<![CDATA[The control of chaotic and hyper-chaotic systems represents a crucial area of research in the field of nonlinear dynamic systems. In this study, we focus on applying chaos control techniques to a permanent magnet synchronous motor (PMSM), a system known to exhibit chaotic behavior under certain conditions. To achieve this, a sliding mode control (SMC) strategy integrated with a Lyapunov-based observer is proposed. The core concept involves designing a candidate Lyapunov function that governs the application of the control law, ensuring system stability while effectively suppressing chaotic dynamics. Through numerical simulations, the proposed sliding mode controller demonstrates its effectiveness in rapidly eliminating chaotic behavior and stabilizing the PMSM system toward a predefined reference trajectory. Notably, the system achieves error convergence within approximately 0.7 seconds under full control (four channels). When control channels are reduced to two, the system still maintains stability, showing flexibility and cost efficiency. In a further simulation, the chaotic PMSM is subjected to two unknown external disturbances, and the proposed controller continues to maintain stability with only a slight increase in convergence time. These quantitative results affirm the robustness, accuracy, and practicality of the proposed control method. This research confirms that integrating sliding mode control with a Lyapunov observer is an effective approach for chaos suppression in PMSMs, offering promising insights for the development of advanced control strategies in nonlinear electromechanical systems.]]>
