Koopman-Based Nonlinear Identification and Model Predictive Control of a Turbofan Engine

summary

The gist

The gist The proposed approach uses an adaptive Koopman-based model predictive controller (AKMPC) to achieve robust multivariable control of a two-spool turbofan engine by identifying a time-varying

In short

The study developed an adaptive Koopman-based model predictive controller (AKMPC) for controlling a two-spool turbofan engine. It uses a physics-based model and a metaheuristic method (MH-EDMD) to create a single, reusable Koopman model that captures spool speed and pressure ratio dynamics. This approach outperforms other methods, especially under varying flight conditions, by handling nonlinearities and constraints effectively.

Key concepts

Koopman Operator: A mathematical tool that transforms a complex nonlinear system into an infinite-dimensional linear system. Instead of modeling the engine's complicated physics directly, the Koopman operator allows engineers to use simpler linear methods to predict its future behavior, making control easier.
MH-EDMD: A metaheuristic extended dynamic mode decomposition method used for identifying the time-varying Koopman system. It uses optimization techniques like genetic algorithms to find the best nonlinear parameters that accurately describe how the engine's spool speeds and pressure ratio change over time.
Adaptive Koopman MPC (AKMPC): A control strategy that uses a constantly updated, time-varying Koopman model within a model predictive framework. It incorporates a disturbance observer to correct for errors caused by changes in flight conditions, making it robust for real-world engine operation.
Physics-based Model: A detailed simulation of the engine's physical components (compressors and turbines). This model generates the necessary training data to teach the Koopman system how the physical engine behaves under different operating conditions.

Terminology used across episodes

Reinforcement Learning (RL) — explained in 25 episodes
Federated Learning — explained in 16 episodes
Retrieval-Augmented Generation (RAG) — explained in 16 episodes
Interpretability — explained in 15 episodes
Sample Complexity — explained in 15 episodes
Generalization — explained in 13 episodes

This episode discusses

Koopman-Based Nonlinear Identification and Model Predictive Control of a Turbofan Engine · Paper Radio

The paper

Koopman-Based Nonlinear Identification and Model Predictive Control of a Turbofan Engine · Read on arXiv

David Grasev

Department of Aviation Technology, University of Defence, Brno, Czech Republic

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 adapted, 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 that can be reused across multiple control strategies. Using the identified time-varying Koopman model, an adaptive Koopman-based model predictive controller (AKMPC) with a disturbance observer is developed and compared with a Koopman-based feedback linearization controller (K-FBLC) and its integrator-augmented version (K-FBLC-I). The Koopman representation further enables nonlinear GTE output limiters, such as rotor-acceleration and turbine-inlet-temperature limits, to be expressed as linear constraints in the AKMPC. The controllers are evaluated for two control 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 all strategies achieve comparable performance in sea-level conditions, the AKMPC demonstrates improved performance under varying flight conditions due to its ability to capture nonlinear dynamics, handle constraints, and compensate for model mismatch. Moreover, the EPR control strategy improves the thrust response. The study highlights the applicability of Koopman-based control and the advantages of the AKMPC framework for robust turbofan engine control.

DOI: 10.1049/cth2.70169

Transcript

Introduction to the show: ident: AI Radio. Generated commentary on the latest Artificial Intelligence papers.

Tom: Today's paper: "Koopman-Based Nonlinear Identification and Model Predictive Control of a Turbofan Engine".

Jane: The gist The proposed approach uses an adaptive Koopman-based model predictive controller (AKMPC) to achieve robust multivariable control of a two-spool turbofan engine by identifying a time-varying low-order Koopman system…

Tom: First, who's behind it and why it matters.

Title and authors: Tom: The paper's full title is "Koopman-Based Nonlinear Identification and Model Predictive Control of a Turbofan Engine," and the authors are David Grasev from the University of Defence in Brno.

Jane: It’s clear they are focusing on making the control system adaptable, which is a big deal when you’re dealing with machinery that operates under wildly different pressures and temperatures depending on where it flies.

Lu: They start by developing this physics-based component-level model to create the training data needed for the identification process, which is a solid foundation for getting accurate predictions.

Meng: Getting that initial data right is crucial because if the training data isn't good, any subsequent control strategy built on top of it just won't perform well in practice.

Lalam: And they use this physics model not just to train, but also to validate the controllers, which means they’re checking if what they learned actually works when you run it through a simulation.

The paper's summary: Tom: The core of what this paper does is using that identified time-varying Koopman model to create an adaptive Koopman-based model predictive controller, or AKMPC, which includes a disturbance observer.

Jane: That means when the actual engine starts behaving differently than the model predicts—maybe due to unexpected turbulence or atmospheric changes—the disturbance observer steps in to correct that mismatch.

Lu: They compared this AKMPC against a standard Koopman-based feedback linearization controller, or K-FBLC, and also an integrator-augmented version of that, called K-FBLC-I.

Meng: The comparison shows that the AKMPC is better at handling those real flight condition variations because it can adjust its model online while still maintaining a stable control structure.

Lalam: They also explored how this Koopman representation allows nonlinear limits, like rotor acceleration and turbine inlet temperature, to be turned into simple linear inequality constraints within the model predictive framework.

The paper's improvements: Tom: One big improvement they highlight is that the method lets them handle those nonlinear GTE output limiters directly using linear inequality constraints thanks to the Koopman framework.

Jane: That’s significant because traditionally, handling those kinds of non-linear limits in a model predictive controller can be tricky and computationally heavy.

Lu: They used an extended dynamic mode decomposition, or MH-EDMD, which is more sophisticated than classical EDMD because it uses a metaheuristic method like a genetic algorithm to optimize the nonlinear parameters of the observable functions.

Meng: That optimization process sounds intense, trying to find the best parameters while also keeping prediction error low across the entire training time series.

Lalam: They even designed a specific objective function for this identification process that penalizes prediction error accumulated over all that training data and explicitly includes penalties for lightly unstable eigenvalues during model construction.

Conclusion: Tom: So, to wrap up, the authors show that this approach lets them get accurate predictions for both spool speeds and EPR, which is what they needed to make the whole system work.

Jane: Across sea-level conditions and varying flight conditions, the AKMPC consistently shows better tracking performance in terms of IAE—Integral Absolute Error—and overshoots compared to the other control strategies tested.

Lu: The paper points out that while all these control strategies performed well at sea level, the AKMPC really shines when you move into those varying flight conditions because of its ability to capture the nonlinear dynamics.

Meng: Computationally, they confirmed that running the online AKMPC update—including both the Koopman prediction and the quadratic programming part—is computationally tractable in their MATLAB implementation.

Lalam: The overall implication is that this framework gives engineers a flexible control method that can be reused across different control formulations, which is a big step for making these systems practical.

Tom: We’ve seen how they used the MH-EDMD and AKMPC to identify and then apply a robust nonlinear model for turbofan engine control. That’s what we have today with "Koopman-Based Nonlinear Identification and Model Predictive Control of a Turbofan Engine."

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