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MATLAB Assignment Description Image [Solution]
Or in equation form: a(s) = a(s) Se (s) -x de (s) We want the response in the time domain, and the input de is easier to define in the time domain, so we are going to use the MATLAB® function Isim. 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 Isim (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 = Isim(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, let's 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.

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MATLAB Assignment Description Image [Solution]
(trailing edge up) is defined as a negative elevator angle and will cause the nose of the aircraft to go up. The pilot would pull back on the control stick to cause an up elevator. A down elevator (trailing edge down) is defined as a positive elevator angle and will cause the nose of the aircraft to go down. The pilot would push the control stick forward to cause a down elevator. The graphic below from RIT shows the elevator angle definitions. For those not familiar with aircraft, the pitch is the angle the aircraft makes with the horizontal, and the angle of attack is the angle a the aircraft makes with the oncoming air. horizontal tail elevator hinge Figure 1: Elevator angle definition. Graphic from RIT (https://people.rit.edu/pnveme/EMEM682n/StaticStab/index_StatStab.html). u (8) Three transfer functions have been given to your team. The function relates the change in forward velocity of de (s) the aircraft to a change in the elevator angle, the function (3) relates the change in angle of attack of the aircraft (8) relates the change in pitch angle of the aircraft to a change de(s) de (8) to a change in the elevator angle, and the function 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, 0₁, and 01). 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: de (s) a(s) a(s) Se (s)

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MATLAB Assignment Description Image [Solution]
U₁ = 673 ft S α₁ = 2.5 deg 0₁ = 2.5 deg u(s) -407.9s² + 19040s + 18200 Se (s) 684.3s +798.4s³ + 1061s² + 6.665s + 4.894 a(s) -25.55s³ - 1136s² - 5.031s-6.011 de(s) 0 (s) de(s) 684.3s +798.4s³ +1061s² + 6.665s + 4.894 684.3s +798.4s³ + 1061s² + 6.665s + 4.894 -1156s²-572.5s - 6.679

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