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In this paper, a mathematical model of permanent-magnet synchronous motor (PMSM) with initial rotor position uncertainty is derived and its control methodology is proposed. Based on Lyapunov stability theory, an observer-based robust adaptive position and speed-tracking control system for the PMSM is developed given that all parameters including load inertia and motor parameters are unknown, acceleration is not measurable and friction and external disturbances are bounded. An incremental encoder which provides relative position of the rotor is used along with stator current signals to achieve stable control. The simulation and experimental results have proven the stability and efficacy of the proposed control law.