Control of PMAC motor drives by a predictive recursive algorithm is presented in the paper. The proposed algorithm, allows to impose the reference values the current components, in d-q rotor reference frame. The algorithm permits to directly impose the control signals of the inverter. The time required for the execution of the algorithm, does not permit to impose the control vector in the actual sampling interval. Therefore, it is imposed with a delay of one sampling time. To avoid this time delay, two procedures are available. The first one resort to very fast processors, like FPGAs,; the other one is based on a predictive observer algorithm which allows to impose the vector control without the delay. The state observer requires to introduce sampled data of two sampling time before. Hence, a more powerful computing unit must be used. The simulation study of the drive controlled by the proposed algorithms is performed using Matlab-Simulink tool. The results are compared with that obtained by simulating the traditional drive, where the d-q components of the current are imposed using PI controllers and PWM technique. The comparison highlights the better performance of the direct digital control algorithms proposed with respect to that of the traditionally controlled drive.