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ACS6101 – Control Systems Design Assignment

ACS6101 – Foundation for Control Systems

Control Systems Design Assignment

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 https://www.sheffield.ac.uk/ssid/assessment/grades-results/submission-marking

Unfair means

This is an individual assignment. You should not discuss the assignment with other students or work together with other students in its completion. The assignment must be wholly your own work. References must be provided to any other work that is used as part of the assignment. Any suspicion of the use of unfair means will be investigated and may lead to penalties. For more information see https://www.sheffield.ac.uk/ssid/unfair-means

Extenuating circumstances

If you have any medical or special circumstances that you believe may affect your performance on the assignment, then you should raise these with the Module Leader at the earliest opportunity. You will also need to submit an extenuating circumstances form. For more information, see https://www.sheffield.ac.uk/ssid/forms/circs

Feedback

No later than two weeks after the submission deadline. The feedback will include overall mark, individual component marks as well as written comments on performance on the assignment (electronic format). Note that final marks may be subject to change as a result of unfair means.

Learning Outcomes

On completion of the assignment, students should demonstrate:

● Understanding of the design methodologies for lead and lag compensators based on root locus and Bode diagram.

● Ability to design and test a controller starting from performance specifications.

● Ability to use MATLAB in the design process.

Help

This assignment briefing and the lecture notes 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 the most appropriate approach to solve the assignment is and also how to present your results. This is part of what you are being assessed on and will assess your knowledge and understanding of the lecture notes.

Notes

● Remember that in an assignment, there is often no standard “staff answer”. You have the freedom to investigate any aspect of the problem that you think is relevant. Credit will be given for those students who display creative and investigative skills in their submitted work.

● If you cannot meet the specification of the problem exactly with your solution, submit that part you have succeeded with rather than nothing at all. Credit will be given to those students who have carried out a second iteration of the design process and have succeeded to improve the performance compared with the initial design.

● You are reminded that this assignment must be carried out independently and the written submission must be the student’s own work. Your assignments will be submitted through Turn-it in and checked for potential plagiarism – any unfair means identified will be investigated, and penalties may be applied.

Assignment Briefing

● Your assignment should be written as a worded document, not just a series of mathematical steps.

● Within your answer to each question, you should provide an introduction to the solution, provide the solution as the ‘body’ of your answer, and conclude your answer, with respect to the performance specification provided. Each answer should be self-contained, and not refer to a previous or subsequent question.

● Make sure that you explain clearly all the steps in your calculations, write down the equations used, explain the notation, and the choices you made during the design process.

● The report should be word processed. Use Arial 11 point font throughout. Page margins should be set to ‘normal’ (top-bottom-left-right margins all set at 2.54cm).

● Line spacing must be set to “1”.

● Figures should be incorporated into the document in appropriate places (not as appendices) and suitably sized for the information contained.

● You must include your registration number at the top of every page.

● Appendices are not allowed and will not be marked.

Marking Criteria

The assignment contains two questions. Each question is worth 20 marks and there are 5 additional marks for report writing skills. To assess your report writing skills, marks will be awarded for report structure, clarity of writing, use of figures/pictures as well as references. The marks awarded for each subtask of each question are provided in the assignment brief below, and will be used in the marking process.

Questions

1) Consider the unity feedback control system where the plant transfer function is given by:

a. Using the frequency domain approach, determine the gain K required to give an overshoot, in response to a step input, of no more than 10%. Explain how you achieved your result.

(6 marks)

b. Using frequency domain approach, design a phase-lead compensator to achieve a velocity error constant no less than 25 and a step response overshoot of no greater than 10%. Describe each stage of your design. If specifications are not met, perform additional design iterations.

(9 marks)

c. Use MATLAB to plot the response of the control system, (designed in b.), to a unit ramp, showing both system output and ramp input, and evaluate the percentage steady state error to the ramp input signal.

(3 marks)

d. Use MATLAB to evaluate the performance of your final design in the time and frequency domain. Present these in tabular form – see Table 1, and provide a written conclusion for your design.

(2 marks)

2) Consider the unity feedback control system where the plant transfer function is given by:

a. Determine the location of the dominant poles of the closed-loop transfer function in order to achieve the following performance specification for a unit step input:

○ The settling time for a step input should be less than 2.5 seconds

○ The overshoot should be no more than 20%

(4 marks)

b. Demonstrate analytically that the desired poles do not belong to the uncompensated root locus.

(4 marks)

c. Use the root locus approach to design a cascaded phase-lead compensator with the zero placed in −1, to yield the desired specifications. Describe clearly each stage of your design. If specifications are not met, perform additional design iterations.

(6 marks)

d. Design a phase-lag compensator in series with the phase-lead compensator in part c. such that the steady state error ess for a parabolic input 0.5At² is less than 2.5% of A. Describe each stage of your design.

(4 marks)

e. Use MATLAB to evaluate the performance of your final design in the time and frequency domain. Present these in tabular form – see Table 1, and provide a written conclusion for your design.

(2 marks)