Abstract
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.
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Data availability
The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.
Abbreviations
- \(\alpha\) :
-
Mixture throttle opening.
- \(\beta\) :
-
Fuel throttle opening.
- \(\dot{m}_a\) :
-
Mass flow of fresh air into mixer.
- \(\dot{m}_c\) :
-
Mass flow through compressor.
- \(\dot{m}_f\) :
-
Mass flow of natural gas.
- \(m_{hc}\) :
-
Threshold parameter.
- \(\dot{m}_{mt}\) :
-
Mass flow through mixture throttle.
- \(\dot{m}_{mc}\) :
-
Mass flow into cylinder.
- \(\dot{m}_t\) :
-
Mass flow through turbine.
- \(\eta _c\) :
-
Compressor isentropic efficiency.
- \(\eta _e\) :
-
Engine efficiency coefficient.
- \(\eta _m\) :
-
Turbocharger mechanical efficiency.
- \(\eta _t\) :
-
Turbine isentropic efficiency.
- \(\eta _{ch}\) :
-
Volumetric efficiency.
- \(\kappa\) :
-
Specific heat ratio.
- \(\kappa _c\) :
-
Critical pressure ratio.
- \(\lambda\) :
-
Coefficient of excess air.
- \(\omega\) :
-
Engine speed.
- \(\xi\) :
-
Mixing ratio between natural gas and air.
- \(C_a\) :
-
Discharge coefficient of mixer air entrance.
- \(C_f\) :
-
Discharge coefficient of fuel throttle.
- \(C_m\) :
-
Discharge coefficient of mixture throttle.
- \(c_p\) :
-
Mean value of the specific heat capacity.
- \(H_m\) :
-
Mixer corrected parameter.
- J :
-
Effective engine inertia.
- \(k_b\) :
-
Friction coefficient.
- \(p_0\) :
-
Atmospheric pressure.
- \(p_1\) :
-
Boost pressure.
- \(p_2\) :
-
Intake manifold pressure.
- \(p_3\) :
-
Exhaust pressure.
- \(R_a\) :
-
Gas constant of air.
- \(R_f\) :
-
Gas constant of natural gas.
- \(R_m\) :
-
Gas constant of mixed gas.
- \(S_a\) :
-
Flow area of mixer air entrance.
- \(S_f\) :
-
Effective flow area of fuel valve.
- \(S_m\) :
-
Max flow area of mixture throttle.
- \(S_{thvm}\) :
-
Max flow area of fuel valve.
- \(T_0\) :
-
Atmospheric temperature.
- \(T_1\) :
-
Boost temperature.
- \(T_2\) :
-
Intake manifold temperature.
- \(T_3\) :
-
Exhaust temperature.
- \(t_d\) :
-
AFR time delay.
- \(\tau _e\) :
-
Indicated torque.
- \(\tau _L\) :
-
Load torque.
- \(\tau _p\) :
-
Mechanical loss and pumping loss torque.
- \(t_{s1}\) :
-
MPC controller control period.
- \(t_{s2}\) :
-
Adaptive Kalman filter control period.
- \(V_d\) :
-
Engine displacement.
- \(V_m\) :
-
Intake manifold volume.
- \(V_T\) :
-
Pipe volume from mixer to exhaust.
- \(V_t\) :
-
Pipe volume from mixer to mixture throttle.
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Acknowledgements
This work was supported by the National Natural Science Foundation of China (Grant No. 62403212).
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This work was supported by the National Natural Science Foundation of China (Grant No. 62403212).
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Wenyu Xiong conceived the study, designed the experiments, and wrote part of the manuscript. Qichangyi Gong conducted the experiments, analyzed the data and wrote part of the manuscript. Songtao Huang, Jie Ye, and Jinbang Xu performed data curation, validation, and provided critical feedback on the manuscript. All authors reviewed and approved the final manuscript.
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Xiong, W., Gong, Q., Huang, S. et al. Model predictive control with adaptive Kalman filter for premixed turbocharged natural gas engine. Sci Rep (2026). https://doi.org/10.1038/s41598-026-39850-4
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DOI: https://doi.org/10.1038/s41598-026-39850-4
