DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Next-Cycle Optimal Dilute Combustion Control via Online Learning of Cycle-to-Cycle Variability Using Kernel Density Estimators

Abstract

Dilute combustion using exhaust gas recirculation (EGR) presents a cost-effective method for increasing the efficiency of spark-ignition (SI) engines. However, the maximum amount of EGR that can be used at a given condition is limited by a rapid increment of cycle-to-cycle variability (CCV). This study describes a methodology to design a model-based stochastic optimal controller to adjust the cycle-to-cycle fuel injection quantity in order to reduce CCV and further extend the dilute limit. Given the complexity and chaotic nature of combustion events, the controller was enhanced with online learning in order to identify the statistical properties of combustion efficiency, which are needed to generate predictions for next-cycle events. This study showed that a kernel density estimator (KDE) can be used to learn the combustion properties in real time and can be incorporated into the feedback policy in order to calculate the optimal control command. Experimental results suggested that the dilute limit can be extended from 18.5% to 21% EGR fraction at an operating condition relevant for highway cruising. Additionally, the proposed controller can achieve a large CCV reduction with less fuel enrichment compared to previous methods, overall contributing to an increase in 0.2% indicated fuel conversion efficiency.

Authors:
ORCiD logo [1]; ORCiD logo [1]; ORCiD logo [1]; ORCiD logo [1];  [1]
  1. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Publication Date:
Research Org.:
Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)
Sponsoring Org.:
USDOE Office of Energy Efficiency and Renewable Energy (EERE)
OSTI Identifier:
1847545
Grant/Contract Number:  
AC05-00OR22725
Resource Type:
Accepted Manuscript
Journal Name:
IEEE Transactions on Control Systems Technology
Additional Journal Information:
Journal Volume: 0; Journal Issue: 0; Journal ID: ISSN 1063-6536
Publisher:
IEEE
Country of Publication:
United States
Language:
English
Subject:
33 ADVANCED PROPULSION SYSTEMS; Internal combustion engines; Stochastic systems; Statistical learning; Optimal control; Kernel density estimation

Citation Formats

Maldonado Puente, Bryan, Kaul, Brian, Schuman, Catherine, Young, Steven, and Mitchell, Parker. Next-Cycle Optimal Dilute Combustion Control via Online Learning of Cycle-to-Cycle Variability Using Kernel Density Estimators. United States: N. p., 2022. Web. doi:10.1109/TCST.2022.3149423.
Maldonado Puente, Bryan, Kaul, Brian, Schuman, Catherine, Young, Steven, & Mitchell, Parker. Next-Cycle Optimal Dilute Combustion Control via Online Learning of Cycle-to-Cycle Variability Using Kernel Density Estimators. United States. https://doi.org/10.1109/TCST.2022.3149423
Maldonado Puente, Bryan, Kaul, Brian, Schuman, Catherine, Young, Steven, and Mitchell, Parker. Tue . "Next-Cycle Optimal Dilute Combustion Control via Online Learning of Cycle-to-Cycle Variability Using Kernel Density Estimators". United States. https://doi.org/10.1109/TCST.2022.3149423. https://www.osti.gov/servlets/purl/1847545.
@article{osti_1847545,
title = {Next-Cycle Optimal Dilute Combustion Control via Online Learning of Cycle-to-Cycle Variability Using Kernel Density Estimators},
author = {Maldonado Puente, Bryan and Kaul, Brian and Schuman, Catherine and Young, Steven and Mitchell, Parker},
abstractNote = {Dilute combustion using exhaust gas recirculation (EGR) presents a cost-effective method for increasing the efficiency of spark-ignition (SI) engines. However, the maximum amount of EGR that can be used at a given condition is limited by a rapid increment of cycle-to-cycle variability (CCV). This study describes a methodology to design a model-based stochastic optimal controller to adjust the cycle-to-cycle fuel injection quantity in order to reduce CCV and further extend the dilute limit. Given the complexity and chaotic nature of combustion events, the controller was enhanced with online learning in order to identify the statistical properties of combustion efficiency, which are needed to generate predictions for next-cycle events. This study showed that a kernel density estimator (KDE) can be used to learn the combustion properties in real time and can be incorporated into the feedback policy in order to calculate the optimal control command. Experimental results suggested that the dilute limit can be extended from 18.5% to 21% EGR fraction at an operating condition relevant for highway cruising. Additionally, the proposed controller can achieve a large CCV reduction with less fuel enrichment compared to previous methods, overall contributing to an increase in 0.2% indicated fuel conversion efficiency.},
doi = {10.1109/TCST.2022.3149423},
journal = {IEEE Transactions on Control Systems Technology},
number = 0,
volume = 0,
place = {United States},
year = {Tue Feb 01 00:00:00 EST 2022},
month = {Tue Feb 01 00:00:00 EST 2022}
}

