ACS6101: Foundations of Control Systems
Period: Weeks 13
Dr Viktor Fedun, v.fedunsheffield.ac.uk, Room C9 Amy Johnson Building Professor George Panoutsos, g.panoutsossheffield.ac.uk, Room B15 Amy Johnson Building
Assignment weighting
50 of module
Assignment released
Week 2
Assignment Due and Submission Instructions
End of Week 6 Sunday 23.59, 10 Nov. You must submit the completed assignment to the relevant ACS6101 MOLE page, via Turnitin, as a single document Part APart B. You must include your registration number at the top of every page. Your report should be word processed, using minimum size font 11, minimum 2.5cm margins all around.
Penalties for Late Submission
Late submissions will incur the usual penalties of a 5 reduction in the mark for every working day or part thereof that the assignment is late and a mark of zero for submission more than 5 working days late. For more information see http:www.shef.ac.ukssidexamspolicies.
Feedback
No later than 23 weeks after the submission deadline. The feedback will include the overall mark, individual component marks as well as written comments on performance on the assignment electronic format. You will also have the opportunity for onetoone feedback. General feedback on the whole class performance will also be provided via email and on MOLE. Note that final marks may be subject to change as a result of unfair means.
Unfair Means
The assignment should be completed individually. You should not discuss the assignment with other students and should not work together in completing the assignment. The assignment must be wholly your own work. References must be provided to any other work that is used as part of this assignment. Any suspicions of the use of unfair means will be investigated and may lead to penalties. See http:www.shef.ac.ukssidexamsplagiarism for more information.
Special Circumstances
If you have medical or personal circumstances which cause you to be unable to submit this assignment on time or that may have affected your performance, please complete and submit a special circumstances form along with documentary evidence of the circumstances. See: http:www.shef.ac.ukssidformsspecial
particularly noting point 6 Medical Circumstances affecting ExaminationsAssessment.
Help
This assignment briefing, the lecture notes, and the laboratory handouts all available on MOLE provide all the information that is required to complete this assignment. It is not expected that you should need to ask further questions. Remember that you need to decide on what is the most appropriate approach to carry out the simulations and present your results. This is also part of what you are being assessed on and will assess your knowledge and understanding of the taught material for ACS6101. However, if you need clarifications on the assignment then please feel free to email the relevant lecturer.
You must complete both parts of the assignment !
Part A 25 of overall module markcontent from Week 1
Marking Criteria: Apportioned Marks for questions are Q1: 40 Q2: 60
In doing the assignment Part A, you should be prepared to use the MatLab help system and the course notes, and to do some of your own research to learn about functions or features you may need.
Your answers should consist of the code used to solve the problem and example output where appropriate. Graphs or pictures should be saved in .png format. The code should be headed with comments that include the title, description of the purpose of the code and an explanation that guides the reader through the workings of the code. Comments should also include the question number, your name and the date the code was finished. There is no limit to code length, but the work should not require more than 2030 lines of code for each problem.
Put all of your code, output and plots into a report PDF file format which you will
submit via Turnitin, as a single document Part APart B. Your codes must also be submitted as separate .m files MatLab scripts and function to Dr. V. Fedun via email : v.fedunsheffield.ac.uk.
You may discuss with other students how to approach each problem, but you must write all your own code and all your own report. Your submission will be checked for plagiarism using turnitin.
For each question, marks will be awarded for:
the quality of your description;
whether your code runs or not;
elegance and design show that you have thought about the best way to
solve the problem;
simplicity and clarity simple and clear is better, sensible variable names,
formatting, comments etc.;
readability description, indenting, presentation, comments etc;
correctness giving exactly the right answers;
consistency.
Question 1
Write a script to do the following:
a create the following matrices and vector y:
2 4.1 2 3 2 1.1 2 3.3 4.1 2 5 8.1
1 3 2.2 1.5
1 3 9 2
5 8 4 3 10 16 8 6 2 3 1 8
1 y 2 2
4
b in well presented way and with some attempt to guard against poor user input, ask the user to choose one of the matrices and assign it to a variable A.
c if the determinant of A is nonzero, find the eigenvalues and eigenvectors of A and the solution x to the equation Axy, or display an appropriate message otherwise
clear the workspace and command window at the start of each run and output all results to the command window.
Question 2
Differential equations to model the HIRES reaction problem1 are:
0234 5 8
1.710.438.3200.007 1.718.75
10.0300.4320.0353
8.321.7101.122
1.74530.4340.435
280460.6921.7130.4340.695 280461.815
280461.815
a Create a function called HIRES.
The function should have two input args ordered like this: t, x.
The function should return one output arg a 81 sized vector called xdot computed within
the body of the function using the equations above.
Note: The arg t is unused within the function but is necessary to be in the arg list if HIRES is passed to one of Matlabs ode solvers.
b Write a script that
calls the Matlab function ode45, using your HIRES function as an input, to obtain a
solution over a time interval 0 to 300 seconds, with initial conditions 1, 0, 00,20,30,40,50,60.0057. Make your call ofode45for the function HIRES in anonymous function style rather than as a string. See matlab help for guidance.
