## Dynamic Optimization Projects

#### Final Project Presentations

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).

#### Project Proposal

- Identify something that you would like to optimize that is related to a dynamic system, preferably in engineering.
- Draw a diagram of the system with all parameters and variables labeled.
- List a few articles (2-3) that give related results or locate authors that have worked in this area.
- List factors that cannot change that influence the dynamic outcome (constants / parameters).
- 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?
- List equations that describe the dynamic response such as equations of motion, mass balance, energy balance, etc.
- 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.
- 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).
- List factors that may influence the success of the project. Where are the uncertainties and how will these uncertain factors be addressed?
- 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 Report

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:

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

#### Prior Reports

- Aquaponics
- Battery Storage
- Combined Scheduling and Control - Files
- Double Inverted Pendulum - Files
- Enhanced Oil Recovery - Files
- Ethanol Bioreactor Optimization - Files
- Gas Compressor - Files
- Grid Scale Energy Storage - Files
- Home Energy Optimization
- Home Energy MPC
- Hot Air Balloon MPC
- Hybrid Power Generation Systems - Files
- Hybrid Vehicle Optimization - Files
- Orbital Rendezvous
- Pigeon and Eagle Tracking - Files
- Rocket Landing - Files
- Self-Balancing Bot
- Solid Oxide Fuel Cell - Files
- Unipol Reactor
- Unmanned Aerial Vehicle Mass Estimation - Files
- Vehicle Fuel Optimization - Video
- Zero-Carbon Grid - Video - Files

#### Example Presentation

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