Step 1-Rigid Body Airplane/Quadrotor Model 1. Model the dynamics of the airplane in the horizontal, lateral or both planes. a) Derive the nonlinear differential equations of motion of a rigid body with six degrees of freedom. Assume the motion is in a horizontal or lateral plane and obtain a simplified model valid in that plane. b) Build an alternative MATLAB/Simulink simulation model for the mathematical model you obtained and compare with the available MATLAB/Simulink model. Step 2 - Vehicle Model in the Horizontal or Lateral Plane c) Determine all forces and moments applied to the airplane you have chosen and include them in the model you found in Step 1. Obtain a set of nonlinear differential equations describing the airplane dynamics in the horizontal/lateral, or both planes. Build a Simulink block for each force and moment term and connect them to the Simulink block you have built in Step 1. Group all blocks into a superblock. Step 3 - Autopilot (Flight Controller) Design Assuming you are measuring the whole state, design an autopilot for the linearized/nonlinear airplane dynamics to make the airplane follow a step-type of command input with constant velocity (of your choice). You can use any controller design technique you want (feel free to use an existing technique as described in the references or to do some research into new design techniques). Build a Simulink block for your autopilot to achieve good performance for the available, Qball-X4, F-16 or FDC 1.4 and/or your own model. Show simulations of the closed-loop system for the following situations: e) Linear Controller in feedback with linear airplane dynamics f) Linear Controller in feedback with nonlinear airplane dynamics g) What are your conclusions? h) How would you modify your design to account for random errors in the measurements and nonlinearities in the dynamics? 2) For the F-16 aircraft given in the course website, 1) develop nonlinear and linearized mathematical models; 2) design an autopilot (flight controller, with your own choice of control algorithm(s) to be used/developed) in the longitudinal/lateral plane or both longitudinal and lateral motions to make the vehicle follow a step type, rectangular/circular trajectory command/reference input; 3) implement, test and analyze your developed control algorithm(s) in the F-16 nonlinear MATLAB/Simulink simulation environment.