TAMU, MEEN 364, 2014, Exam

MEEN 364 Exam 2 Spring 2014

Texas A&M University

Department of Mechanical Engineering

MEEN 364 Dynamic Systems and Controls

Exam 2 Apr. 3, 2014, 7 PM to 9 PM, CHEM Rm100 Name : Please circle your section below: Section (Lab Time): 501 (M 1:50-4:40 PM) 502 (T 8:00-10:50 AM) 503 (T 2:20-5:10 PM)

504 (W 1:50-4:40 PM) 505 (R 11:10-2:00 PM) 506 (W 8:00-10:50 AM)

507 (T 11:10-2:00 PM) 508 (R 2:20-5:10 AM)

NOTE: NO CALCULATORS, BOOKS, NOTES OR MOBILE PHONES "On my honor, as an Aggie, I have neither given nor received unauthorized aid on this academic

work."

Signature: ________________________________________

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Problem 1 [20 points] A) Find the Laplace transform of the following signal:

() = () +

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B) Use the Laplace Transform to find the solution () to the following differential equation:

() () + () = with initial conditions (0) = 0 and (0) = 1.

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Problem 2 [20 points] Consider the following block diagram:

A) Determine the transfer function between the input disturbance () and the output (). B) Determine the transfer function between the reference () and the output (). C) For the transfer function from part B, if = 3, determine the location of the poles and

zeroes.

D) Using the transfer function from part B, if = 3, determine the final value, if any, of the system output for a unit step reference input?

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Problem 2 (continued)

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Problem 3 [20 Points] Consider the following mass-slider-bar system:

A slider of mass m, is shown connected to the walls by two springs of stiffness k, on either side. The sliders initial position is the static equilibrium position. Viscous friction between the slider and the ground is modeled by the coefficient b. Attached to the center of the block at a pivot point is a slender, uniform bar of mass m, and length l. There is viscous damping at the pivot point as well modeled by the coefficient, c. Assume the moment of inertia for the bar about its mass center to be IG. The equations of motion are given by the following equations: Slider: 2 + 12 cos 2 sin + + 2 = 0 Bar:

+ 142 + 12 cos + + 12 sin = 0 A) Determine the equilibrium position(s) of the system.

B) Select one of the equilibrium position(s) of the system, and linearize the system about this

point.

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Problem 4 [20 Points] Consider the block diagram shown below:

It is desired to place the dominant poles of the closed loop system at the locations shown below:

sin(30) = 12 cos(30) = 32

Assume second order dominance, with the third pole of the closed-loop system placed at a distance 10 times the distance of the dominant poles from the imaginary axis. A) Determine the values of the constants, Kp, Kd and KI to place the poles as desired. B) Neglecting the effect of the closed loop zeroes, determine the percent overshoot and the

approximate settling time assuming a unit step input. C) Determine the final value of (), if one exists, assuming a unit step input. 13



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Problem 5 [20 Points] Consider the open loop transfer function is given as:

() = 49( 2)(0.05 + 1)240()( + 0.1)(2 7 + 49) For this transfer function:

A) Required: Sketch the combined magnitude plot for the transfer function (). Clearly label the break point frequencies and the slope of the asymptotes.

Optional: Sketch the individual magnitude plots in the plot spaces provided for each term of

the transfer function (). Note: These individual plots are only to assist in awarding partial credit, if necessary.

B) In the table provided, list the phase contribution of each term of () as 0 and , and then provide the total phase at these frequencies. A phase plot of () is NOT required.

C) Is this system stable? Is this system minimum-phase? Briefly justify your answers.

x log 10 (x) x log 10 (x) x log 10 (x) x log 10 (x) x log 10 (x)0.1 -1.000 2.1 0.322 4.1 0.613 6.1 0.785 8.1 0.9080.2 -0.699 2.2 0.342 4.2 0.623 6.2 0.792 8.2 0.9140.3 -0.523 2.3 0.362 4.3 0.633 6.3 0.799 8.3 0.9190.4 -0.398 2.4 0.380 4.4 0.643 6.4 0.806 8.4 0.9240.5 -0.301 2.5 0.398 4.5 0.653 6.5 0.813 8.5 0.9290.6 -0.222 2.6 0.415 4.6 0.663 6.6 0.820 8.6 0.9340.7 -0.155 2.7 0.431 4.7 0.672 6.7 0.826 8.7 0.9400.8 -0.097 2.8 0.447 4.8 0.681 6.8 0.833 8.8 0.9440.9 -0.046 2.9 0.462 4.9 0.690 6.9 0.839 8.9 0.9491.0 0.000 3.0 0.477 5.0 0.699 7.0 0.845 9.0 0.9541.1 0.041 3.1 0.491 5.1 0.708 7.1 0.851 9.1 0.9591.2 0.079 3.2 0.505 5.2 0.716 7.2 0.857 9.2 0.9641.3 0.114 3.3 0.519 5.3 0.724 7.3 0.863 9.3 0.9681.4 0.146 3.4 0.531 5.4 0.732 7.4 0.869 9.4 0.9731.5 0.176 3.5 0.544 5.5 0.740 7.5 0.875 9.5 0.9781.6 0.204 3.6 0.556 5.6 0.748 7.6 0.881 9.6 0.9821.7 0.230 3.7 0.568 5.7 0.756 7.7 0.886 9.7 0.9871.8 0.255 3.8 0.580 5.8 0.763 7.8 0.892 9.8 0.9911.9 0.279 3.9 0.591 5.9 0.771 7.9 0.898 9.9 0.9962.0 0.301 4.0 0.602 6.0 0.778 8.0 0.903 10.0 1.000

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A) Required: Plot of |()|

Optional: Individual Magnitude Plots for each term of ()

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B) Required: Table of ()

Term Phase for Phase for

Total

C) Is this system stable? Is this system minimum-phase? Briefly justify your answers.

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Problem 1 (20 points) __________ Problem 2 (20 points) __________ Problem 3 (20 points) __________ Problem 4 (20 points) __________ Problem 5 (20 points) __________ Total (100 points) __________

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TAMU, MEEN 364, 2014, Exam

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