This paper presents a new method for estimating the speed of an induction motor based on adaptive control theory. The method, called the speed adaptive flux observer, is used for direct field-oriented control without speed sensors. The observer uses a state observer that can allocate poles arbitrarily, allowing it to work effectively even at low speeds. The observer is implemented on a digital signal processor (DSP: NEC μPD77230). The induction motor is described by state equations in the stationary reference frame. The state observer estimates the stator current and rotor flux. An adaptive scheme is proposed to estimate the rotor speed, which is derived using Lyapunov's theorem. The adaptive scheme allows the observer to estimate the rotor speed even when speed sensors are not available. The proposed speed adaptive flux observer is tested experimentally. The results show that the observer can accurately estimate the motor speed even in transient states. The observer is also tested under varying parameter conditions, such as changes in stator and rotor resistance. The results show that the observer can compensate for these variations by updating the estimated parameters. The proposed method is applied to direct field-oriented control of an induction motor without speed sensors. The control system uses the estimated rotor speed for control. The results show that the system can operate stably even at zero speed and can respond quickly to changes in load and speed. The paper concludes that the proposed speed adaptive flux observer is effective for direct field-oriented control of an induction motor without speed sensors. The method is robust to parameter variations and can be used in a wide range of applications.This paper presents a new method for estimating the speed of an induction motor based on adaptive control theory. The method, called the speed adaptive flux observer, is used for direct field-oriented control without speed sensors. The observer uses a state observer that can allocate poles arbitrarily, allowing it to work effectively even at low speeds. The observer is implemented on a digital signal processor (DSP: NEC μPD77230). The induction motor is described by state equations in the stationary reference frame. The state observer estimates the stator current and rotor flux. An adaptive scheme is proposed to estimate the rotor speed, which is derived using Lyapunov's theorem. The adaptive scheme allows the observer to estimate the rotor speed even when speed sensors are not available. The proposed speed adaptive flux observer is tested experimentally. The results show that the observer can accurately estimate the motor speed even in transient states. The observer is also tested under varying parameter conditions, such as changes in stator and rotor resistance. The results show that the observer can compensate for these variations by updating the estimated parameters. The proposed method is applied to direct field-oriented control of an induction motor without speed sensors. The control system uses the estimated rotor speed for control. The results show that the system can operate stably even at zero speed and can respond quickly to changes in load and speed. The paper concludes that the proposed speed adaptive flux observer is effective for direct field-oriented control of an induction motor without speed sensors. The method is robust to parameter variations and can be used in a wide range of applications.