STUDENT NAME:
TUTOR NAME:
Dr Khaled Goher
PROGRAMME:
MODULE CODE: EGR2006M
MODULE TITLE:
Control Systems
SUBJECT:
Dynamic System Modelling of Control
COURSEWORK TITLE:
Dynamic System Modelling of Control
COURSEWORK WEIGHTING (%): 40%
Issue Date:
6.12.2019
Due Date:
3.2.2020
Feedback Date: 26.2.2020
PERFORMANCE CRITERIA:
TARGETED LEARNING OUTCOMES
To be able to derive mathematical models for different systems.
To be able to obtain a transfer function following block diagram reduction.
To be able to analyse the transient response of various dynamic systems due to different
inputs.
Important Information – Please Read Before Completing Your Work
All students should submit their work by the date specified using the procedures specified in the Student Handbook. An assessment that has been handed in after this deadline will be marked initially as if it had been handed in on time, but the Board of Examiners will normally apply a lateness penalty.
Your attention is drawn to the Section on Academic Misconduct in the Student’s Handbook.
All work will be considered as individual unless collaboration is specifically requested, in which case this should be explicitly acknowledged by the student within their submitted material.
Any queries that you may have on the requirements of this assessment should be e-mailed to kgoher@lincoln.ac.uk. No queries will be answered after respective submission dates.
You must ensure you retain a copy of your completed work prior to submission.
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COURSEWORK BRIEF:
This is the 1st coursework which carries 40% weight of the total grade. This will be marked out of 100 marks which are distributed for all questions.
Please follow the these instructions:
Provide a neat work.
NO and writing. You need to Type your work.
Provide your answer in the allocated blank space following each question. Provide neat drawings for block diagrams.
Mention clearly any assumptions in bullet points.
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Question 1: (Total 10 Marks)
For the two mass-spring system shown in the Figure 1, Let the output y=x1 and the control input u=F(t), where x1 =displacement of the first mass M1 and x2= displacement of the second mass M2 and F(t) is a force on mass M1. Ks=spring constant=100 N/m, M1=M2=1kg.
a. Draw the free body diagram of the two masses and derive the time-variant equation of the system.
b. Use Laplace transform to get the transfer function G(s)=X(s)/F(s), assuming zero
initial conditions, and hence show that G(s)
M2s2 Ks
M s2 K M s2 K K 2
2s1ss
x2
F(t)
Ks
x1
M2
M1
Fig. 1
Question 2:
For the given system below in Figure 2:
R(s)
(Total 10 Marks)
Y(s)
12
s3 8s2 19s12
Fig. 2
Obtain the unit impulse system response and compute y (t) at t = 1.5 sec, is the system stable?
Question 3: (Total 10 Marks) For the following closed-loop system in Figure 3:
a. Writethecharacteristicequationoftheclosedloopsystem
b. For what values of k the system is stable
c. For k = 10 estimate the maximum percentage overshoot and settling time due to a
unit step input.
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function:
Using the
a. b. c.
d. e.
following inputs:
u(t)=unitramp u(t) = unit impulse u(t) = unit step
u(t) e2t u(t) = e2t
R(s) + –
Y(s)
a. Inallcases;drawthesystemresponseusingMatlab. Page 4 of 7
G(s) k(s 2) s(s20)(s1)
Fig. 3
Question 4:
The HIV (AIDS) linearized model, Figure 4, can be shown to have the following transfer
520 10.3844
2.6817 0.11 0.0126
Fig. 4
It is desired to develop a policy for drug delivery to maintain the virus count at prescribed levels. For the purpose of obtaining an appropriate , the feedback shown in the figure will be used. As a first approach; consider , a constant to be selected. Use the Routh – Hurwitz criterion to find the range of the gain K to keep the closed loop system stable
Question 5: (Total 30 Marks)
For the system represented by the following time-variant differential equation:
d2x(t)5dx(t)4x(t) 2u(t) dt2 dt
(Total 10 Marks)
b. In all cases, find the system time response and check if the system converging to certain value? If yes, find this value.
c. In all cases, if the system is converged, find the time elapsed till convergence and comment on the result obtained.
d. Is the system response depends on the type of input?
Question 6: (10 points)
For the hydraulic servo system, shown in Figure 5, the following represent the differential equation of motion.
Derive the system transfer function.
Question 7: (Total 10 Marks)
Reduce the following black diagrams and identify the transfer function in the following Figures 6.1 and 6.2. Please carefuly consider the following:
You need to show detailed steps of the diagram reductions.
Each step will carry a weight of the marks assigned to each block diagram.
mybykyFpiston KAK1xAy 2
Fig. 5
a.
Fig. 6.1
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b.
Fig. 6.2
8.1. Build a Simulink Model for the system, in Figure 7, and run it for 50 seconds using:
Ramp input U: Slope = ‘’5’’, Start time ‘’10’’, Initial input ‘’1’’. Get the displacement X2.
Fig. 7
8.2. Repeat the simulation for 50 seconds if the value of each mass is increased to 8 kg.
Use the same input in 8.1.
a. GetthedisplacementsX1,X2andX3at.
b. Gettheaccelerationsofallthe3masses.
c. Does changing the values of the masses has an impact on the system output X2? Explain.
Question 8:
(Total 10 Marks)
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MARKING CRITERIA:
Coursework will be marked according to the following university criteria.
90-100%: a range of marks consistent with a first where the work is exceptional in all areas;
80-89%: a range of marks consistent with a first where the work is exceptional in most areas.
70-79%: a range of marks consistent with a first. Work which shows excellent content, organisation and presentation, reasoning and originality; evidence of independent reading and thinking and a clear and authoritative grasp of theoretical positions; ability to sustain an argument, to think analytically and/or critically and to synthesise material effectively.
60-69%: a range of marks consistent with an upper second. Well-organised and lucid coverage of the main points in an answer; intelligent interpretation and confident use of evidence, examples and references; clear evidence of critical judgement in selecting, ordering and analysing content; demonstrates some ability to synthesise material and to construct responses, which reveal insight and may offer some originality.
50-59%: a range of marks consistent with lower second; shows a grasp of the main issues and uses relevant materials in a generally business-like approach, restricted evidence of additional reading; possible unevenness in structure of answers and failure to understand the more subtle points: some critical analysis and a modest degree of insight should be present.
40-49%: a range of marks which is consistent with third class; demonstrates limited understanding with no enrichment of the basic course material presented in classes; superficial lines of argument and muddled presentation; little or no attempt to relate issues to a broader framework; lower end of the range equates to a minimum or threshold pass.
35-39%: achieves many of the learning outcomes required for a mark of 40% but falls short in one or more areas.
30-34%: a fail; may achieve some learning outcomes but falls short in most areas; shows considerable lack of understanding of basic course material and little evidence of research.
0-29%: a fail; basic factual errors of considerable magnitude showing little understanding of basic course material; falls substantially short of the learning outcomes for compensation.
MARKING SCHEME:
Contents of the assignments (90%) – this includes responding correctly to the questions.
Format and organsiation of the submission (10%)
Begin your work on the following page if you are word processing your coursework.
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