Download Midterm Exam for EECS C128/ ME C134: Control Systems and more Exams Signal Processing and Analysis in PDF only on Docsity!
EECS C128/ ME C134Midterm Tues Oct. 19, 20101110 - 1230 pm Name: SID:
- Closed book. One page formula sheet. No calculators.
- There are 4 problems worth 100 points total.
Problem Points Score 1 30 (^23 ) 4 20 In the real world, unethical actions by engineers can cost money, careers, and lives. The penalty for unethical actions on this exam will be a grade of zero and a letter will be writtenfor your file and to the Office of Student Conduct.
tan−1 1 2 = 26. 6 ◦^ tan−^1 1 = 45◦ tan−1 1 3 = 18. 4 ◦^ tan−1 1 4 = 14◦ tan−^1 √3 = 60◦^ tan−^1 √^13 = 30◦ sin 30◦^ = 12 cos 60◦^ = √ 23 20 log 10 1 = 0dB 20 log 10 2 = 6dB 20 log 10 √2 = 3dB 20 log 10 12 = − 6 dB 20 log 10 5 = 20db − 6 dB = 14dB 20 log 10 √10 = 10 dB 1 /e ≈ 0. 37 1 /e^2 ≈ 0. 14 1 /e^3 ≈ 0. 05 √ 10 ≈ 3. 16
For the system below, letProblem 1 (30 pts) H y(s) = 1, G(s) =^ (s+6)^8 , and^ D(s) =^1 s. [4 pts] a) For w(t) = 0, determine E R((ss)) =
[4 pts] b) for r(t) = 0, determine (^) WY^ ( (ss)) =
[4 pts] c) If r(t) = 0 and w(t) is a unit step, find y(t) =
[4 pts] d) If r(t) = 0 and w(t) is a unit step, find limt→∞ e(t) =
[4 pts] e) If r(t) = tu(t) and w(t) = 0, find limt→∞ e(t) =
grid 8 pixels
Controller
r(t)
error e(t) u(t)
output y(t)
Sensor
referenceinput controlinput
D(s) plantG(s)
y (t) s
w(t)
H (s) y
Problem 2. (30 pts) Given open loop transfer function G(s):
G(s) = (^) (s + 1)(s 500(+ 11)(s^ + 21)s (^2) + 2s + 101) For the root locus: [2 pts] a) Determine the number of branches of the root locus =
[4 pts] b) Determine the locus of poles on the real axis
[3 pts] c) Determine the angles for each asymptote:
[4 pts] d) The approximation for the asymptote intersection point is s =
[9 pts] e) The angle of departure for the poles are: s = −1: s = −11: s = −1 + 10j: s = − 1 − 10 j:
[8 pts] f) Sketch the root locus below using rules 1-4 discussed in class.
Problem 3. Bode Plot (20 points)
for[10 pts] a) Sketch, labeling slopes, the magnitude and phase of^ G(s) on the graph below G(s) = (^) (s + 20)(^800 s (^2) + 2s + 4) [4 pts] b) label gain and phase margin in Bode plot [6 pts] c) based on the Bode plot, estimate the following: phase margin = degrees, cross over frequency ωc = rad/sec gain margin = dB
Magnitude (dB)
10 −1^100 101
Phase (deg)
Bode Diagram
Frequency (rad/sec)
