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Koopman-Based Nonlinear Identification and Adaptive Control of a Turbofan Engine

David Grasev

Abstract

This paper investigates Koopman operator-based approaches for multivariable control of a two-spool turbofan engine. A physics-based component-level model is developed to generate training data and validate the controllers. A meta-heuristic extended dynamic mode decomposition is developed, with a cost function designed to accurately capture both spool-speed dynamics and the engine pressure ratio (EPR), enabling the construction of a single Koopman model suitable for multiple control objectives. Using the identified time-varying Koopman model, two controllers are developed: an adaptive Koopman-based model predictive controller (AKMPC) with a disturbance observer and a Koopman-based feedback linearization controller (K-FBLC), which serves as a benchmark. The controllers are evaluated for two control strategies, namely configurations of spool speeds and EPR, under both sea-level and varying flight conditions. The results demonstrate that the proposed identification approach enables accurate predictions of both spool speeds and EPR, allowing the Koopman model to be reused flexibly across different control formulations. While both control strategies achieve comparable performance in steady conditions, the AKMPC exhibits superior robustness compared with the K-FBLC under varying flight conditions due to its ability to compensate for model mismatch. Moreover, the EPR control strategy improves the thrust response. The study highlights the applicability of Koopman-based control and demonstrates the advantages of the AKMPC-based framework for robust turbofan engine control.

Koopman-Based Nonlinear Identification and Adaptive Control of a Turbofan Engine

Abstract

This paper investigates Koopman operator-based approaches for multivariable control of a two-spool turbofan engine. A physics-based component-level model is developed to generate training data and validate the controllers. A meta-heuristic extended dynamic mode decomposition is developed, with a cost function designed to accurately capture both spool-speed dynamics and the engine pressure ratio (EPR), enabling the construction of a single Koopman model suitable for multiple control objectives. Using the identified time-varying Koopman model, two controllers are developed: an adaptive Koopman-based model predictive controller (AKMPC) with a disturbance observer and a Koopman-based feedback linearization controller (K-FBLC), which serves as a benchmark. The controllers are evaluated for two control strategies, namely configurations of spool speeds and EPR, under both sea-level and varying flight conditions. The results demonstrate that the proposed identification approach enables accurate predictions of both spool speeds and EPR, allowing the Koopman model to be reused flexibly across different control formulations. While both control strategies achieve comparable performance in steady conditions, the AKMPC exhibits superior robustness compared with the K-FBLC under varying flight conditions due to its ability to compensate for model mismatch. Moreover, the EPR control strategy improves the thrust response. The study highlights the applicability of Koopman-based control and demonstrates the advantages of the AKMPC-based framework for robust turbofan engine control.

Paper Structure

This paper contains 30 sections, 58 equations, 23 figures, 8 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Turbofan GTE Component-Level Model
  3. Component Models
  4. Koopman Operator
  5. Eigenfunctions
  6. Identification
  7. Metaheuristic EDMD Algorithm
  8. Actuator Dynamics
  9. Kalman Filter Design
  10. Considered Controllers
  11. Koopman Adaptive Model Predictive Control
  12. Constraints
  13. Disturbance Observer
  14. Feedback Linearization Using a Koopman-Derived Model
  15. Results
  16. ...and 15 more sections

Figures (23)

  • Figure 1: Turbofan GTE diagram with the main components considered in this paper.
  • Figure 2: Schematic diagram of Koopman eigenfunction lifting and evolution.
  • Figure 3: The AKMPC diagram showing the interaction between the Koopman system and MPC optimization.
  • Figure 4: (a) Thrust and (b) fuel flow steady-state validation against the GasTurb 15 simulation software in $H = 0$ km, $M_0 = 0$ and $H = 10$ km, $M_0 = 0.8$.
  • Figure 5: Transient performance validation against the GasTurb 15 simulation software for the sea-level conditions. The fuel flow is rescaled for better visualization.
  • ...and 18 more figures