Description
I am looking for someone proficient in using MATLAB for team domain and S domain calculation, and Simulink. The ideal candidate should have a strong command of these tools and be able to craft insightful reports detailing the projects completed.
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Assessment Cover Sheet
Assessment Title
Designing a Speed Controller for a DC Motor
Programme Title:
Bachelor of Engineering Technology
Course No.:
EN7230T
Course Title:
Instrumentation and Automatic Control
Student Name:
Student ID:
Section Number:
Tutor Name:
Dr. Ali Ridha
By submitting this assessment for marking, either electronically or as hard copy, I confirm the
following:
➢
➢
➢
➢
This assignment is my own work
Any information used has been properly referenced.
I understand that a copy of my work may be used for moderation.
I have kept a copy of this assignment
Do not write below this line. For Polytechnic use only.
Assessor:
Date of Marking:
Grade/Mark:
Assessment Weight: 60% of total mark
Comments:
Course Project Descriptor (EN7230T)
Instructions
1) Please ensure that you submit your report by the specified due date through the Turnitin link
provided on Moodle.
2) The date of your upload on Moodle will be considered as the official “Date of Submission” for
calculating any late submissions.
3) Adhering to the late submission rule is crucial as it will be applied in case of any tardy
submissions.
4) Kindly note that the deadline for this project is Sunday the 31st of March 2024.
Learning Outcomes
The tasks included in this assignment fulfill the Learning Outcomes of the course as follows:
1) Demonstrate advanced knowledge of core principles of control and instrumentation.
2) Critically analyze and evaluate transient response characteristics of first and second order
systems.
3) Apply and demonstrate instrumentation and control strategies for feedforward and feedback
control systems.
4) Formulate, apply, and present tuning methods for finding suitable PID controller parameters
to meet an industry standard requirement for a defined control design problem.
The completion of this project carries a weightage of 60% towards your final grade. The project
entails designing a speed controller for a DC motor using MATLAB/Simulink. The specific time frame
for the project will be announced by your tutor.
Deliverables
By the project deadline, please submit:
1) The MATLAB/Simulink files used to design your proposed controller.
2) A MATLAB/Simulink simulation model of the complete control system.
3) A project report explaining how you determined the controller design and why you made
those particular design choices.
The report should include details of your calculations and reasoning behind the design. Simulation
results and analysis can help show the effectiveness of the approach.
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Course Project Descriptor (EN7230T)
Guidelines for the Project Report
Prepare a comprehensive project report that encompasses the following tasks. Justify your selection
of the controller and demonstrate how it meets the criteria for the transient response design
specifications. Ensure that the report is clear and transparent by following these guidelines:
•
Present your results using appropriate MATLAB/Simulink plots and code (very, very strict
rule).
•
Include all m-files (editable text, no pictures) and Simulink block diagrams in the appendix
section of your report (not-so-strict rule).
•
Label the axes of each graph, including a figure legend when necessary. Specify the units in
the label itself, such as “speed (m/s)” or “time in milliseconds [ms],” to provide clarity about
the measured quantities (very, very strict rule).
•
To avoid sending multiple figures, consider using the subplot() function to group related
figures (not-so-strict rule).
•
Add comments within each m-file to describe the purpose of the MATLAB code or command
(very, very strict rule).
•
Give each graph a descriptive title and ensure that all axes are labeled and scaled accurately
(very, very strict rule).
•
If a plot includes multiple lines, include a legend that explains each curve (very, very strict
rule).
•
Do not include Simulink ‘Scope’ images in the report, as they lack proper labeling (very, very
strict rule).
•
When creating Simulink block diagrams, minimize overlapping and crossing lines as much as
possible. Rearrange icons to establish a clear left-to-right path (very, very strict rule).
•
Number your plots and graphs sequentially, such as Fig. 1, Fig. 2, and so on (very, very strict
rule).
