AMME3500 Systems Dynamics and Control
Design Project 1
Due: 23.59, Sunday Week 6
Weight: 20% of your total mark.
Approved Late Submissions: If you receive an approval for a submission extension, you should add a
comment along with your submission over Canvas stating your extended due date (when you submit the
work, on the top-right corner of the Canvas portal you will be able to see a button “Add Comment”).
You may also indicate your extension under the title of your report.
Late Submissions: According to our University policy, late submissions without approval will be sub-
jected to penalties: the penalty will be 5% of the total assignment mark per day; and when it is more than
ten calendar days late, a mark of zero for the assignment will be awarded.
Project Summary: This project asks you to design some of the basic components of an autonomous
car: the cruise control system and a controller for automatically changing lanes. For the parameters of
the vehicle model (masses, lengths, etc), look up or estimate numbers for your car if you own one, or the
car of a family member. This assignment draws most directly on knowledge of linearisation, second-order
systems and second-order control systems. The approach you should take is that your tutor is your boss at
your first job after graduation, and they have asked you to prepare design proposal. Therefore the report
should be of a professional standard.
1 Project Description: Cruise Control
Let a vehicle be moving in a straight line with its velocity described by v(t) at time t. We assume an
engine controller has been designed, so that the control input u is the force demanded from the engine:
Here ρ is density of air in kg/m3, CD is a dimensionless drag coefficient, and A is cross-sectional area
of the vehicle in m2 (looking from the front). Reasonable values for cD for a car are about 0.25 to 0.45
(Wikipedia has an interesting list). For your car, look up, measure, or estimate A and cD. You are asked
to complete the following design and testing tasks.
Task 1 (Linearization): Select three pairs of equilibriums (ve, ue). Linearize the system dynamics (1)
under the three pairs of equilibriums, respectively. Select initial conditions for v(0), and simulate the
three linearized dynamics to obtain three trajectories of v(t). Plot the three trajectories and explain their
similarities and differences.
Task 2 (Controller Design): Now fix the equilibrium from any of the three choices in Task 1. Design a
controller for the linear model that will precisely achieve any desired speed (reference). Demonstrate the
effectiveness of your design by numerical experiments on the linear model.
Task 3 (Validations): The controller designed in Task 2 needs to be tested before real-world validations.
There are two challenges: the controller is designed from the linear model, but the true system dynamics
1
in (1) is nonlinear; there may be disturbances. We suppose the vehicle encounters a sudden transition
from flat ground to a very steep uphill slope of 8% grade 1. The carry out the following analysis and
design for Task 3.
(1) Establish the corresponding equation of motion of the vehicle by extending the equation (1) to the
case with the slope accounted for. Show why and how the new equation of motion is of the form
where d is a disturbance.
(2) Substitute your linear controller for reference tracking from Task 2 into the system (2), and obtain
the closed-loop dynamics. Simulate the closed-loop dynamics for different reference speeds, based
on which draw a conclusion on the performance of your controller in this validation. Discuss how
the feedback gains in the controller affect the system response characteristics such as steady-state
error.
Suggested Approach: To begin the work of this part, you should be familiar with Sec 4.1 of textbook
and the lecture material (Lecture 2) on linearisation. Then Lecture 3 and Prelab in Week 3 will have
useful knowledge and practice in terms of controller design and Simulink modeling. The Lab 1 in Week 4
will also be quite relevant, among other course materials.
2 Lateral Control (Lane Changing)
For this section we look at lateral (side-to-side) motion of the vehicle, in particular for automatic lane
changes.
A schematic of the vehicle with relevant quantities is shown below. See textbook Chapter 3, Example 3.10
and Chapter 6, Example 6.12 “Vehicle steering” for a more detailed analysis. For this question, you should
assume v > 0 is constant, and the control input is δf , the steering wheel angle.
1Note that the grade of a slope is not the angle of its inclination, but rather the tangent of the angle of inclination
times 100.
2
The motion of the centre of mass (CoM) position (x, y) is described by the following differential equations
(you might like to verify this, but it is not part of the assignment). Note the coupling to longitudinal
dynamics through v(t).
In addition, we have the following algebraic equation between δf and the CoM rotation angle β:
tan(β) =
lr
lf + lr
tan(δf ).
For your car, look up the wheelbase lr + lf . For simplicity you may assume that lr = lf .
We assume the vehicle is mostly moving in the x direction (meaning: the first differential equation can be
ignored), and it is the lateral position y that we want to control.
