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ECMM136
UNIVERSITY OF EXETER
FACULTY OF ENVIRONMENT, SCIENCE AND
ECONOMY
ENGINEERING
Term 2, 2023
Systems Analysis in Engineering
Module Convenor: Dr Halim Alwi
Systems Analysis Using MATLAB and SIMULINK
Date Set: 3rd October 2023
Date Due: 30th March 2023 (Thursday) @ 1200 (to be confirmed)
Return Date: 4Th May 2023 (to be confirmed)
Method of submission and file type: eBART (zip)
This coursework comprises 30% of the overall module assessment.
This is an individual exercise, and your attention is drawn to the guidelines on collaboration
and plagiarism in the College guidelines.
(See http://intranet.exeter.ac.uk/emps/studentinfo/studentservicesandprocedures/studentresponsibilities/
and http://intranet.exeter.ac.uk/emps/studentinfo/subjects/engineering/assessment/academicmisconduct/
for further detail).
This coursework tests your understanding of Systems Analysis using MATLAB and
SIMULINK.
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System description: Longitudinal model of a B747-100/200
This coursework deals with the system analysis of an aerospace system. Specifically, the
coursework deal with modelling, simulation and control as well as sensitivity/uncertainty
analysis of the longitudinal axis of a B747-100/200 aircraft.
To help with the general understanding of the system, the typical longitudinal axis states and
inputs of an aircraft are given in Figure 1.
Figure 1: aircraft longitudinal axis (states and inputs)
A simplified model, known as a linear parameter varying (LPV) model, can be used to
represent the actual B747-100/200 aircraft. The states of the model are () ∈ ℝ5×1 given
by:
() = [ ℎ] (1)
which represents pitch rate (rad/s), speed (m/s), angle of attack (rad), pitch angle (rad) and
altitude (m). The inputs are () ∈ ℝ3×1 given by:
() = [ ]
(2)
which represent elevator (rad), stabilizer (rad) and thrust (N). The underlying equation of the
LPV model is given by the following equation:
̇() = ()() + ()() (3)
Where the matrices () ∈ ℝ5×5 and () ∈ ℝ5×3 are defined as:
() = 0 + ∑
7
=1
(4)
() = 0 + ∑
7
=1
(5)
The LPV varying parameter is given by:
Elevator
Stabiliser
Positive
deflection
Positive
rotation
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= [1 2 3 4 5 6 7] = [
2 2 3 4] (6)
which is a function of the angle of attack and the speed .
The control requirement for the flight path angle (rad) (defined as = − ), and the
velocity tracking performance specifications are given in Table 1 below:
Controlled states Performance specification
Flightpath angle 0 to 3 deg in 10 s
Velocity 0 to 10 m/s in 10 s
Table 1: Controlled states and their performance specification
The typical range for the inputs are given below:
Inputs Typical range
Elevator [-1 1] deg
Stabilise [-1 1] deg
Thrust [−1 × 10
5 1 × 105] N
Table 2: Inputs and their typical range of operation
The signals and used in LPV parameters in (6) may contain uncertainties, and their
range of uncertainties are specified below:
LPV signal source Uncertainty Range
[-1 1] deg
[-5 5] m/s
Table 3: The LPV signal source uncertainties
Preparation
• To complete this coursework, you need to download the zip file "B747_LPVplant.zip"
file from the Coursework section on the ELE page for this module.
• To use the file within MATLAB, you need to save the zip file to a local directory, unzip the
file and select the directory as your current folder in MATLAB.
• The zip file contains two files. The "B747_LPVplant.mat" file contains all the matrices
for () and () associated with the LPV model (see equations (3)-(6) above) while the
file "B747_LPVplant_init.m" is the main MATLAB program.
• You should use the "B747_LPVplant_init.m" file to initialise all the parameters in the
model and other programs/codes to solve the tasks associated with this coursework.
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Tasks
Using MATLAB and SIMULINK, complete task 1 to task 5.
Task 1 (30 marks)
Create a SIMULINK model to represent the longitudinal axis of the B74-100/200 using
equations (1)-(6) given above.
To test whether your model is implemented correctly in SIMULINK, you can perform a simple
test by perturbing the state pitch rate by 1 deg/s at the beginning of the simulation and
check the behaviour of all the states in the model.
Remarks:
• Some information on simple aircraft modelling can be found here.
• States perturbation can be made by setting nonzero initial conditions in the states
integrator.
• Be careful about units while modelling. Note that some of the units for the inputs and
states of the model (1)-(6) are in rad or rad/s, while the specifications given in Table 1-
Table 3 are in deg or deg/s.
Task 2 (10 marks)
Perform a sensitivity/uncertainty analysis of the open-loop systems using the one-factor-at-a-
time method and plot the tornado graph. Identify the parameters (input/uncertainties) that
affect the system's states the most.
Remarks:
• Note that, for sensitivity/uncertainty analysis, the nominal values of all the states () and
inputs () are zero.
• The sensitivity/uncertainty analysis must be performed for all inputs () as well as the
uncertainties in the LPV parameters.
• Step inputs (with magnitude set as a variable) can be used as a type of input
signals ().
Task 3 (10 marks)
Implement two PID controllers to track flight path angle γ (using the elevator) and velocity V
(using thrust). Tune the PID controllers to ensure the tracking performance in Table 2 are
satisfied, with minimal coupling effect.
