First, it is vital to understand that four inputs are required to achieve the required outputs: (1) The initial state of the aircraft (given to you in your Aircraft Assignment paper). (2) The transfer functions (given to you in your Aircraft Assignment paper). (3) A change (in this case, it is the elevator deflection, given to you in each problem). (4) Time (also given to you in the overall assignment).

Based on coding the above inputs into MATLAB, your objectives for each problem (1.-5.) are to: (a) Create a plot of de (deg) vs. Time (s). (b) Create a plot of U (ft/s) vs. Time (s). (c) Create a plot of alpha (deg) vs. Time (s). (d) Create a plot of theta (deg) vs. Time (s).

The function u(s)e(s)u(s)e(s)relates the change in forward velocity of the aircraft to a change in the elevator angle, the function (s)e(s)(s)e(s)relates the change in angle of attack of the aircraft to a change in the elevator angle, and the function (s)e(s)(s)e(s)relates the change in pitch angle of the aircraft to a change in the elevator angle. The transfer functions assume all angles are in radians, so make sure to convert to radians when using the transfer functions and to convert back to degrees when reporting any results. The velocity is assumed to be in ft/s. Your team was also given the initial cruise conditions of the aircraft (U1,1,and1).(U1,1,and1).To find the actual response of the aircraft, you will need to add the output response from the transfer functions to the initial cruise conditions.

Taking the pitch transfer function as an example, the block diagram looks like:

Or in equation form:

We want the response in the time domain, and the input ee is easier to define in the time domain, so we are going to use the MATLAB function lsim. This function can plot the time response of a system due to different inputs and also output the data to a variable. The syntax for plotting the response is

lsim (sys, U,T)

The sys is the transfer function, U is the input defined in the time domain, and T is the input time. The syntax for saving the response is the same except that a variable is on the left-hand side of the equation

Y = lsim(sys, U,T)

For this assignment, all the time arrays will be 150 s with intervals of 0.05 s

T = 0:0.05:150;

This creates an array with a size of 3001, and every second is 20 intervals apart (e.g. T(21) = 1, T(41) = 2, T(61) = 3). As an example, lets create an elevator step input of -5 degrees. The step input starts at time equals 0 s

input_de(1:3001) = -5*pi/180;

The input must be the same size as the time array and the degrees must be converted to radians. Another example is to create a doublet of 3 degrees that lasts 6 seconds and starts at 1 second.

input_de(1:20) = 0;

input_de(21:80) = 3*pi/180;

input_de(81:140) = -3*pi/180;

input_de(141:3001) = 0;

A doublet is a typical control surface maneuver to test the response of an aircraft. The elevator is deflected down a certain amount for a certain time and then deflected up for the same amount and at the same time.

u(s) e (s) a(s) e (s) (s) e (s) (U1,01, and 6,) u(s) e (s) a(s) e (s) (s) e (s) (U1,01, and 6,)