I have some samples of readings from an accelerometer (unit: g) and I did a FFT (on MATLAB) on the vector generated from these samples to see its frequency spectrum. Then I have isolated the peaks and located its frequency. OK, now the control theory question. Let's say, to simplify the example, the only peak is 2 g at the frequency of 10 Hz. The accelerometer acquired the samples over a vibration system, so I assume it is undamped oscillating endelessly at a natural frequency of 10 Hz. My transfer function would be:
$$F(s) = \dfrac{(10\cdot2\pi)^2}{s^2 + (10\cdot2\pi)^2} = \dfrac{3948}{s^2 + 3948}$$
I multiplied by $2\pi$ before raising because it's given in Hz and I have to convert it into rad/s (right?)
I intend to make a PID control (on Simulink) to analyze some parameters, as overshoot, settling time, etc.
The REAL question is: how do I "tell" the system that the amplitude of it is 2 g? Is it like a gain that I insert before the transfer function block?