MAE 3723 Matlab Exam Fall 2016
Instructions
For each problem, create and run one or more Matlab programs to solve the problem.
To submit your solution, for each problem, paste the text of your programs into the posted Word document, and then paste into that Word document the Matlab results produced by your program (from the Workspace and/or Plots).
You may also insert any comments you think are useful, into the word document (please type all such comments in RED).
After you have completed the exam, you must upload this single file containing your solutions for the entire exam, to the D2L drop box created for the exam. Note: you may upload this file multiple times to the D2L drop box (as a way to keep safe backup copies of your work). If you do upload multiple copies, only the LAST file uploaded will be graded. Earlier versions will be ignored!
As a safety precaution you may also e-mail your final solution file to yourself, and maeonline@okstate.edu
PLEASE SAVE THIS FILE OFTEN (and to different file names) DURING THE EXAM, TO AVOID LOSING YOUR WORK BECAUSE OF AN ACCIDENT, OR A PROGRAM CRASH!
Rules for the exam:
You may use any Matlab or other text-like files contained on your computer hard drive, or contained on a “thumb drive” that you bring to the exam. You may NOT download Matlab files from the web, search the web for help, or use the web to communicate with anyone during the exam.
You may use a calculator, pen and paper if you find it helpful. You will not be able to turn-in your handwritten material.
There are 5 problems on this exam!
1.
(30 points) The following pair of differential equations describe the behavior of the FLUX Capacitor used in a highly customized DeLorean automobile. IMPORTANT – you may or may not understand the physics of a FLUX Capacitor, but that doesn’t matter. The differential equations are given, and you should be able to put them into Matlab can solve them!
I 𝑑𝑑2𝐹𝐹 = mjf ∗ 𝑖𝑖 − c 𝑑𝑑𝐹𝐹 − k ∗ 𝐹𝐹 𝑑𝑑𝑑𝑑2 and 𝑑𝑑𝑑𝑑
L 𝑑𝑑𝑑𝑑 = v−mjf∗ 𝑑𝑑𝐹𝐹 −R∗𝑖𝑖 𝑑𝑑𝑑𝑑 𝑑𝑑𝑑𝑑
In these equations:
t (time) is measured in seconds
i (temporal reluctance) is measured in amps 𝐹𝐹 (time warp flux) is measured in jigawatts
𝑑𝑑𝐹𝐹
𝑑𝑑𝑑𝑑 (time warp flux rate) is measured in jigawatts/second
𝑑𝑑2𝐹𝐹 (𝑑𝑑𝑖𝑖𝑡𝑡𝑡𝑡 𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤 𝑤𝑤𝑎𝑎𝑎𝑎𝑡𝑡𝑎𝑎𝑡𝑡𝑤𝑤𝑤𝑤𝑑𝑑𝑖𝑖𝑎𝑎𝑎𝑎) is measured in 𝑗𝑗𝑖𝑖𝑗𝑗𝑤𝑤𝑤𝑤𝑤𝑤𝑑𝑑𝑑𝑑𝑗𝑗/𝑤𝑤𝑡𝑡𝑤𝑤 𝑗𝑗𝑡𝑡𝑎𝑎𝑎𝑎𝑎𝑎𝑑𝑑 𝑗𝑗𝑠𝑠𝑠𝑠𝑤𝑤𝑤𝑤𝑡𝑡𝑑𝑑 𝑑𝑑𝑑𝑑2
With the following values for the constant parameters:
I = 20, k = 300, mjf = 5, L = 0.1, R = 0.5, c = 50, and v = 12
NOTE: All units for the variables and the constants are consistent as given, and no unit conversions of any kind are necessary.
Required:
a) Use Matlab to solve the equations. All initial conditions have a value of zero. Run the simulation for 3 seconds.
b) Plot F (time warp flux) as a function of time. Be sure to use meaningful plot labels.
c) On a separate graph, plot i (temporal reluctance) as a function of time. Be sure to use meaningful plot labels.
2. (25 points) For the system given in problem 1, the constant c is defined as the flux damping factor. Perform a parameter study on the effect of the flux damping factor, using values of:
c = 10, c = 50, c = 100 Produce two different plots:
a) F vs time for the 3 different flux damping values, all on one plot, nicely labeled, with a legend entry to identify each curve.
b) i vs time for the 3 different flux damping values, all on one plot, nicely labeled, with a legend entry to identify each curve.
3. (15 points) For the system given in problem 1, compare linear flux damping 𝑎𝑎 𝑑𝑑𝐹𝐹 as given in the
2 𝑑𝑑𝑑𝑑
equations of problem 1, with nonlinear flux damping 𝑎𝑎 �𝑑𝑑𝐹𝐹� , using a flux damping value of
𝑑𝑑𝑑𝑑 Remember, the SIGN of the damping term should change when 𝑑𝑑𝑑𝑑
Produce two different plots:
a) F vs time for the linear and nonlinear models, both on the same plot, nicely labeled, with a legend entry to identify each curve.
b) i vs time for the linear and nonlinear models, both on the same plot, nicely labeled, with a legend entry to identify each curve.
c = 50.
𝑑𝑑𝐹𝐹
changes sign.
4.
𝑖𝑖(𝑑𝑑) = 23(1 − 𝑡𝑡−2.8𝑑𝑑)
5.
(15 points) The transfer function for the DeLorean’s time transport system given below.
Use the Matlab tf() function to plot the response of this system to a step input of magnitude 2.
(15 points) For the system given in problem 1, the analytical solution for i (temporal reluctance) is
claimed to be:
Plot two curves on the same graph: The MatLab solution for i (as computed in problem 1) along with this claimed analytical solution, for the purpose of comparing the Matlab solution to this claimed analytical solution. Be sure to use meaningful plot labels. Use legends to identify each curve. Comment on how well the analytical solutions matches the Matlab solution.