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Self-tunable approximated explicit MPC: Heat exchanger implementation and analysis

Lenka Galčíková, Juraj Oravec

TL;DR

The paper addresses the challenge of controlling heat exchangers with nonlinear and asymmetric dynamics by introducing a self-tunable approximated explicit MPC that adjusts controller aggressiveness online without manual retuning. The approach combines two boundary explicit MPCs with an online interpolation controlled by a tuning parameter, and adds a novel self-tuning mechanism based on the size and direction of reference changes, including a two-region scaling to handle asymmetry. Experimentally, the method is implemented on a laboratory heat exchanger, demonstrating reduced sum-of-squared errors, lower overshoot/undershoot, and faster settling times compared to fixed controllers, while maintaining constraint satisfaction and showing fast computation. The work advances practical real-time tunability in explicit MPC, enabling better energy efficiency and robustness in changing operating conditions, with potential extensions to multivariable systems.

Abstract

The tunable approximated explicit model predictive control (MPC) comes with the benefits of real-time tunability without the necessity of solving the optimization problem online. This paper provides a novel self-tunable control policy that does not require any interventions of the control engineer during operation in order to retune the controller subject to the changed working conditions. Based on the current operating conditions, the autonomous tuning parameter scales the control input using linear interpolation between the boundary optimal control actions. The adjustment of the tuning parameter depends on the current reference value, which makes this strategy suitable for reference tracking problems. Furthermore, a novel technique for scaling the tuning parameter is proposed. This extension provides to exploit different ranges of the tuning parameter assigned to specified operating conditions. The self-tunable explicit MPC was implemented on a laboratory heat exchanger with nonlinear and asymmetric behavior. The asymmetric behavior of the plant was compensated by tuning the controller's aggressiveness, as the negative or positive sign of reference change was considered in the tuning procedure. The designed self-tunable controller improved control performance by decreasing sum-of-squared control error, maximal overshoots/ undershoots, and settling time compared to the conventional control strategy based on a single (non-tunable) controller.

Self-tunable approximated explicit MPC: Heat exchanger implementation and analysis

TL;DR

The paper addresses the challenge of controlling heat exchangers with nonlinear and asymmetric dynamics by introducing a self-tunable approximated explicit MPC that adjusts controller aggressiveness online without manual retuning. The approach combines two boundary explicit MPCs with an online interpolation controlled by a tuning parameter, and adds a novel self-tuning mechanism based on the size and direction of reference changes, including a two-region scaling to handle asymmetry. Experimentally, the method is implemented on a laboratory heat exchanger, demonstrating reduced sum-of-squared errors, lower overshoot/undershoot, and faster settling times compared to fixed controllers, while maintaining constraint satisfaction and showing fast computation. The work advances practical real-time tunability in explicit MPC, enabling better energy efficiency and robustness in changing operating conditions, with potential extensions to multivariable systems.

Abstract

The tunable approximated explicit model predictive control (MPC) comes with the benefits of real-time tunability without the necessity of solving the optimization problem online. This paper provides a novel self-tunable control policy that does not require any interventions of the control engineer during operation in order to retune the controller subject to the changed working conditions. Based on the current operating conditions, the autonomous tuning parameter scales the control input using linear interpolation between the boundary optimal control actions. The adjustment of the tuning parameter depends on the current reference value, which makes this strategy suitable for reference tracking problems. Furthermore, a novel technique for scaling the tuning parameter is proposed. This extension provides to exploit different ranges of the tuning parameter assigned to specified operating conditions. The self-tunable explicit MPC was implemented on a laboratory heat exchanger with nonlinear and asymmetric behavior. The asymmetric behavior of the plant was compensated by tuning the controller's aggressiveness, as the negative or positive sign of reference change was considered in the tuning procedure. The designed self-tunable controller improved control performance by decreasing sum-of-squared control error, maximal overshoots/ undershoots, and settling time compared to the conventional control strategy based on a single (non-tunable) controller.
Paper Structure (11 sections, 1 theorem, 17 equations, 12 figures, 2 tables)

This paper contains 11 sections, 1 theorem, 17 equations, 12 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Theoretical backgrounds
  3. Explicit model predictive control
  4. Tunable explicit model predictive control
  5. Self-tunable explicit model predictive control
  6. Methodology
  7. Tuning parameter based on the size of reference change
  8. Self-tunable technique for systems with asymmetric behavior
  9. Results and discussion
  10. Conclusions
  11. Greek letters

Key Result

Lemma 3.2.1

Given control law in eq:PWA_control_law, its approximation given by the convex combination in eq:tunable_u, and given scaled tuning parameter $\widetilde{\rho}$ according to Definition def:rho_tilde. Then the control action approximated into the form: preserves the closed-loop system stability and recursive feasibility of the original control law in eq:PWA_control_law.

Figures (12)

  • Figure 1: Scheme of the self-tuning control evaluation.
  • Figure 2: Laboratory heat exchanger Armfield Process Plant Trainer PCT23: cold medium pump (1), heating medium pump (2), cold medium tanks (3), heater for heating medium (4), heat exchanger (5).
  • Figure 3: Scheme of Armfield PCT23. Heat exchanger (I), peristaltic pump for cold medium (II), peristaltic pump for heating medium (III), tank for cold medium (IV), heater for heating medium (V), temperature sensors ($\mathrm{T}$ -- controlled temperature, $\mathrm{T}_\mathrm{C}$ -- cold outlet cold medium temperature, $\mathrm{T}_\mathrm{H}$ -- heating medium temperature), and electric power for maintaining the temperature of the heating medium (W).
  • Figure 4: Polytopic partition of the upper boundary explicit MPC.
  • Figure 5: Polytopic partition of the lower boundary explicit MPC.
  • ...and 7 more figures

Theorems & Definitions (11)

  • Remark 2.1
  • Remark 2.2
  • Remark 2.3
  • Remark 3.1
  • Definition 3.1: Decision function
  • Definition 3.2: Scaling of the tuning parameter
  • Remark 3.2
  • Lemma 3.2.1
  • proof
  • Remark 3.3
  • ...and 1 more