Answer Happy

This is the first part of a continuing example, which will span
multiple
assignments. As part of this example, you will eventually design an
autopilot that controls the
pitch angle 𝜃(𝑡) of an airplane over time 𝑡 by deflecting the
elevator, which is a control surface
near the rear of the plane, by an angle 𝛿(𝑡). The figure below
(adapted from [1]1) illustrates
the definitions of these angles (𝛼(𝑡) is the angle of attack,
while the other variables and axes
shown in the figure are not relevant in this problem).
The aircraft pitch is governed by the following approximated and
linearized equations, where
𝑞(𝑡) is the pitch rate and the coefficients are obtained from
numerical values of parameters for
a Boeing commercial aircraft.
The control input is the elevator deflection angle 𝑢(𝑡) = 𝛿(𝑡)
and the output is the pitch angle
𝑦(𝑡) = 𝜃(𝑡). Derive the transfer function 𝐻(𝑠) = 𝑌(𝑠)/𝑈(𝑠) =
Θ(𝑠)/Δ(𝑠), where Θ(𝑠) and Δ(𝑠) are
the Laplace domain representations of 𝜃(𝑡) and 𝛿(𝑡),
respectively.
х. u Ꮎ a r 8. Elevator
= ά å = -0.313a + 56.7q + 0.2328 ġ = -0.0139a – 0.426q + 0.02038 0 = 56.79 =