please help me with these question by using MATHLAB.

VTOL UAVs are unmanned aircrafts that can take-off, hover, and land vertically. One of them is the quadrotor UAV, as presented in Figure 1. Automatic take-off is one of the automatic flight phases in the operation of these vehicles. To ensure that the UAVs can reach a desired height, this project proposes to design the automatic take-off control system using a PID controller Figure 1 VTOL UAVS Consider the following nonlinear vertical dynamics of a VTOL UAV with a mass m: m = Tcoscose - W where z is the height, T is the thrust, W is the weight of the UAV, and 9, are the roll and 8 pitch of the UAV, respectively. Assume that there is no external disturbance, all the motors have same performance, and all the propellers are perfectly balanced a. Construct the state-space model by linearizing the system dynamics using the given assumptions. Given that the states x = [z z]" and z can be measured using on-board sensors b. Design a PID controller such that the UAV will take-off from the ground and then hover at a height of 1m. Kindy consider the following 3 cases for the design: manual tuning of a PID controller, auto-tuning of a PI controlier, and (11) auto-tuning of a PID controller. The auto-tuning can be performed using the MATLAB function "pidtunel)". Let m = 2.0kg. Compare and discuss these results