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The vector control of an induction motor in the rotor flux linkage oriented reference frame, with magnetic saturation included, is considered. The magnetic saturation is represented by the non-linear magnetising curve of the iron core. The rotor flux linkage model and the voltage decoupling in the traditional vector control scheme are modified to account for the magnetic saturation of the iron core. The mixed stator current - rotor flux linkage' model of the saturated induction machine is used in the control design, simulation and experimental realisation. Experimental results show that the proposed control with the included saturation offers a number of benefits, such as reduced stator current and smaller speed tracking error.