Not a VTOL person, but from the free-body diagram, Newton's 2nd Law can be applied with the basic assumptions of relatively low altitude compared to the Earth radius, and air resistance is neglected. The basic equation of motion is given by

where the weight of VTOL system, . Rearranging that . Since the accelation of the VTOL is the second-order derivative of the altitude with respect to time, , then . Taking the Laplace transform with zero initial conditions, you get

which can be rearranged to obtain the transfer function from plant inputs to plant output Here, is the command input and is the disturbance. If can be accurately estimated, then you can design to counter the effect of the disturbance, and is the PID thing that you need to design Gp = tf(1, [m 0 0])

Gp =
1
---------
4.536 s^2
Continuous-time transfer function.

Gc = pidtune(Gp, 'PIDF', 0.95)

Gc =
1 s
Kp + Ki * --- + Kd * --------
s Tf*s+1
with Kp = 0.76, Ki = 0.0338, Kd = 4.2, Tf = 0.193
Continuous-time PIDF controller in parallel form.

Gcl = minreal(feedback(Gc*Gp, 1))

Gcl =
4.961 s^2 + 0.8757 s + 0.03861
------------------------------------------------
s^4 + 5.181 s^3 + 4.961 s^2 + 0.8757 s + 0.03861
Continuous-time transfer function.

Gu = minreal(feedback(Gc, Gp))

Gu =
22.5 s^4 + 3.972 s^3 + 0.1752 s^2
------------------------------------------------
s^4 + 5.181 s^3 + 4.961 s^2 + 0.8757 s + 0.03861
Continuous-time transfer function.

t = linspace(0, 50, 5001);

lsim(Gu, u, t/10), grid on

The Simulink model should look like this: