Scientific Reports • Article in Press
Model predictive control with adaptive Kalman filter for premixed turbocharged natural gas engine
Authors: Wenyu Xiong, Qichangyi Gong, Songtao Huang, Jie Ye & Jinbang Xu
DOI: https://doi.org/10.1038/s41598-026-39850-4
Published: Received: 26 October 2025 | Accepted: 9 February 2026 | Published online: 14 February 2026
We are providing an unedited version of this manuscript to give early access to its findings. Before final publication, the manuscript will undergo further editing. Please note there may be errors present which affect the content, and all legal disclaimers apply.
Abstract: Enhancing Engine Performance with Adaptive AI Control
Robust control of natural-gas engines under unknown load disturbances remains challenging due to strong couplings and delays in multi-input multi-output (MIMO) dynamics. This paper presents a control framework that integrates rate-based model predictive control (MPC) with a gain-scheduling scheme driven by an adaptive Kalman filter to enhance performance under unknown load disturbances. A novel adaptation mechanism enables the Kalman filter to rapidly track transient changes in load torque while attenuating steady-state estimation noise. The online torque estimate is used to compute local equilibrium operating points and generate a gain-scheduling parameter matrix that adaptively adjusts MPC behavior to improve transient response. Experimental validation on a laboratory engine demonstrates that the estimator converges quickly during load transients and maintains low steady-state noise; when combined with gain scheduled MPC, the proposed controller significantly reduces speed and air-fuel-ratio deviations and shortens settling time following step load changes. The results indicate improved disturbance rejection and practical applicability for power-generation engines.
Executive Impact: AI-Driven Performance Gains
Our adaptive AI control framework delivers tangible improvements for natural gas engine performance, stability, and reliability.
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Reduction in Speed Settling Time
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Reduction in Max Speed Deviation
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Reduction in AFR Fluctuation
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Kalman Filter Update Rate
Deep Analysis & Enterprise Applications
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The Pre-mixed Turbocharged Natural Gas Engine Model
Our analysis begins with a fourth-order nonlinear model that accurately captures the complex dynamics of the engine. This dual-input, dual-output system models key variables like engine speed, fuel-air ratio, intake manifold pressure, and boost pressure. The control inputs are the mixture throttle opening (α) and the fuel throttle opening (β), both of which are strongly coupled to the outputs.
A critical challenge addressed is the significant and variable AFR transport delay, which must be accurately predicted for effective control. This detailed modeling forms the foundation for our advanced control strategies, ensuring that the AI can accurately interpret and predict engine behavior.
Model Predictive Control (MPC) Framework
The core of our control solution is a rate-based Model Predictive Control (MPC) formulation. We linearize the nonlinear engine model around various equilibrium points, discretize it, and reformulate it using incremental variables. This approach inherently ensures zero steady-state tracking error without requiring complex integral state augmentation.
The MPC minimizes a quadratic cost function, coordinating multiple actuators through an explicit cost function. This design allows for the precomputation of most matrices offline, reducing the online computational burden to solving a quadratic programming (QP) problem at each sampling instant. This efficiency is crucial for embedded system deployment, especially when handling variable transport delays through an innovative prediction-based iteration method.
Adaptive Kalman Filter & Gain Scheduling for Robustness
To overcome persistent challenges of unknown load disturbances and measurement noise, we integrate an adaptive Kalman filter (A-KF) with a gain-scheduling strategy. The A-KF is designed to rapidly track transient load changes while suppressing steady-state estimation noise, striking a critical balance often missed by conventional filters.
A novel load-detection-based adaptive strategy dynamically adjusts the filter's responsiveness. This allows for fast convergence during transients (e.g., when a load change occurs) and then reduces noise during steady-state operation. The estimated load torque drives a low-complexity gain scheduling strategy, adjusting MPC behavior and feedforward compensation to maintain optimal performance across varying engine operating conditions without the need for full controller switching.
Experimental Validation and Results
Our proposed AFK-MPC framework was rigorously validated on a laboratory natural gas engine-generator set. The experiments compared the performance of three Kalman filter configurations (Low-speed, High-speed, and Adaptive) and three control strategies (D-PI, LMPC, and AFK-MPC).
Results unequivocally demonstrate the superiority of AFK-MPC. The adaptive Kalman filter quickly converges during load transients with minimal noise. When combined with gain-scheduled MPC, our system achieved:
- Significantly reduced speed and air-fuel-ratio deviations.
- Shortened settling times following step load changes.
- Enhanced disturbance rejection, confirming its practical applicability for power-generation engines.
Enterprise Process Flow: Adaptive Kalman Filter Mechanism
Kalman Filter Output ê(k)
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Sliding Window Average êsw(k)
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Absolute Value |êsw(k)|
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Hysteresis Comparator (Eup/Elow)
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Adjust m₁₁ (High for transient, Low for steady-state)
5.146s
Average Speed Settling Time (±2%) achieved with AFK-MPC, outperforming D-PI (6.875s) and LMPC (7.943s).
| Metric | D-PI (Conventional PI) | LMPC (Rate-Based MPC) | AFK-MPC (Our Proposed System) |
|---|---|---|---|
| Average Speed Settling Time (±2%) [s] | 6.875 | 7.943 | 5.146 |
| Max Speed Deviation (rpm) | -167 / +155 | -281 / +269 | -138 / +149 |
| Average AFR Settling Time (±2%) [s] | 12.95 | 11.26 | 12.136 |
| Max Deviation of λ | -0.2 / +0.11 | -0.098 / +0.052 | -0.086 / +0.084 |
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Estimated Annual Savings
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Our AI Implementation Roadmap
A structured approach to integrating adaptive control into your engine systems, ensuring seamless transition and maximized benefits.
Phase 1: Discovery & Model Development
Initial consultation to understand your specific engine architecture and operational goals. Data collection and detailed modeling of your unique system dynamics, building upon our proven frameworks.
Phase 2: Adaptive Algorithm Prototyping
Development and customization of the adaptive Kalman filter and MPC algorithms tailored to your engine's characteristics. Simulation-based testing and refinement to ensure robust performance across various load conditions.
Phase 3: System Integration & Testing
Seamless integration of the AI control software with your existing engine control unit (ECU) hardware. Rigorous laboratory and on-site testing to validate real-world performance, stability, and compliance with emission standards.
Phase 4: Deployment & Continuous Optimization
Full deployment of the adaptive control system into your operational fleet. Ongoing monitoring, data analysis, and iterative optimization to continuously improve efficiency, reduce emissions, and extend engine life.
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