Lecture 33 - Model Predictive Control

Model Predictive Control (MPC) uses a mathematical representation of the process to predict and manipulate the future response of a system. Instead of a feedback strategy like PID control, MPC is actively making compensating moves to stay within constraints, drive to an economic optimum, and maximize or minimize certain quantities. Lecture 33 is an introduction to MPC and multivariable control.

• Lecture 33 Notes
• Lecture 33 Worksheet
• Download Excel and MATLAB Files for MPC

MPC requires the numerical solution of dynamic equations. Below is a tutorial on solving differential and algebraic equations.

• Download Files for Dynamic Simulation

Course Review

We'll also take some time to review material for closed-loop control analysis. We formerly had an exam at this point in the semester but have replaced it with a second lab project. It is helpful to revisit the last couple weeks and get the big picture of where we are headed.

This review includes PID equations in the Laplace domain, stability analysis of proportional-only controllers, model predictive control, and optimization topics. A full listing of the topics are detailed in the attached worksheet.

• Lecture 33 Review

Model Predictive Control in Practice

Discussion Questions

Test the lecture's ideas before or after class - commit to an answer first, then check it with a classmate or an AI tutor.

1. PID reacts to the error that already exists; MPC acts on errors it predicts. What two ingredients does MPC require that a PID loop does not, and what happens to MPC performance when the model behind it is wrong?
2. A refinery pays for an MPC application on a distillation column that already has working PID loops. Where does the economic benefit come from - what can MPC do about constraints and interactions that the independent PID loops cannot?
3. MPC solves an optimization over a prediction horizon but implements only the first move, then re-solves at the next sample. Why throw away the rest of the plan? What would go wrong if the whole open-loop plan were executed?
4. Modern examples run on exactly this idea: battery fast-charging pushes current to the edge of a temperature constraint, and data-center cooling anticipates compute load instead of chasing it. For one of these, name the manipulated variables, the constraint that makes MPC worth it, and the disturbance the prediction absorbs.

Tip: The Distillation Column Control Studio is a 32-stage multivariable process where single-loop control visibly struggles with interaction - a taste of why MPC exists. To go further than this lecture, the follow-on course is Dynamic Optimization (MPC and moving horizon estimation, with code).