Task 1 (Linearization): Linearise the dynamics about constant speed motion v(t) ≈ v0 > 0 with small
angles, i.e. φ ≈ 0, β ≈ 0, δf ≈ 0. Show that we get
a second-order differential equation describing how y(t) depends on δf (t); and thus
a transfer function from steering-wheel angle δf to lateral position y that has the form
Calculate the values of A and B for your car (note that A and B will depend on v0).
Task 2 (Controller Design): For the second-order differential equation describing describing how y(t)
depends on δf (t), design a controller for δf (t) so that y(t) should be able to change from one position to
another. Explain why this means the controller will steer the vehicle for smooth and accurate transition
from lane to lane.
Task 3 (Validations): Carry out the following two experiments:
(1) Simulate and plot the closed-loop system response of the linear model for lane-change ma-
noeuvre at a variety of speeds, e.g. 40, 60, 80 km/h. Explain the performance of the controller in
terms of achieving its goal in smooth and accurate lane change.
(2) Test the closed-loop system response when the vehicle is reversing at v0 = 8, 16 km/h. In
comparison with the responses obtained with v0 being positive, discuss the effect and physical
meaning of the system zero (zero of transfer function) when the vehicle is reversing.
Suggested Approach: To begin this part of the work, you should primarily get familiar with content in
Lecture 4 and Lecture 5. The Lab 2 scheduled in Week 5 will also be quite relevant.
3 Report Format
You must submit a professional-quality report as a machine-readable pdf (i.e. not scanned images) through
Canvas. By professional-quality report, it means your report should be a self-contained, consistent, and
coherent article, instead of a collection of equations, numerical plots, and answers to design questions.
3
The report must use the template double-column IEEE Conference Articles. The template, in Word or
Latex, can be found at IEEE Templates. Your report must consist of the following sections and subsections:
1. Introduction
2. Longitudinal Controller
2.1 Linearization
2.2 Controller Design
2.3 Validations
3. Lateral Controller
3.1 Linearization
3.2 Controller Design
3.3 Validations
4. Discussion and Conclusions
The subsections 2.1, 2.2, 2.3, and 3.1, 3.2, 3.3 must fully address the required tasks in above project
description.
The full report must be no more than 8 pages including EVERYTHING, e.g., the cover page and ap-
pendix. Your marks will depend not only on technical correctness, but also the way you motivate your
design choices, and the way you analyse and present the results.
The report must be entirely your own work, except where clearly indicated otherwise. Any references to
external material (papers, books, or websites) must follow the academic honesty guidelines.
Further information on academic honesty, academic dishonesty, and the resources available to all students
can be found on the academic integrity pages on the current students website:
https://sydney.edu.au/students/academic-integrity.html.
Further information for on research integrity and ethics for postgraduate research students and students
undertaking research-focussed coursework such as Honours and capstone research projects can be also be
found on the current students website: https://sydney.edu.au/students/research-integrity-ethics.html.
4 Marking Criterion and Procedure
4.1 Mark Breakdown and Criterion
The mark breakdown is indicated below. The marks should serve as a guideline for how much space to
allocate to each section.
Section 1: Introduction (5%): Clear explanation of the motivation of study; Precise and comprehensive
introduction to project scope; Organization of report.
Section 2: Longitudinal Controller (40%): Thorough investigations, clear explanation of the working, and
complete and correct presentation of the required results.
Subsection 2.1: Linearization (10%)
4
Subsection 2.2: Controller Design (15%)
Subsection 2.3: Validations (15%)
Section 3: Lateral Controller (40%): Thorough investigations, clear explanation of the working, and com-
plete and correct presentation of the required results.
Subsection 3.1: Linearization (10%)
Subsection 3.2: Controller Design (10%)
Subsection 3.3: Validations (20%)
Section 4: Conclusions (5%): Summary of the project and results; Highlight the most significant discover-
ies/understandings; Discussion on possible improvements and future directions
Presentation and clarity (10%): Pointed and critical analysis, fluent and logical arguments in the controller
design, thorough simulation discussions of the results.
4.2 Marking Procedure
You report will be assigned to a random marker from our teaching staff, and the marking will follow
strictly the above criterion.
4.3 Feedback
You may receive two types of feedback:
(1) A detailed mark breakdown of your total mark under Canvas rubrics: the score for each of the above
items listed above. Therefore, you will be able to see how well you have been doing in all parts of the
report.
(2) Additional comments and/or suggestions from the marker.
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