DC Motor
The DC motor is a widely used actuator in control systems. It is capable of producing rotary motion
directly and, when combined with wheels, drums, or cables, can also generate translational motion.
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Course Project Descriptor (EN7230T)
The electric equivalent circuit of the motor’s armature and the free-body diagram of the rotor are
depicted in the accompanying figure.
In this specific scenario, we will consider the voltage source ( ) applied to the motor’s armature as
the input to the system, while the rotational speed of the shaft ( ̇) will serve as the output. Both the
rotor and the shaft are assumed to possess rigid characteristics. Additionally, we adopt a viscous
friction model, meaning that the friction torque is proportionate to the angular velocity of the shaft.
The physical parameters for our particular example are as follows:
Parameter
Description
Value
moment of inertia of the rotor
0.05 kg⋅m2
motor viscous friction constant
0.1 N⋅m⋅s
electromotive force constant
motor torque constant
electric resistance
0.5 Ω
electric inductance
0.8 H
0.05
V
rad⋅s
0.05
V
rad⋅s
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Course Project Descriptor (EN7230T)
System’s Model Derivation
Typically, the torque produced by a DC motor is directly related to both the armature current and
the strength of the magnetic field. However, in this particular case, we will assume that the magnetic
field remains constant, resulting in the motor torque being solely proportional to the armature
current . This relationship is expressed by the equation below, where the proportionality factor is
denoted as . This configuration is commonly referred to as an armature-controlled motor:
=
(1)
The back electromotive force (emf), represented as , is directly proportional to the angular velocity
of the shaft. This relationship is governed by a constant factor as follows:
= ̇
(2)
In the International System of Units (SI), the constants for motor torque and back electromotive force
(emf) are equivalent, meaning that is equal to . For simplicity, we will denote this common
constant as to represent both the motor torque constant and the back emf constant.
Using the information provided in the preceding figure, we can derive the following governing
equations by applying Newton’s second law and Kirchhoff’s voltage law:
̈ + ̇ =
(3)
+ = − ̇
(4)
Transfer Function
By employing the Laplace transform, we can represent the aforementioned modeling equations,
given in (3)-(4), in terms of the Laplace variable :
( + )Θ( ) = ( )
(5)
( + ) ( ) = ( ) − Θ( )
(6)
By eliminating ( ) between the two equations mentioned in (5)-(6), we obtain the following openloop transfer function:
( ) =
Θ̇( )
=
( ) ( + )( + ) + 2
(7)
In this transfer function, the rotational speed Θ̇( ) is regarded as the output, while the armature
voltage ( ) is regarded as the input.
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Course Project Descriptor (EN7230T)
Tasks
Part 1: Open-Loop System
In open-loop systems, there is no sensor to measure the output and compare it with the user-defined
set-point via a feedback stream, and thus there is no compensator for the mismatch between input
and output. This system can be illustrated as follows:
1.1 Substitute the numeric values of the system parameters in ( ) and re-express it again.
1.2 Using MATLAB, code the above transfer function and find the plot of its step response .
1.3 From these plots, calculate the difference between the input signal and the output signal. Will
the output reach the input, or will it have a steady-state error?
For the step response mentioned in 1.2, each student should use the following amplitude:
Student ID
202306651
202306689
202306645
202306760
202306666
202306637
202306758
202306691
202306707
202306761
202306629
202306757
202306613
0.25
0.50
0.75
1.00
1.25
1.50
1.75
2.00
2.25
2.50
2.75
3.00
3.25
Student ID
202306706
202306708
202306596
202306632
202306765
202306598
202306631
202306633
202306602
202306695
202306721
202306661
202306720
3.50
3.75
4.00
4.25
4.50
4.75
5.00
5.25
5.50
5.75
6.00
6.25
6.50
Student ID
202306764
202306684
202306719
202306638
202306626
202306620
202306667
202306705
202306603
202306747
202306671
202306615
202306690
6.75
7.00
7.25
7.50
7.75
8.00
8.25
8.50
8.75
9.00
9.25
9.50
9.75
Part 2: Feedforward Control System
One of the main objectives of embedding a control system is to ensure that the output signal,
represented by Θ̇( ), closely resembles the input signal, represented by ( ).
