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Selective Harmonics Elimination is a high-efficiency modulation method for multilevel inverters that allows handling very high voltage applications. It eliminates the most significant harmonics and fixes the desired fundamental component. The main issue of these techniques is the complex process to obtain the appropriate switching-angles, being necessary to calculate them offline, meaning that if some disturbances occur, the system will not be compensated. This article proposes a real-time selective harmonic elimination for a single-phase cascaded multilevel inverter. The control strategy maintains constant the fundamental component of the output voltage while removing its third, fifth, and seventh order harmonics. The switching-angles are dynamically adapted to compensate for variations in the input voltage and the load. This is done by obtaining a virtual dynamic system using Groebner basis, an adaptation of the Newton-Raphson method, and implementing a digital PI controller into the virtual dynamical model. This adaptive modulation technique is validated experimentally in a 200 W, 9-levels Cascaded Full Bridge Inverter, canceling the harmonics and regulating the fundamental components in all the tests. The developed theory can be adapted or extended for any multilevel inverter modulated by selective harmonic elimination.