Driving Force

Force driving system is due to fan:

$$f\approx K_f\omega$$

where $K_f$ is constant, $\omega$ is rotation rate of fan.

Similarly:

$$\omega \approx k_m{V}_m$$

where $k_m$ constant, $V_m$ is voltage applied to motor.

NOTE

Then:

$$\ddot{y}\left(t\right)=Ku\left(t\right),K=\left[\frac{K_f{K}_m}{m}\right]$$

treating $V_m\left(t\right)=u\left(t\right)$ as the input to the system