The assignment is provided with the file name "Design Project_1". I have further added two files by the name of "Simulink1" and "Simulink2" which might help with the assignments. Please note that the assignment is to be completed by using the simulink software. For the submission, please provide the word document along with the simulink files that you have used to finish the work.
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AMME3500 Systems Dynamics and Control Design Project 1 Due: 23.59, Sunday Week 6 Weight: 20% of your total mark. 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. We suggest you design and test your controllers using simple linearised models, but then also simulate on the true nonlinear coupled dynamics to verify performance. 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: mv̇ + 1 2 AρcDv 2 = u (1) 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 in (1) is nonlinear; there may be disturbances. Suppose the vehicle encounters a sudden transition from flat ground to a very steep uphill slope of 15% grade 1. 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. 1 For the first part of this task, 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 mv̇ + 1 2 AρcDv 2 = u+ d (2) where d is a disturbance. For the second part of this task, 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. 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; and know how to build Simulink blocks for dynamical systems. 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. 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). ẋ = v cos(ψ + β) ẏ = v sin(ψ + β) ψ̇ = v lr sin(β) 2 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 G(s) = As+B s2 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: Simulate and plot the closed-loop system response of the linear model for lane-change manoeuvre 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. Next, test the closed-loop system response when the vehicle is reversing at v0 = −10, −20 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. 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. 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 https://www.ieee.org/conferences/publishing/templates.html 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 the cover page and appendix if you decide to include them. 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%) • 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%) 4 • 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 team, 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. 5 Project Description: Cruise Control Lateral Control (Lane Changing) Report Format Marking Criterion and Procedure Mark Breakdown and Criterion Marking Procedure Feedback Introduction to Simulink AMME3500/8501/9501 Simulink Tutorial 1 1 • Block diagram environment for simulation and design of dynamical system • System-level design • Simulation • Automatic code generation • Verification of embedded systems Overview 2 User Interface 3 Blocks • Generate output signals based on input signals 4 Dynamical System Simulation • Examples • Steps: • Select blocks • Connect blocks • Verification 5 Used Blocks 6 Select blocks 7 Connect blocks 8 Verification 9 Verification 10 Select blocks 11 Connect blocks 12 Verification 13 Verification 14 How to save data? Screenshots are not recommended because data is lost. 15 How to save data? 16 How to save data? 17 How to generate a plot? • Again, screenshots are not recommended • File >> Save >> choose *.jpeg or other 18 AMME3500 Simulink Tutorial 2 Overview • Control design • Simulink validation • Presentation Problem 1: Water Tank ℎ ?? = ? ? = 1 ?? = ? ℎ ℎ · + ? ℎ = ? System dynamics: Design a controller for Test the controller equilibrium: parameter: ℎ∗ = 2,5,8 ? = 0.3,0.7,1 equilibrium: ℎ∗ = 4 parameter: ? = 0.5 Control Design • Linearized system • PI controller •