ISTANBUL TECHNICAL UNIVERSITY Department of Mechanical Engineering MAK 333E – SYSTEM DYNAMICS AND CONTROL MIDTERM EXAM 1 (Fall 2015-2016) Instructor: Assoc. Prof Dr. Erdinç ALTUĞ Student Number : Name and Surname :
Date : November November 6, 2015 (Exam duration is 100 minutes.) Signature : 1
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QUESTIONS and ANSWERS Problem 1:
[20 pnts] The pnts] The system shown below is used to control the engine speed of a system.
a) Determine the input and the output of this system. b) Is this a open-loop or closed-loop system? Why?
c) By clearly showing the actuator, controller and sensor, draw the block diagram of the system. Figure 1. A system
Answer:
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Sum
Problem 2:
[20 pnts] A second order system given by the following differential equation.
ɺyɺ + 5yɺ + 4 y = f (t )
IC : y(0) = 1, yɺ (0) = 0 and f(t) is a unit impulse
a) Solve the differential equation using Laplace Transform b) Verify the value of y(0) and y( ∞) using initial value and final value theorems. Answer:
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Problem 3:
[15 pnts] Linearize the following non-linear equation around the operating points 100 2 yi = 10 and xi = 20 . z = 0.2 x + . If new operating points are y = 11 and x = 18, what is the y percentage error? Answer:
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Problem 4:
[15 pnts] Find the transfer function G (s) = Y(s) / X(s) for the block diagram given below using graphical reduction techniques only. Show your steps clearly.
Figure 2. A block diagram
Answer:
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Problem 5:
[30 pnts] Consider the system shown in Figure 3.
Figure 3. A two-mass mechanical system a) By drawing free-body-diagrams and showing each force clearly, determine the equations of motion. a b Y c Y (s) b) Write equations in the form 1 1 1 = 1 , and determine the transfer function G ( s ) = 1 . R( s ) a2 b2 Y2 c2 Note that;
