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DeePC vs. Koopman MPC for Pasteurization: A Comparative Study

Branislav Daráš, Patrik Valábek, Martin Klaučo

Abstract

Data-driven predictive control methods can provide the constraint handling and optimization of model predictive control (MPC) without first-principles models. Two such methods differ in how they replace the model: Data-enabled predictive control (DeePC) uses behavioral systems theory to predict directly from input--output trajectories via Hankel matrices, while Koopman-based MPC (KMPC) learns a lifted linear state-space representation from data. Both methods are well studied on their own, but head-to-head comparisons on multivariable process control problems are few. This paper compares them on a pasteurization unit with three manipulated inputs and three measured outputs, using a neural-network-based digital twin as the plant simulator. Both controllers share identical prediction horizons, cost weights, and constraints, so that differences in closed-loop behavior reflect the choice of predictive representation. Results show that both methods achieve feasible constrained control with comparable tracking error, but with a clear trade-off: KMPC tracks more tightly under the chosen cost, while DeePC produces substantially smoother input trajectories. These results help practitioners choose between the two approaches for thermal processing applications.

DeePC vs. Koopman MPC for Pasteurization: A Comparative Study

Abstract

Data-driven predictive control methods can provide the constraint handling and optimization of model predictive control (MPC) without first-principles models. Two such methods differ in how they replace the model: Data-enabled predictive control (DeePC) uses behavioral systems theory to predict directly from input--output trajectories via Hankel matrices, while Koopman-based MPC (KMPC) learns a lifted linear state-space representation from data. Both methods are well studied on their own, but head-to-head comparisons on multivariable process control problems are few. This paper compares them on a pasteurization unit with three manipulated inputs and three measured outputs, using a neural-network-based digital twin as the plant simulator. Both controllers share identical prediction horizons, cost weights, and constraints, so that differences in closed-loop behavior reflect the choice of predictive representation. Results show that both methods achieve feasible constrained control with comparable tracking error, but with a clear trade-off: KMPC tracks more tightly under the chosen cost, while DeePC produces substantially smoother input trajectories. These results help practitioners choose between the two approaches for thermal processing applications.

Paper Structure

This paper contains 18 sections, 12 equations, 4 figures, 3 tables, 1 algorithm.

Table of Contents

  1. INTRODUCTION
  2. Problem Statement and Control Objectives
  3. Problem Formulation
  4. Case Study Description
  5. Data-Enabled Predictive Control
  6. DeePC
  7. Behavioral Systems Theory and Willems' Lemma
  8. Hankel Matrix Construction
  9. Regularized DeePC
  10. Koopman-based MPC
  11. Simulation-based Experiments
  12. Data Collection
  13. Optimization Problem
  14. Controller Parameters
  15. Koopman MPC Setup
  16. ...and 3 more sections

Figures (4)

  • Figure 3: Pasteurization unit scheme. Manipulated inputs: $u_1$ feed (product) flow rate, $u_2$ hot-water circulation flow rate, $u_3$ electric-heater power. Measured outputs: $y_1$ holding-tube outlet temperature $T_1$, $y_2$ hot-tank temperature $T_2$, $y_3$ heat-exchanger outlet temperature $T_3$.
  • Figure 4: Construction of the DeePC past window of length $T_{\mathrm{ini}}$ from measured data. The extracted suffix defines the initialization variables used in \ref{['eq:deepc_reg_constraint_ini']}.
  • Figure 5: Graphical interpretation of past-output usage in regularized DeePC: the selected past trajectory is matched through \ref{['eq:deepc_reg_constraint_up']} (with slack on the output part), while future trajectories are optimized under constraints.
  • Figure 6: Closed-loop comparison of KMPC (blue) and DeePC (red) over approximately 5.5 hours. Left column: outputs $T_1$, $T_2$, and $T_3$. Right column: inputs $u_1$, $u_2$, and $u_3$. The dashed green line is the $T_1$ reference.