Usually, the vector control of the induction machine (IM) is done by using cascade control structures with conventional linear PI controllers, the inner loop being designed for current control, and the outer loop for rotor flux and speed control. In this paper, starting from the dq model of the IM with the rotor magnetic flux space vector aligned along the d axis, advanced control algorithms are proposed for the two control loops of the cascade structure. For the current inner loop, after the decoupling control of the two dq currents, predictive algorithms with constraints are used to control and limit the currents. Since the outer loop has a nonlinear affine multivariable plant model, a homotopy-based variant of feedback linearization is used to obtain a non-singular decoupling matrix of the feedback transformation even when the rotor flux is zero at the start-up of the motor. During the continuous variation of the homotopy parameter, the model of the plant is variable, in which case the model free algorithms are properly used to control the flux and speed of the IM. The comparative analysis obtained for the cascade structure with conventional PI controllers and advanced algorithms, respectively, shows that the last lead to improve the dynamical performance of the IM.