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ACS6116 Advanced Control 
Assignment 
Dr Paul Trodden 
 
Room C10, AJB 
P. Trodden 
Spring 2019–2020 Assignment 
ACS6116 
Advanced Control 
Assignment weighting 
25% (of the total mark for ACS6116) 
Assignment released 
Monday 23rd March 2020 (Easter vacation week 1) 
Assignment due 
To be confirmed— by the end of the academic year 
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.uk/ssid/exams/policies. 
Feedback 
This will include the overall mark, individual component marks and comments on performance 
on the assignment. The attached assessment criteria (at the back of this document) provides a 
guide to what areas the feedback will be provided on. Note that marks may be subject to change 
as a result of unfair means. 
Unfair means 
The assignment should be completed individually. You should not work together to complete 
the assignment—it 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.uk/ssid/exams/plagiarism 
for more information. 
Exenuating circumstances 
If you have extenuating circumstances that 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. 
sheffield.ac.uk/ssid/forms/circs, particularly noting point 6 (Medical Circumstances af- 
fecting Examinations/Assessment). 
Assignment briefing 
This laboratory assignment will assess your fundamental understanding ofmodel predictive con- 
trol and your ability to design MPC controllers and simulate and analyse MPC-controlled sys- 
tems. 
The assignment comprises an open-ended design and/or analysis exercise: you are asked to 
choose one of the listed topics, and tackle the described problem. Each problem includes ele- 
ments of design, simulation, and analysis. 
Produce a report (limit: 4 pages in the provided template) containing your answer. 
In order to create a level playing field between candidates’ submissions, you are asked to 
prepare your submission using the document templates supplied on MOLE. This is a 10pt, two- 
column format, which allows ample space for this assignment even with the 4-page limit. (Please 
note that no appendices are necessary and even though you may wish to include them, they 
probably will not be read.) 
It is up to you how you tackle the problem and stucture your answer. However, it is suggested 
that you look at (i) the help below and (ii) the attached assessment criteria (at the back of this 
document) for guidance on what to include. 
Assessment criteria 
The assessment criteria for this exercise are derived from themodule learning outcomes, which 
are: 
1. Describe and explain the principles of more than one advanced control technique. 
2. Analyse practical performance specifications and convert these into functional require- 
ments on controllers. 
3. Design, implement and evaluate an advanced control system against these requirements. 
P. Trodden 
Spring 2019–2020 Assignment 
ACS6116 
Advanced Control 
4. Compare and contrast different advancedcontrol solutions to aparticular control problem 
or application. 
5. Describe the receding-horizon principle, and hence compare and contrast LQ-optimal con- 
trol and MPC. 
6. Construct a constrained finite-horizon optimal control problem — including constraint, 
model and cost definition — re-formulate it as an optimization problem, and recall and 
evaluate the analytical expression for the control law in the unconstrained case. 
7. Analyse, design, implement and simulate MPC controllers with guaranteed properties, in- 
cluding feasibility, stability and offset-free tracking. 
In particular, learning outcomes 2, 3, 6 and 7 are relevant to this assessment, and the attached 
assessment criteria — the marksheet that will be used to assess the assignment — are derived 
from these. The marksheet indicates the criteria that will be used in assessing your answer, and 
also the expectation for each criterion in order to achieve a mark within the specified ranges. It 
is suggested that you study this marksheet before completing the assignment. 
These assessment criteria are deliberately broad, in order to accommodate the three quite 
different topics available. Some topics may require more emphasis on certain criteria than oth- 
ers; however, no student will be disadvantaged by topic choice. 
Please note that a 4-page limit, using the supplied template, applies to your report, and you 
should consider carefully how you can effectively meet the assessment criteria within this limit. 
Guidance 
• This assignment briefing, lecture slides, and the laboratory exercise document provide the 
main information that is required to complete this assignment. You may wish, however, to 
consult the literature relevant to your problem (especially for Topics 2 and 3) and review 
it in your report. 
• Basic M programming is required, including the use of functions and loops; however, 
in tackling the assignment you may use the MPC-specific M functions (used in the 
laboratory exercises) available on theMOLE page for ACS6116, plus any code you developed 
during the laboratory exercises. 
• The non-assessed exercises which you completed in the laboratory are good preparation 
for this assignment. However, the laboratory exercises were well structured, whereas this 
assignment is open-ended: you need to decide what is the most appropriate approach to 
solve this assignment, and also how to present your results. 
• Regarding the report, you are recommended to consult the attached assessment criteria 
for guidance on what to include and to what level of detail. In particular, the assessment 
criteria suggest that your report might need to include, among other things, 
– Details of the optimal control problem / MPC formulation you used, including the 
correct identification and implementation of constraints. 
– A description and explanation of how the controller was designed and tuned in or- 
der to meet the specification, including the selection of all parameters, with correct 
explanations and justifications. 
– Clear reporting and discussion of results (including clear, labelled plots), and critical 
evaluation of the controller. (Think about more than just, for example, “Did my con- 
troller meet the spec.?” — what are the strengths and weaknesses of your solution? 
What could be improved?) 
– Some analysis, evaluation and/or qualification of stability and feasibility — does your 
design come with stability and feasibility guarantees? If so, what are these, and how 
are they achieved? What else can you say or show? 
This is not an exhaustive list, and what you should include will vary depending on the topic 
you choose. However, a suggested outline for any report is 
1. Abstract 
P. Trodden 
Spring 2019–2020 Assignment 
ACS6116 
Advanced Control 
2. Introduction 
3. Problem statement 
4. Design 
5. Results 
6. Analysis and discussion 
7. Conclusion 
This might not be the ideal structure for your report, however, and you may wish to com- 
bineor change someof these sections, depending on the topic you choose and theprogress 
you make. 
You do not need to include the code that you write, but you may do so (e.g. snippets of 
code) if you think it adds value to your report. 
Please note that, in order to achieve the highest marks, you will need to go beyond simply 
implementing the methods that you have learned in the lectures and practised in the lab. 
That is 
• Should you need clarification or have questions on any part of the assignment then please 
just ask! (Talk to me in class, email () or come to my office (C10, 
Amy Johnson Building)). 
Submit your report via MOLE/Turnitin by 23:59:59 on Tuesday 28th April 2020 
P. Trodden 
Spring 2019–2020 Assignment 
ACS6116 
Advanced Control 
Topic 1: Frequency control in a power system 
The operation of an isolated power system under primary frequency control is modelled by the 
following block diagram. 
sTg + 1 
Governor 
sTt + 1 
Turbine 
Ms+ D 
Power 
system 
50 
Regulator 
pv pmpref ! f+ 
� 
A steam turbine produces mechanical power, pm, which is subsequently converted to electri- 
cal power at a nominal frequency (f = 50Hz) via a synchronous generator connected to the grid. 
Changes in power demand (from consumers/loads) and other uncertainties cause deviations in 
frequency,f = f�f. The control objective is to maintain these frequency deviations,f, close 
to zero. To aid this, a governor controls the steam flow input to the turbine in response to the 
error between the reference power pref and the regulated frequency deviation !=R, where 
R > 0 is the regulation factor. 
The primary frequency control loop present in the system does not, unfortunately, offer ade- 
quate control. Therefore, the aim is to design a secondary frequency control loop that will adjust 
the reference power pref in response to frequency deviations in order to improve transient 
performance. To this end, a continuous-time state-space model of the system is given as:24 _!_pm 
_pv 
35 = 
24 �D=M 1=M 00 �1=Tt 1=Tt 
�1=(RTg) 0 �1=Tg 
3524 !pm 
pv 
35+ 
24 00 
1=Tg 
35pref 
f = 
 
