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In this paper, the speed control problem of induction motors suffering from substantial friction force is considered. Here, a semi-current-fed model for induction motors and LuGre's dynamic model for friction force are used. To reflect practical situations, rotor resistance, torque load, and friction parameters are assumed to be unknown. In the design methodology, a double-observer structure is applied to estimate the immeasurable friction states. On the other hand, in light of the principles of vector control and field orientation, a set of virtual desired variables (VDVs) are introduced to synthesize the control law. Therefore, using only measurable signals of rotor speed, stator voltage and current, an asymptotic adaptive tracking controller is designed. Numerical simulations and experiments are carried out to verify the theoretical results and show satisfactory performance.