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Integral action for bilinear systems with application to counter current heat exchanger

Francesco Ripa, Daniele Astolfi, Boussad Hamroun, Diego Regruto

Abstract

In this study, we propose a robust control strategy for a counter-current heat exchanger. The primary objective is to regulate the outlet temperature of one fluid stream by manipulating the flow rate of the second counter-current fluid stream. By leveraging the energy balance equations, we develop a structured bilinear system model derived by using a uniform spatial discretization of each stream into a cascade of homogeneous volumes and by considering the heat transfer and convective phenomena within the exchanger. We introduce two control strategies: (i) an output feedback controller incorporating a state observer and (ii) a purely integral control law. The effectiveness of the proposed control strategy is validated through real experiments on a real heat exchanger.

Integral action for bilinear systems with application to counter current heat exchanger

Abstract

In this study, we propose a robust control strategy for a counter-current heat exchanger. The primary objective is to regulate the outlet temperature of one fluid stream by manipulating the flow rate of the second counter-current fluid stream. By leveraging the energy balance equations, we develop a structured bilinear system model derived by using a uniform spatial discretization of each stream into a cascade of homogeneous volumes and by considering the heat transfer and convective phenomena within the exchanger. We introduce two control strategies: (i) an output feedback controller incorporating a state observer and (ii) a purely integral control law. The effectiveness of the proposed control strategy is validated through real experiments on a real heat exchanger.

Paper Structure

This paper contains 18 sections, 11 theorems, 101 equations, 6 figures, 1 table.

Table of Contents

  1. Introduction
  2. Output Feedback Regulation
  3. Problem statement
  4. Separation principle for integral feedback
  5. Integral gain feedback
  6. Numerical illustration
  7. Proofs
  8. Stability results
  9. Proof of Proposition \ref{['thm:forwarding']}
  10. Proof of Theorem \ref{['thm:separation_principle']}
  11. Proof of Theorem \ref{['thm:singular_pert']}
  12. Temperature regulation of the counter-current heat exchanger
  13. Modelling
  14. Formal verification of the assumptions
  15. Experimental results
  16. ...and 3 more sections

Key Result

Proposition 1

Suppose Assumption ass:standing_assumption holds. Given $(r,{u_{ss}})\in R\times \mathcal{U}$ satisfying eq:regulator_equations, the equilibrium $({x_{ss}},0)$, is globally asymptotically stable and locally exponentially stable for the closed-loop dynamics eq:bi_linear_system, eq:bi_integral_action,

Figures (6)

  • Figure 1: Counter-current exchanger with inlet and outlet heat flux directions.
  • Figure 2: Schematic representation of the PIGNAT Heat Exchanger.
  • Figure 3: Actual Heat Exchanger.
  • Figure 4: Subfigures arranged vertically (from top to bottom) showing: the input signal, the system output, and the output disturbance.
  • Figure 5: The first subfigure shows the observation error; the second subfigure displays both the system output and the estimated output.
  • ...and 1 more figures

Theorems & Definitions (26)

  • Proposition 1
  • proof
  • Theorem 1
  • proof
  • Remark 1
  • Theorem 2
  • proof
  • Definition 1: Zero-state detectability
  • Theorem 3
  • proof
  • ...and 16 more