(459d) Teaching Data-Centric Process Control Using Experiential Learning

Process control should be one of the most exciting chemical engineering undergraduate courses! This presentation describes our experience transforming "Chemical Process Control" into "Data Analytics, Optimization, and Control" at the University of Notre Dame (required in the second semester of the junior year). In six hands-on experiments, students practice data-centric modeling and analysis using the Ardunio-based Temperature Control Lab (TCLab) hardware. The semester learning goals are:

1. Develop mathematical models for dynamical systems from data and first principles using modern statistical methods;
2. Predict dynamical system performance using numerical methods;
3. Analyze, implement, tune, and debug feedback controllers using the hands-on laboratory;
4. Formulate and solve optimization problems for decision-making;
5. Demonstrate mastery of at least two of the above skills in an open-ended group project.

The goal of this presentation is to share our strategy to modernize process controls. The main body of the talk describes the course organization and assessment mechanisms. We conclude by sharing our plans to future improve the course by incorporating more data science topics including maximum likelihood estimation, Fisher information, model-based design of experiments, and model selection.

The semester topics are organized into three parts, as described below.

Part 1: Data-Centric Modeling of Dynamical Systems

Classical process control focuses on frequency-domain analysis. While the frequency domain perspective provides beautiful insights into certain aspects of controls (e.g., time delays and responses to periodic inputs), it requires dedicating a significant portion of the semester to teaching Laplace transformations. Instead, we emphasize state-space modeling, which naturally complements the (partial) differential (algebraic) equation models taught in other core chemical engineering courses such as transport, kinetics, and thermodynamics. As prerequisites, our students have completed five mathematics courses (Calculus I, II, III, linear algebra and linear ODEs, differential equations) and a numerical methods and data analysis course. We build upon this foundation by using numerical simulation and eigendecompositions to assess the properties of dynamical systems. For example, for the TCLab, we perform step tests and nonlinear regression to estimate heat transfer coefficients and heat capacities in one- and two-compartment linear ODE models to describe the temperature of the TCLab hardware as a function of time and external heating. Assessments in Part 1 include:

• Homework 1 reviews Python programming, numeric integration, nonlinear regression, nonlinear root finding (Newton's method), and uncertainty propagation.
• Lab 1 explores fitting a first-order linear model to step-test data from the TCLab.
• Lab 3 compares the quality of fit for one and two-component linear models.

Part 2: Feedback Control

Next, we introduce feedback control, motivated by various applications. Using the TCLab, we implement and compare control strategies to maintain time-varying temperature setpoints to temper dark chocolate. This experiment is a proxy for other temperature control applications, such as biomanufacturing and energy storage. We emphasize model-based design, developing dynamic models for the TCLab and control system, and examining how changing the control gains impacts the eigenvalues. Assessments in Part 2 include:

• Lab 2 explores relay (on/off) control.
• Lab 4 explores proportional-integral control, including practical aspects such as velocity form, anti-windup reset, and bumpless transfer.

Part 3: Computational Optimization

Finally, we introduce computational optimization as a tool for data-driven decision-making. Students learn about mathematical modeling and computational optimization in Pyomo using production planning and formulation optimization problems such as gasoline blending. These problems provide a foundation for dynamic optimization problems with the TCLab, including optimal control, state estimation, and parameter estimation. Assessments in Part 3 include:

• Homework 2 introduces optimization modeling in Pyomo, emphasizing business analytics problems.
• Lab 5 explores open-loop optimization, state estimation, and parameter estimation for the TCLab using Pyomo.
• Lab 6 implements model predictive control. Using the dark chocolate tempering experiment, students quantitatively compare the performance of the four control techniques -- relay, PI, open-loop optimal, and close-loop model predictive control.

Lectures conclude about two-thirds through the semester with an exam. During the last four weeks, students focus on open-ended team projects.

Material for this course is available online at https://ndcbe.github.io/controls/Readme.html. Prof. Jeffery Kantor was responsible for many of the innovations in this course. He sadly passed away in July 2023.