THE OPEN UNIVERSITY OF SRI LANKA
DEPARTMENT OF MECHANICAL ENGINEERING
B.TECH HONOURS IN ENGINEERING – LEVEL 04
ACADEMIC YEAR 2017/2018
DMX4543- CONTROLS SYSTEMS ENGINEERING
ASSIGNMENT NO 02
PLEASE READ THE FOLLOWING INSTRUCTIONS BEFORE ANSWERING THE ASSIGNMENT
INSTRUCTIONS:
1. This assignment is based on Unit 01, Unit 02, and Unit 03. You may require referring addition resources for
more information.
2. Answer all questions
3. Submission of assignments can be done by any of the following methods
I.
By registered post to the address given below
THE COURSE CO-ORDINATOR IN DMX4543
DEPARTMENT OF MECHANICAL ENGINEERING
THE OPEN UNIVERSITY OF SRI LANKA
P.O.BOX 21, NAWALA
NUGEGODA
II.
Depositing it into the assignment box located outside the Mechanical Engineering Research Laboratory at
Science & Technology building, Nawala.
III.
Personally handing it over to the respective Coordinator. (Make sure that it is day stamped).
4. Deadline for submission: 2nd November 2018. Please note that late submissions will not be entertained.
(Q1)
Automatic steering of a ship would be a particularly useful application of feedback control theory. In the
case of heavily traveled seas, it is important to maintain the motion of the ship along an accurate track.
An automatic system would be more likely to maintain a smaller error from the desired heading than a
helmsman who re-corrects at infrequent intervals. A mathematical model of the steering system has been
developed for a ship moving at a constant velocity and for small deviations from the desired track. For a
large tanker, the transfer function of the ship is,
𝐺(𝑠) =
𝐸(𝑠) 0.164(𝑠 + 0.2)(−𝑠 + 0.32)
= 2
,
𝛿(𝑠)
𝑠 (𝑠 + 0.25)(𝑠 − 0.009)
Where 𝐸(𝑠) is the Laplace transform of the deviation of the ship from the desired heading and 𝛿(𝑠) is
the Laplace transform of the angle of deflection of the steering rudder. Verify that the frequency response
of the ship 𝐸(𝑗𝜔)/𝛿(𝑗𝜔) is that shown in Figure Q1.
Page 1 of 3
Figure Q1
(Q2)
Consider the automatic ship-steering system discussed in Problem Q1. The frequency response of the
open-loop portion of the ship steering control system is shown in Figure Q1. The deviation of the tanker
from the straight track is measured by radar and is used to generate the error signal, as shown in Figure
Q2. This error signal is used to control the rudder angle 𝛿(𝑠).
Figure Q2
a) Is this system stable? Discuss what an unstable ship-steering system indicates in terms of the
transient response of the system. Recall that the system under consideration is a ship attempting to
follow a straight track.
Page 2 of 3
b) Is it possible to stabilize this system by lowering the gain of the transfer function 𝐺(𝑠)?
c) Suggest a suitable feedback compensator to stabilize this system. Explain.
(Q3)
There have been significant developments in the application of robotics technology to nuclear power
plant maintenance problems. Thus far, robotics technology in the nuclear industry has been used
primarily on spent-fuel reprocessing and waste management. Today, the industry is beginning to apply
the technology to such areas as primary containment inspection, reactor maintenance, facility
refinement, and accident recovery activities. These developments suggest that the application of
remotely operated devices can significantly reduce radiation exposure to personnel and improve
maintenance program performance. The device is shown in Figure Q3. The open-loop transfer function
is,
𝐾𝑒 −𝑠𝑇
𝐺(𝑠) =
(𝑠 + 1)(𝑠 + 3)
Figure Q3
a) Determine a suitable gain 𝐾 for the system when 𝑇 = 0.5𝑠, so that the overshoot to a step input
is less than 30%.
b) Determine the steady-state error.
c) Design a compensator.
END
Page 3 of 3