How to Derive Inverse Transformation for Nonlinear Plant to Output Pure 50Hz Sine Wave

We have a PC with digital-to-analog converter. With help of this converter we generate "pure" sine: y(t)=A*sin(2pi*f*t+ psi) with industrial frequency 50 Hz. This signal goes as input to electricity generating plant which has a goal to raise this signal and give to its own output. During this signal raise it gets distorted (there is some non-linear element in the plant scheme) and on the output of the plant we get not "pure" signal (using Furier expansion we have harmonics of higher than 50 Hz frequencies: 100 Hz, 150 Hz, 200 Hz and so on). We can see these higher frequencies when we analyze signal from the analog-to-digital converter (the same PC with digital-to-analog converter) that arrives from the output of the same(as in beginning of this post) electricity generating plant and the signal gets decreased to the same level as it was at input of electricity generating plant. THE PROBLEM IS: feed the electricity generating plant with signal that on the output it will be "pure" sine(there is a constraint: difference between main harmonic and any other from the first eleven not less than 52 decibel).

Any ideas how to implement this?

It seems odd to me that you have EVERY harmonic. Are sure that your plant output and the PC output is good by testing it independently from the PC?. Could the software that reads the plant output in the PC be bad? What happens if you put the signal from the PC back into the PC?.

The DAC is probably driven by a dedicated processor on the DAC board, or from software on the PC. Either could be affected by the PC operating system?

You could make a very big lookup table of the sin wave output levels and adjust it so that the plant output was a sin wave, but this would be very tedious and the pc would have to be able output the signal without pauses, such as interrupts. This probably couldn't be done with the existing operating system. Could the PC software/hardware that generates the sin wave be affected by operating system software in the PC?

All hardware and software on PC where DAC and ADC are situated were tested for error-prone so problems with hardware and software are exluded.

So the problem is not to adjust output to the sine wave but to PROVIDE SUCH FUNCTION TO THE INPUT THAT THE OUTPUT WOULD BE SINE WAVE. There is a constraint: difference between main harmonic and any other from the first eleven not less than 52 decibel.