Oversampling means to sample at significantly more than the Nyquist Rate. I can well understand it in signal re-construction: more samples can improve the ADC's resolution, signal-to-error ratio, etc.
However, when in a control system, I have some difficulities understanding it. Assume that the frequency of the process variable is $f$, so the Nyquist Rate is $2f$, and we sample at $2f$ (the controller will take action upon each sample). Maybe we don't get a stable process variable, so we decide to improve the sampling rate.
Next, we sample at $20f$, a sampling frequency 10 times higher (also the controller takes action upon each sample), and this time we obtain a stable process variable. However, because the controller action is also 10 times faster, the frequency of the process variable is no longer $f$, but much higher, say $f'$. Now the Nyquist Rate becomes $2f'$.
Comparing sampling frequency $20f$ and new Nyquist rate $2f'$, they may be very close, so we cannot call it "oversampling".
Is my understanding towards oversampling and Nyquist rate correct?