50 0 0 
24 !pm 
pv 
35 
In this model, the input, u = pref, is the change in reference power to the turbine governor 
(in per unit (p.u.) – that is, normalized with respect to a base value), and the output, y = f, is 
the frequency deviation (Hz). The states are the (deviations from operating points in) angular 
frequency, !, mechanical output power of the steam turbine, pm, and output power refer- 
ence from the turbine governor,pv. For the particular power system under consideration, the 
model parameters are 
M = 10;D = 0:8;R = 0:1;Tt = 0:5;Tg = 0:2 
Your task is to design, implement and tune an MPC controller for this system in order to 
meet the specification on the following page. You may assume that the state is available for mea- 
surements. To obtain the discrete-time prediction model for controller, use a sampling time of 
0:1 seconds and zero-order hold sampling (i.e. sysd = c2d(sysc,0.1) in M). 
Specification 
The controlled power system shall 
• have guaranteed stability 
• at all times, satisfy the constraints jprefj 0:5 and jfj 0:5 
• have as large an operating region as possible 
• from any initial state in the operating region, have the frequency settle to jfj 
0:01 Hz within 2 seconds 
(40 marks) 
P. Trodden 
Spring 2019–2020 Assignment 
ACS6116 
Advanced Control 
Topic 2: Rocket landing control 
The SpaceX company achieved the first successful propulsive vertical landing of an orbital-class 
rocket stage in December 20151. The rocket in question, Falcon 9, is equipped with Merlin 1D 
rocket engines, capable of vectored thrust, and grid fins which deploy from the stage-1 fuselage 
following separation; these actuators allow sufficient controllability of the rocket to permit a 
safe vertical landing. From a technical point of view, the successful landings were also enabled by 
theoretical advances in how the kind of nonlinear optimal control problem associated with safe 
rocket landing can be modelled and solved2. 
A simplified model of the rocket landing problem—assuming that “nose-up” stabilization is 
handled separately—views the rocket as a point mass, m, with position r = 
 
A non-exhaustive list of suggestions for what your investigation could include: 
• Whether the system can be stabilized, by tuningQ, R and N, without using stabilizing termi- 
nal ingredients (i.e., a stabilizing P and/or terminal set). 
• Whether the use of stabilizing terminal ingredients can stabilize the system and, if so, what 
those terminal ingredients should be. 
• How sensitive the problem is to the magnitude of the output constraint; for example, if the 
limit on y(k) is increased to 1+ , what value of is needed to ease the instability problem. 
• Exploration of the region of feasibility (set of states for which the problem is feasible) and 
region of attraction (set of states from which the system may be stabilized). 
(40 marks) 
3K. R. Muske and J. B. Rawlings (1993), Model predictive control with linear models, AIChe Journal 39(2), 262–287. 
https://doi.org/10.1002/aic.690390208 
P. Trodden 
Spring 2019–2020 Assignment 
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