The mathematical model of the pitch motion is: $$\frac{d^2\theta}{dt^2}=-20\,\frac{d\theta}{dt}-4\theta+5u,$$ where $\theta$ is the pitch angle to be controlled and $u$ is the control input, provided by the aerodynamic action of the movable fins.
The pitch angle is measured using an inclinometer. The manufacturer data sheet demonstrates that the instrument response to a step input can be modeled as a first order system with a time constant $\tau$ of $0.25$ seconds, and therefore its mathematical model is: $$\frac{d\theta}{dt}=-\frac1\tau\,\theta+4.$$
For the first model I have $Y(s)=5/(s^2+20s+4)$ and for the second I have $Y(s)=4/(s+(1/\tau)).$
I am rather unsure if these are correct as I am not the best at Laplace transforms!