Use the options arg with your solver to set RelTol to 1e3 and AbsTol to 1e 6.
Use tic and toc to find the execution time for the ode45 call and save to a suitably named variable.
c Add to your script to repeat the task again, only this time use ode15s.
d Further add to your script to
Plot the eight returned components of xdot from your ode45 call in one set of axes in a
subplot, and the eight returned components of xdot from your ode15s call in another
subplot, arranging the subplots one above the other in the same figure.
Use a logarithmic xaxis.
Label the axes as Concentration for the y axis assume units are moldm3, Time for the x
axis assume units are seconds, and add a legend placed northeast within each plot to
identify the eight reagents.
Set the figure to occupy the left half of full screen when the script is run.
Create a twoline title for each plot, giving the title of the plot in line 1 and the execution
speed, and AbsTol, RelTol values on the second line. Make the second line of the title blue colour and fontsize 9.
e Further add to your script to produce a second figure and
In the second figure make eight subplots eight rows, one column and in each subplot
overlay a plot of the first 100 points of data obtained from ode45 and ode15s.
Plot ode15s as a green line and ode45 as black dots.
1 Ref: https:www.radford.eduthompsonvodef90webproblemsdemosnodislinDemosPitagoraDemoHiresdemohires.pdf
Give each subplot a title, axes labels and a legend.
Set the figure to occupy the right half of full screen when the script is run.
Part B 25 of overall module markcontent from Week 2
THIS PART OF THE ASSIGNMENT MUST BE COMPLETED IN 8 SIDES OF A4 PAPER. NO MARKS WILL BE AWARDED FOR SOLUTIONS BOYOND THE LIMIT OF 8 SIDES.
This assignmentreport will assess your fundamental understanding of systems modelling and simulation, including basic use of MATLABSimulink. The assignment is based on content from Week 2, part of ACS6101
The assignment is divided into two sections: B1 Basic concepts B2 Advanced concepts. The expectation is for section B1 to assess your understanding of the basic concepts in the module and associated learning objectives, while section B2 is to challenge your understanding in more advanced topics.
In your report you need to address all questions in each part, include your working methodology, the resulting MatlabSimulink plotsdiagrams, and brief discussion of the results.
Marking Criteria
This this is the marksheet below that will be used to assess the assignment. The marksheet indicates the marks available for each part of the assignment and also indicates some of the factors that will be used in assessing the qualitycorrectness of your work. It is strongly recommended that you study this marksheet before completing the assignment.
Assignment Task
Marking Guideline
Apportioned Mark
Section B1
Task 1
This is a theoryrelated task, marks will be awarded for demonstration of correct understanding of the topic
5
Task 2
This is a theoryrelated task, which also includes a practical aspect. Marks will be awarded for demonstration of correct understanding of the topic as well as correct final solution and methodology.
5
Section B2
Task 1
This is a theoryrelated task, marks will be awarded for demonstration of correct understanding of the topic
5
Task 2
This is a theoryrelated task, which also includes a practical aspect. Marks will be awarded for demonstration of correct understanding of the topic as well as correct final solution and working out methodology.
8
Overall Report for Part B
To assess your report writing skills, marks will be awarded for report structure, clarity of writing, use of figurespictures as well as references.
2
Total: 25
Please answer all questions in Section B1 and Section B2. Section B1
Task 1
Derive a linear approximation mathematical model of the pendulum system shown in Figure 1 to describe the relationship between the torque developed on the mass M and the angle theta between the rod and the vertical plane. State clearly your assumptions and your modelling methodology.
Figure B 1
Task 2
For the mechanical system simplified car suspension shown in Figure 2:
a. Derive the mathematical model of the system in the time domain to describe the displacement associated with the three masses M1 wheel, M2 chassis and M3 car seat, and represent the mathematical model in its matrix form
b. Derive the transfer function model of the system
c. Derive a state space representation of the system, and represent it in its state space matrix form.
Clearly state any assumptions you may make.
Figure B 2
Section B2
Task 1
What is a signal flow graph, and how does it compare against the block diagram representation? For the system modelled in Part A, Task 2 derive the signal flow graph working methodology and diagram.
Task 2
In this part of the assignment the aim is to study the behaviour of a dynamic system, via modelling and simulation methods.
Using the ACS6101 handout Practical simulation experiments using SIMULINK select one system only for this part of the assignment. You must follow the rule:
Sum all the numbers of your student registration number you can find this in you Ucard to a single digit ODDEVEN NUMBER, then select a system according to the list provided below.
For example: Student ID: 0123456789, sum of all digits: 012345678945, 459 ODD NUMBER, System: 1: Depth Control for a Torpedo.
System selection List:
System 1. ODD NUMBER Depth Control for a Torpedo
System 2. EVEN NUMBER Positioning System
you need to show in your report the above calculation and the resulting system that is selected for analysis
For the simulation system, in your report you should include 1 A brief introduction to the system and its modelling. 2 your main results obtainedwith justifications of work when necessary from completing each task as in the lab sheet, and 3 a brief conclusion section that summarises the analysis of the system.
END OF ASSIGNMENT BRIEFING
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