Remarks:
• Use square inputs as the command signals. For example, for the command signals for
flight path angle , first, perform +3 deg for 10 s and followed by -3deg for the following
10 s to return the command signal back to zero.
• To ensure decoupled performance, the command signals for flight path angle and
velocity need to be set at a different time.
• The SIMULINK standard PID block to tune the PID controllers can be used to aid the
tuning process.
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Task 4 (30 marks)
Implement the "Latin Hypercube sampling" method (or at least the "brute-force" method) and
perform the sensitivity/uncertainty analysis for the closed-loop system. Identify the
parameters that affect the performance of the two PID controllers (the tracking of flight path
angle and speed ).
Save all the variables in the simulation results as a mat file. This will need to be submitted as
part of the submission files (see Instructions section later).
Remarks:
• For sensitivity/uncertainty analysis, the nominal values of all the states () and inputs
() are zero.
• The sensitivity/uncertainty analysis must be performed for all command signals as well
as the uncertainties in the LPV parameters.
• To analyse the performance of the PID controllers, you can analyse the error signals ()
between the commanded signals and the actual measurements.
• To create a random number, use MATLAB command “rand”
Task 5 (10 marks)
Discuss the possibility of using the genetic algorithm to help tune the controller that will be
able to handle all variations in the command signals and uncertainties. Discuss how can this
be achieved using MATLAB and/or SIMULINK.
Remark:
• You can use the knowledge provided in Workshop 7 or 8 or lecture notes on genetic
algorithms to help you with this question.
Presentation (10 marks)
• Marks will be given for clarity of writing and overall readability of the report.
• Diagrams, figures and graphs must be neatly presented, with labels and titles and all
pages must be numbered.
• All discussions must use the correct use of mathematical notation, sufficient comments
and clear workings/procedures for the marker(s) to follow your process.
• Where practicable, you should also show how you have checked your answers.
• MATLAB codes and SIMULINK diagrams must be clearly described with sufficient
comments.
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Instructions
• This coursework submission has two parts:
a) A report in PDF
b) Simulation files that implement the model *. It should contain:
i. One m file and
ii. one SIMULINK (slx) file
iii. one mat file.
• ZIP all four files (PDF, m, slx and mat) before submitting to eBart**
• File naming convention***:
o CWeBartCandidateNumber.pdf
o CWeBartCandidateNumber_init.m
o CWeBartCandidateNumber.slx
o CWeBartCandidateNumber.mat
For example:
o CW123456.pdf
o CW123456_init.m ****
o CW123456.slx ****
o CW123456.mat ****
o CW123456.zip
Remarks:
* The submitted simulation files should run task 4 (tasks 1-3 can be commented).
** Make sure that the files submitted are the correct file type. An incorrect file type may fail to
open and thus preventing it from being marked.
*** If you are not sure what your eBart candidate is, check the eBart submission page.
**** Note that MATLAB and SIMULINK do not allow filenames to start with numbers.
Therefore, start with the letters CW followed by your eBart candidate number.
The ZIP file for this coursework must be submitted to e-BART (https://bart.exeter.ac.uk -
Faculty: ESE, location: Harrison) by 12:00 noon on the date indicated on the front page of
this document.
In the report, you should address all questions/tasks posed above, which should be brief
and to the point. Include all the modifications made to the original code and functions (if
any). Furthermore, you should include the MATLAB commands or SIMULINK diagrams you
used, and the text or image output produced. Finally, you should include the reasoning and
motivation behind the choices made.
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Instructions (continued)…
MATLAB Version requirement: MATLAB R2022a
If you are using MATLAB later than R2022a, please save your SIMULINK file to the R2022a
version – In SIMULINK, Menu>File>Export Model to>previous version>select R2022a
models.
Report (PDF) formatting requirement:
• The report should not exceed ten A4 pages (or approximately 4000 words - when
excluding plots/figures/codes).
• Only Arial or Calibri Light font styles may be used, and text should be justified left.
• You should use a minimum font size of 11.
• Margins must be at least 2cm in all directions.
• The document size should be standard A4 size, single column.
• All pages must be numbered.
• The report needs to include an introduction and conclusion sections (both need to be as
brief as possible).
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Marking Scheme
Criteria Marks
• Has the SIMULINK model been implemented correctly?
• Does the open-loop model behave as expected when perturbed (by
1deg/s) in the pitch rate () channel?
30
• Does the sensitivity analysis of the open-loop systems using the one-
factor-at-a-time method and plot tornado graph implemented and coded
correctly?
• Do the parameters that affect the system's states have been identified?
10
• Have the PID controllers (to track flight path angle and velocity ) been
designed and implemented correctly (tracking performance with minimal
coupling effects)?
10
• Has the Latin Hypercube (or at least brute-force) sampling method been
implemented correctly?
• Does the sensitivity analysis of the PID tracking performance when
subjected to uncertainties been done?
• Do the parameters that affect performance been identified?
30
• Are there any discussions on the possibility of using the genetic algorithm
to help tune the controller that will be able to handle all variations in the
command signals and uncertainties? And how can this be achieved?
10
• Presentation - clarity of writing and overall readability of the report 10
Total 100