A system and method for exciting an electrical machine with instantaneous non-sinusoidal current waveforms is disclosed. The system includes an inverter that controls current flow and terminal voltages in an electrical machine and a controller programmed to input an initial sinusoidal current demand to the inverter, thereby causing the inverter to output an initial sinusoidal input current. The controller is further programmed to receive feedback on an air gap magnetic field in the electrical machine generated by the initial sinusoidal current demand, determine an instantaneous fundamental component and instantaneous harmonic components of the air gap magnetic field, apply a correction to the instantaneous fundamental component of the air gap magnetic field to generate an ideal fundamental component, generate a non-sinusoidal current demand based on the ideal fundamental component, and input the non-sinusoidal current demand to the inverter, thereby causing the inverter to output a non-sinusoidal current.