sliding mode control (SMC) and back-stepping control (BSC) are presented for AMB systems. These two controller techniques have been applied for various dynamical systems to obtain stable control systems. On the basis of avoiding the chattering in the SMC design, the power rate reaching is introduced in the design of the control action of SMC. In terms of BSC design, Lyapunov-stability theorem is utilized to derive the control low of the controller. A gorilla troops optimization (GTO) has been applied to tune the adjustable parameters of the proposed controllers. According to the computer simulation based on MATLAB software, the results indicate a superior performance and improved in the system response of the SMC as compared to the BSC controller. In addition, the SMC strategy has a good disturbance rejection capability as compared to the BSC strategy.