Questions -

Q1. Create a closed-loop simulation using MATLAB and Simulink as shown in Fig. 2. In these simulations:

a) Design a set of PID controllers to control Euler angles (φ, θ, ψ).

b) Plot the graphs for (φ, θ, ψ) and p, q, r for 30 seconds of simulation time. Assume the initial conditions are all set to zero and the desired Euler angles are (φ_d, θ_d, ψ_d) = (0.3, 0.1, 2.1) rad.

Q2. Explain how one can find the position vector of the vehicle in the inertial frame. Find the transformation matrix between the body frame and inertial frame.

Q3. Suppose that the only force acting on the vehicle is the weight of the vehicle. Also, assume the vehicle has initial position and velocity vectors expressed in the inertial frame as follows:

d = (100, 100, 50) m, d^· = (5, 0, 0) m/s

a) Plot the graphs for d and d^· as expressed in the inertial frame for 10 seconds of simulation time.

Q4. Please do a quick research and explain how one can design a controller to control the position of the vehicle in the inertial frame. Please show the mathematical details of your work.

Report Format - The report should include the following sections:

• Abstract
• Introduction
• Questions
• Conclusions

Attachment:- Assignment File.rar