In the paper a comparative study of the two control structures based on MPC (Model Predictive Control) for an electrical drive system with an induction motor are presented. As opposed to the classical approach, in which DFOC (Direct Field Oriented Control) with four controllers is considered, in the current study only one MPC controller is utilized. The proposed control structures have a cascade free structure that consists of a vector of electromagnetic (torque, flux) and mechanical (speed) states of the system. The first investigated framework is based on the finite-set MPC. A short horizon predictive window is selected. The continuous set MPC is used in the second framework. In this case the predictive horizon contains several samples. The computational complexity of the algorithm is reduced by applying its explicit version. Different implementation aspects of both MPC structures, for instance the model used in prediction, complexity of the control algorithms, and their properties together with the noise level are analyzed. The effectiveness of the proposed approach is validated by some experimental tests.