If we assume zero external disturbances and a perfect match between the model and the actual
system, we can incorporate the following feedforward controller to achieve the objective.
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Course Project Descriptor (EN7230T)
2.1 Find the value of the feedforward gain ( ) that satisfies the condition Θ̇( ) = ( ).
2.2 Find the inverse of the final value of ( ); i.e., calculate ( )−1 when = 0.
2.3 Compare with (0)−1. Are they the same? Why?
Part 3: Feedback Control System
The main inherent weakness of the feedforward control scheme is its inability to mitigate
uncertainty, such as unknown or unconsidered disturbances and/or imperfections in the model. Also,
there is no control on the output performance (such as overshoot, undershoot, raise time, settling
time, and offset or steady-state error). To achieve these criteria, a feedback control scheme is
suggested.
Assume the following block diagram represents the prospective feedback control scheme where a
filter is placed in series with the sensor and the process is affected by an external disturbance:
The disturbance signal is modeled as a step function of magnitude 0.2 and delayed by a time constant
of = 0.1. Thus, the step disturbance in Laplace domain is:
( ) = ℒ{0.2} =
0.2
(8)
and the time delay can be expressed as a rational function using the 2 nd order Padé approximation:
−0.1 ≈
2 − 60 + 1200
2 + 60 + 1200
(9)
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Course Project Descriptor (EN7230T)
The Laplace transform of the measurement unit’s filter is given as follows:
( ) =
1
+1
(10)
Finally, the compensator is a PID controller whose general expression in Laplace transform is:
( ) = +
+
(11)
3.1 Using Simulink, model this closed-loop system and connect the input and output signals to a
two-channel scope.
3.2 Using MATLAB or by hand, find the overall transfer function between ( ) and Θ̇( ) and the
overall transfer function between ( ) and Θ̇( ).
3.3 Apply the online Ziegler-Nichols (Z-N) tuning method to find the PID gains ( , , and ).
3.4 Apply the online Tyreus-Luyben (T-L) tuning method to find the PID gains ( , , and ).
3.5 Check these tuned PID parameters in your Simulink model and compare between the two
tuning methods. Which one has a better result? Why?
3.6 Can you reach a better result? How (state some references)? Show it numerically.
Note: there are 3 parts, each task of part 1 weighs 1 mark, each task of part 2 weighs 1.5 mark, and
each task of part 3 (except the last task) weighs 2 marks, and the last task of part 3 weighs 2.5 marks.
Plagiarism & Collusion
WARNING ON PLAGIARISM & COLLUSION
Plagiarism – is defined as the misrepresentation of another person’s ideas, thoughts or words as though they were
your own. All types of deliverables are covered by this definition, including, written work, diagrams, designs,
engineering drawings and pictures.
At Bahrain Polytechnic, we encourage independent thinking, and you are entitled to criticize other people’s
work and include it in your report. However, you MUST acknowledge your sources. This can be achieved by
quoting and citing the published or unpublished work of others, which include sources from the internet,
books, journal articles, conference proceedings, and any other credible or uncredible sources. A full
reference to the source must be provided in an appropriate format and should be included in your
References/Bibliography section of your report.
Collusion – is defined as an unauthorized conscious collaboration between two or more students in producing work
that is deemed to be identical or largely similar in content and representing the work as though they were their own.
If a tutor suspects a plagiarism and/or collusion offence in a report, then this may result in an allegation of cheating.
Such cases will be dealt with under the Bahrain Polytechnic’s procedure and may result in a severe penalty being
taken against any student found guilty and it may result in the student being expelled from the course indefinitely.
Departments can give advice about the appropriate use and correct acknowledgements of other sources in your own
work.
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