In this study, a mathematical dynamic model of an induction motor as influenced by magnetic circuit saturation is developed. Moreover, a modified structure of indirect vector controller scheme is proposed which involves the saturated value of the magnetizing inductance. In order to overcome the disadvantages of the vector control drive system such as speed sensor and parameter sensitivity, two proposed control systems have been developed. In the first system, a simultaneous stator resistance and motor speed estimation based on a modified Model Reference Adaptive System (MRAS) has been used to obtain accurate estimation for motor speed taking the effect of magnetic flux saturation into account. Online magnetizing inductance estimation has been presented to consider the effect of saturation in the proposed system. In the second system, an effective online method for rotor resistance estimation based on a modified MRAS to achieve high-precise control in a wide range of motor speed taking the effect of magnetic circuit saturation into account.