Mae318bonus

MAE 318 Sensors and Controls Bonus Problems • • • • • •

Students MUST work problems independently; receiving help from any person in any way is not authorized. You may use textbooks and your own notes. Please submit solutions to Dr. Valana Wells, ECG 346b. The final submission date is August 31, 2007 at 5 pm. No solutions will be accepted later than this date for any reason. The final submission date for consideration of a grade change before Fall 2007 semester is August 1, 2007. The maximum number of percentage points available on this bonus test is 30. In order to receive a score of 30, solutions must be correct, complete, organized, legible and presented in a professional manner. Any questions should be directed to Dr. Wells.

1) Given the following nonlinear model, consider the output to be the radius r. Find the transfer function of the linearized model around: r = R, θ& = Ω , u=0, where R, Ω , and µ are constants.

µ &r& − θ& 2 r = − 2 + u r rθ&& + 2r&θ& = 0

2) The circuits in the figures represent a low-pass (a) and a high-pass (b) second order system. Knowing that R=8 Ohm, determine L and C for each circuit so as to achieve a natural frequency of 100 Hz for the low-pass system and 1000 Hz for the high-pass system, and maximum flatness within bandpass for both systems.

L

u

R

C

y

R

L

y

(a) C

u (b)

3) The data contained in the file: “response.txt”, which you can download from the link “assignments” in the blackboard course site, are measurements of the step response of a first order system. The left column is time t, and the right column contains measurements of the step response y(t). Using statistics and the linear least squares, determine the transfer function of the system.