AMME3500代写、代写Python/Java设计编程

日期：2023-04-07 10:02

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.