AMME3500 Systems Dynamics and Control Design Project 2 Due: 11:59pm, Friday Week 13 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 apply the knowledge and tools that have been taught in this course to (1) find and (2) model a real-world dynamical system application, and then to (3) define and (4) solve a problem that you identified for that application. Then you write a report on your work as a scientific article. This assignment is worth 20% of your course mark. 1 Instructions 1.1 Knowledge and tools After Week 9 we will have completed the discussion on following major aspects of dynamical systems: (i) Dynamical behavior analysis from state space: Stability, Steady-state, Time-domain specifications, etc. (ii) Feedback controller design from state space: PID control, State feedback, Output feedback. (iii) Dynamical behavior analysis from frequency responses: The Body Plots. You can use ONE, TWO, or ALL of the above fundamental tools in this design project. 1.2 Finding and Modeling an Application Your project can focus on ANY application. You find such an application by (i) Past experiences: you have ever taken another course where you learned a type of dynamical system; you may have encountered a dynamical system in your own life, e.g., riding a bike, baking a turkey, etc. (ii) Research: you can find an application in a specific domain that you are passionated or simply curious about by researching. Google Scholar and Wikipedia will be your good friend helping you establish a quick overlook to a field. 1In the lectures we mentioned a number of such examples for dynamical systems in real world. The textbook also covers a comprehensive set of examples from various domains. In Week 8, Prof Altafini in this guest lecture presented examples of dynamical systems in social and biological systems. Dynamical systems are everywhere. More specifically, we have the following major categories: • Mechanical systems: vehicles, aircrafts, spaceships, rockets, robotics, Atomic force microscope • Electrical systems: batteries, circuits, power electronics, solar panels • Biological systems: animal groups, populations, RNA-protein dynamics, neurons • Social and political systems: social opinions, voting, wars and conflicts • Economical systems: markets, investments • Biomedical systems: disease treatments, pharmacodynamics • Communication systems: wireless communications, computer-to-computer systems • Transportation, agriculture, food production, warehouse, … The whole world is yours! 1.3 Problem definition and solving Come up with a problem based on the real-world needs; Define the problem clearly; Solve the problem fully or partially. In DP1 Cruise Control, the real-world problem we found was to maintain a constant speed for a car by autonomous feedback control. Then we defined the following tracking problem: y(t) should track a reference signal r by feedback controller design facing uncertainties from the car itself and from the environment, i.e., the slope. And we solved the problem! 1.4 Your approach The approach you should take is that this should be an exploration of the applicability of System Dynamics and Control that you have learned. It is perfectly fine that you identify a dynamical system, saying, the human brain, but it turns out the knowledge and tools so far cannot handle that problem. In that case you give your reasoning on why the current methods would fail, and conclude that we might need tools from the Advanced Control course. So you can take risk. Also note that just as DP1, as engineers, besides applying the tools in textbook, we also investigate and validate the design by considering practical complexities and uncertainties. Such practical challenges may come from • Parameter Uncertainty. The true parameter of the system might differ from what you used in the design, e.g., the passenger uncertainty in DP2. • Disturbance. Your actuator might inevitably have disturbances due to practical conditions, e.g., the uphill slope in DP1. • Nonlinearity. The true system might contain nonlinear dynamics, e.g., the lane-change design in DP1. 2You need to validate these practical conditions for your solutions. Therefore, first you need to ask yourself and establish the following in your design of validation experiments: what parameter uncertainty, disturbance, and nonlinearity can take place under what conditions for my problem? Then these issues can be similarly tested by Matlab/Simulink as what we did in DP1. You can also evaluate the Phase Margin and Gain Margin of your system after you have designed a controller by looking into the look transfer function! Embedding some nice Bode diagrams and/or Nyquist diagrams would make intuitive explanations to the readers. 2 Report Format You must submit a professional-quality report as a machine-readable pdf (i.e. not scanned images) through Canvas. The report should be of a professional standard in the form of a scientific article. We judge your report by the clarity of the motivation and problem, completeness of the analysis and design, and finally the level of innovations (or attempts for innovations). Your report must be at most 8 pages using IEEE-Style word or latex template1 , and must consist of the following sections, where a guideline for how much space to allocate to each section is indicated: 1. Introduction [10%] 2. System Model and Problem Definition [40%] 3. Solutions and Numerical Validations [45%] 4. Conclusions [5%] Unlike your problem sets and PS01, this is an open project where nothing stops you from working on anything. Enjoy such freedom and be a thinker! 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 guidelines introduced in Lecture 1. After the course, if you like to extend this design project and the resulting report to reach a professional technical report or even a published article, we will provide to you further technical and scientific writing supports. 3 Some Tips on Scientific Writing The standard for your report is a professional article. It is actually not hard to make your report a professional one (at least look like a professional one) if you pay attention to the following basic places: (1) Having logical transitions: Your report should present a fluent logical flow of the problem statement – analysis – design – validation – discussion pipeline. For example, after you have established the system equations, you can have a simple sentence “As we see, the system equation turns out to be nonlinear, which is in general difficult to analyze. Therefore, we next use the technique technique to linearize the equations. We begin the linearization by …” (2) Clarifying notation: When you introduce any parameter, variable, give the full and precise defini tions. 1The templates are available under the assignment description of Canvas. 3For example, after introducing a complex equation, you can explain “Here a is.., y represents …,” If too many parameters are involved, you can make a list! See Lab 4 instructions. (3) Detailing the experiments: Give the full details of your numerical experiments, and explain the content and indication of the plots. For example, after you made a plot for a closed-loop response, you should write “Now in Figure ?, we plot the trajectory of the system output y” and then “From the plot, we can see that … happens, which suggests our design has been feasible/questionable for practical use.” A very good practice is, to place yourself as a reader of the report, and ask: Can I understand this part as a reader? If the answer is affirmative then it means it is good writing. 4 Marking Procedure As this is an open project, there are no longer prescribed questions that we all need to answer in the reports. We impose the following marking guidelines for each section of the report. 1. Introduction [10%] The introduction should clearly present an overview of the background of the project, the problem under investigation, and the significance/usefulness of the established solutions. 2. System Model and Problem Definition [40%] This section should present a clear system model, where each parameter/signal is specified; provide a clear problem definition in both practical and mathematical terms. 3. Solutions and Numerical Validations [45%] This section should clearly present the ideas/procedure of the design methods; show the designed controllers and the resulting closed-loop system; pose practical challenges in terms of uncertainty, disturbances, and nonlinearity; and validate the closed-loop system against practical situations. 4. Conclusions [5%] This section should concisely summarize the whole work, and discuss possible weakness/future work of the design. In addition, a total of 10% innovation bonus points will be available for encouraging attempts on new, challenging, and practically important projects. This means you can potentially receive 110 marks for this assignment. 5 Some Guidelines 1. System Model and Problem Definition If it is from literature, then present a thorough literature review on this model. In this literature review, you should explain how the model was derived in the literature, and to what extent the model has been useful. If the model is derived from first principle, then present the detailed derivation process. 2. Solutions and Numerical Validations Test your controller against your model. Explain whether or not the closed-loop dynamics achieves your goals. If the goals are met, explain that by numerical results. If the goals are NOT met, also 4explain that from the numerical results and provide your thoughts on why the controller does not work. Discuss why the particular uncertainty arises from real world, how it influences system equations, test the closed-loop system in the presence of such uncertainty and show numerical results. Discuss why the particular disturbance arises from real world, how it influences system equations, test the closed-loop system in the presence of such disturbance and show numerical results.