Dynamic Optimization Projects

The final project for this course challenges students to apply dynamic modeling, estimation, and optimization techniques to a real-world engineering system. Each project should focus on optimizing a dynamic system by formulating mathematical models, incorporating relevant data, estimating key parameters, and implementing control strategies to improve system performance.

Students will begin by identifying a system of interest, reviewing relevant literature, and defining the key parameters, constraints, and degrees of freedom that influence the system’s behavior. Through a structured approach that includes simulation, sensitivity analysis, and optimization, students will develop solutions that enhance the system’s efficiency, reliability, or effectiveness.

The project is divided into three progress reports, each addressing critical aspects of dynamic system analysis:

Through this project, students will gain hands-on experience with dynamic optimization techniques, enhancing their ability to model, analyze, and control complex systems in various engineering domains.

Project Proposal

  1. Identify a dynamic system application, preferably in engineering.
  2. Draw a diagram of the system with all parameters and variables labeled.
  3. List a few articles (2-3) that give related results or locate authors that have worked in this area.
  4. List factors that cannot change that influence the dynamic outcome (constants / parameters).
  5. List factors that can change to influence the dynamic result (degrees of freedom or manipulated variables). Do these factors vary over the time horizon or is there one value that is adjustable?
  6. List equations that describe the dynamic response such as equations of motion, mass balance, energy balance, etc.
  7. List the contributions to your objective function such as maximization or minimization of certain variables or parameters, target values, or outcomes that are either desirable or undesirable. These are the controlled or measured variables for the application.
  8. List factors that may influence the feasibility of the solution (constraints that limit the objective, upper or lower limits on the degrees of freedom or state variables, rate of change limits, etc).
  9. List factors that may influence the success of the project. Where are the uncertainties and how will these uncertain factors be addressed?
  10. What is the timeline for the project and the anticipated final product for this project?

The dynamic optimization course is divided into 4 sections including (1) modeling, (2) data, (3) estimation, and (4) control/optimization. The purpose of the progress reports is to give intermediate check-points throughout the course. The expectations for each progress report are discussed below.

Project Progress Report #1

The first project progress report should include a description of the input to output dynamic relationships. This should include the constants, parameters, variables, and equations of the dynamic system. This project progress report should show simulation results where a feasible (though not necessarily optimal) solution is obtained. The report should also give an update on the project timeline and discuss any factors that were identified in the project proposal relating to uncertainties. This progress report should also include a discussion of the relevant articles that were identified in the project proposal. The progress report should be the draft section of the final report that includes an introduction, literature review, and model description.

Project Progress Report #2

The second project progress report should include a discussion and results related to estimation and dynamic data (simulated or actual). Include a sensitivity analysis to show the steady state and dynamic relationships between the adjustable parameters and the measured (or controlled) variables. Show estimator results to recover unmeasured states or parameters from either simulated or physical data. If the project does not include physical measurements, include appropriate levels of noise and other real-data aspects such as drift, drop-out, and outliers. The progress report should be a draft section of the final report that includes parameter or state estimation results and discussion.

Project Progress Report #3

The third project progress report should include a discussion and results related to control and optimization. Include a sensitivity analysis to show the steady state and dynamic relationships between the manipulated variables and the controlled variables. Show simulated control and optimization results that achieve a best objective. For this third phase of the project, it is not necessary to show the estimator and controller working together. Uncorrupted data and full state feedback (all states assumed to be measured) are acceptable for this progress report. The progress report should be a draft section of the final report that includes control and optimization results and discussion.

Final Project Presentations

Final presentations will be delivered during the scheduled exam period, allowing students to showcase their findings and receive feedback from peers and faculty. The final report may be formatted as a technical paper suitable for submission to a peer-reviewed conference or journal, reinforcing the emphasis on research and professional communication.

Final project presentations are 10-15 minutes each and can be pre-recorded. The final project presentations will be presented during the final exam time (3 hrs) with a webinar link for remote participants. Following each presentation, there is an opportunity for the audience to ask questions with 5 minutes of Questions and Answers (Q+A).

Final Project Report

Final Project Rubric

An objective of this project is to encourage progress on research projects and publication in peer-reviewed conferences and journals. As such, the final project report can either be a report only for this course or a draft of a manuscript that is prepared for submission. The final project report should include the following elements:

  1. Cover letter introducing the context, significance, and contributions of the paper
  2. Highlights with 4-5 bullet points that summarize the main contributions
  3. Manuscript
    1. Title, authors
    2. Abstract
    3. Introduction / Literature review
    4. Theory / Methods
    5. Simulation results / Sensitivity analysis
    6. Estimation and dynamic optimization results
    7. Discussion
    8. Conclusions
    9. References

The Research & Writing Center (3340 HBLL) is a free resource where trained consultants provide assistance on assignments. Schedule an appointment to receive writing help at all stages of the research and writing process.

Example Reports

Example Presentation

Everton Colling of Petrobras shares his experience with GEKKO for modeling and nonlinear control of distillation.

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