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Spring 2018
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Assignment # 1
Instructions:
๏ท This is an INDIVIDUAL assignment. Every student must submit their own assignment (on proper A4 blank or lined page) with Name, Reg # and Section clearly marked on EACH page ๏ท Questions must be done in sequence. ๏ท Question must be printed before solving it by hand. ๏ท Each Question must be finished before starting of next question, otherwise marks of that QUESTION will be deducted. (half the marks you get in that Question ) ๏ท If you use internet or any book other than Norman S Nise, remember to provide reference in your work [IEEE format] ๏ท Assignment deadline is : o Day before Quiz #1 @ 10.00am โ 10.15am o At Office # G. o No assignments will be accepted after the deadline ๏ท Pencil CANNOT be used ๏ท Show all your workings CLEARLY ๏ท For the questions involving MATLAB , code and graph should be provided. The graphs should have a legend, axis should be labelled and the graphs should be clearly visible.
Question No. 1 2 3 4 5 6 7 8 9 10 Total CLO No 1 1 1 1 1 1 1 1 1 1 Score Max 2 2 2 2 2 2 2 2 2 2 20
For Examiner Only
Spring 2018
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Q-1 Write equation of motion to find transfer function ๐บ(๐ ) = ๐(๐ ) ๐(๐ )โ of the mechanical system shown in Figure 1. The output is y(t) and u(t) is input.
Figure 1
Spring 2018
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Q3. The mechanical system shown in figure 2. Inertia of A is J 1 and inertia of B is J 2. Both rotational masses are NOT fixed at axis of A and B respectively. The J 1 and J 2 experiences rotational and translational motion. Write the motion equations for the system.
Figure 2 - Mechanical system
Spring 2018
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Q4. There are two kind of DC servo motor, field current controlled or armature current controlled. Figure 3 shows electrical diagram of DC motor. Air-gap flux ฯ of the motor is proportional to the field current. Torque developed by the motor is assumed to be related linearly to ฯ and the armature current, which is
constant. Find the transfer function ๐ฎ(๐) = ๐ฝ(๐)๐ฝ ๐
for field current controlled DC
motor.
Figure 3 - Electrical diagram of dc motor
Spring 2018
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Q6- For the system in figure 5, draw free body diagram of the two masses, and
find the transfer function
๐(๐ ) ๐(๐ )
Figure 5
Spring 2018
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Q7 - For the mechanical system in figure 6 write the equation of motion and find the Output x 3 (t) response and draw its graph using MATLAB.
Figure 6
Spring 2018
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Q9 For the system shown in figure 8 X 1 is the displacement associated with M and X 2 is associated with M2.
(a) Derive the transfer functions
๐1(๐ ) ๐น(๐ ) ,^
๐2(๐ ) ๐น(๐ )
(b) If the applied force is a pulse of 1 second with magnitude of 600 N, Find X 1 (s) and X 2 (s)
(c) Using MATLAB, find the values of K 1 and K 2 such that M2 has at least 10 times more oscillations as M2. Plot x1(t) and x2(t) on one graph.
(d) If gravity is taken into account, repeat part a , b, and c.
Figure 8
Spring 2018
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Q10- Find the transfer function
Velocity(s)
๐๐๐๐(๐ ) for the system shown in
figure 9. Velocity(s) is the derivative of x(s). Show complete derivation
and every step. Ignore ๐ฝ๐ ๐๐๐ ๐ท๐.
Values: ๐๐ก = ๐๐ = 1 ; ๐
๐ = 1 ; ๐ฟ๐ = 5 ; ๐ฝ = 0.4 ; ๐ = 0.1 ; ๐ท = 0.5 ; ๐ = 9 ; ๐๐ฃ = 5
๐
1
๐
2 = ๐พ;^ ๐๐ก๐๐โ
(๐ก)[๐๐๐๐ก๐ ] = 1 [๐๐๐๐ก๐
๐.๐ ๐๐]๐ฃ(๐ก)
Figure 9