Works referenced in this record:

Modelling and estimation of combustion variability for fast light-off of diesel aftertreatment
journal, January 2020

  • Maldonado, Bryan P.; Bieniek, Mitchell; Hoard, John
  • International Journal of Powertrains, Vol. 9, Issue 1/2
  • DOI: 10.1504/IJPT.2020.108423

Retard to the Limit: Closed-Loop COVIMEP Control for Aggressive Exhaust Heating
journal, January 2019


Portable In-Cylinder Pressure Measurement and Signal Processing System for Real-Time Combustion Analysis and Engine Control
conference, April 2020

  • Luo, Yilun; Maldonado, Bryan; Liu, Siying
  • WCX SAE World Congress Experience, SAE Technical Paper Series
  • DOI: 10.4271/2020-01-1144

Cylinder charge composition observation based on in-cylinder pressure measurement
journal, January 2019


Synchronization of combustion variations in a multicylinder spark ignition engine
journal, January 2000

  • Daw, C. Stuart; Green, Johney B.; Wagner, Robert M.
  • Proceedings of the Combustion Institute, Vol. 28, Issue 1
  • DOI: 10.1016/S0082-0784(00)80337-9

Combustion phasing for maximum efficiency for conventional and high efficiency engines
journal, January 2014


A Comparison Between Combustion Phase Indicators for Optimal Spark Timing
journal, June 2008

  • Pipitone, Emiliano
  • Journal of Engineering for Gas Turbines and Power, Vol. 130, Issue 5
  • DOI: 10.1115/1.2939012

Low-Order Map Approximations of Lean Cyclic Dispersion in Premixed Spark Ignition Engines
conference, September 2001

  • Wagner, Robert M.; Daw, C. Stuart; Green, Johney B.
  • SAE Technical Paper Series
  • DOI: 10.4271/2001-01-3559

Determination of SI Combustion Sensitivity to Fuel Perturbations as a Cyclic Control Input for Highly Dilute Operation
journal, March 2017

  • Jatana, Gurneesh S.; Kaul, Brian C.
  • SAE International Journal of Engines, Vol. 10, Issue 3
  • DOI: 10.4271/2017-01-0681

Next-Cycle Optimal Fuel Control for Cycle-to-Cycle Variability Reduction in EGR-Diluted Combustion
journal, December 2021

  • Maldonado, Bryan P.; Kaul, Brian C.; Schuman, Catherine D.
  • IEEE Control Systems Letters, Vol. 5, Issue 6
  • DOI: 10.1109/LCSYS.2020.3046433

Cooled exhaust-gas recirculation for fuel economy and emissions improvement in gasoline engines
journal, June 2011

  • Alger, T.; Gingrich, J.; Roberts, C.
  • International Journal of Engine Research, Vol. 12, Issue 3
  • DOI: 10.1177/1468087411402442

Chaos theory-based time series analysis of in-cylinder pressure and its application in combustion control of SI engines
journal, January 2020

  • Di, Huanyu; Zhang, Yahui; Shen, Tielong
  • Journal of Thermal Science and Technology, Vol. 15, Issue 1
  • DOI: 10.1299/jtst.2020jtst0001

Cylinder pressure based combustion phase optimization and control in spark-ignited engines
journal, May 2017


Learning reference governor for cycle-to-cycle combustion control with misfire avoidance in spark-ignition engines at high exhaust gas recirculation–diluted conditions
journal, June 2020

  • Maldonado, Bryan P.; Li, Nan; Kolmanovsky, Ilya
  • International Journal of Engine Research, Vol. 21, Issue 10
  • DOI: 10.1177/1468087420929109

Cycle-to-Cycle Feedback for Combustion Control of Spark Advance at the Misfire Limit
journal, July 2018

  • Maldonado, Bryan P.; Stefanopoulou, Anna G.
  • Journal of Engineering for Gas Turbines and Power, Vol. 140, Issue 10
  • DOI: 10.1115/1.4039728

Observing and modeling nonlinear dynamics in an internal combustion engine
journal, March 1998


Dilute Combustion Control Using Spiking Neural Networks
conference, April 2021

  • Maldonado, Bryan P.; Kaul, Brian C.; Schuman, Catherine D.
  • SAE WCX Digital Summit, SAE Technical Paper Series
  • DOI: 10.4271/2021-01-0534

Neuro emission controller for minimising cyclic dispersion in spark ignition engines with EGR levels1
journal, January 2009

  • Vance, J.; Kaul, B.; Jagannathan, S.
  • International Journal of General Systems, Vol. 38, Issue 1
  • DOI: 10.1080/03081070802193028

Neural Network Controller Development and Implementation for Spark Ignition Engines With High EGR Levels
journal, July 2007

  • Vance, Jonathan Blake; Singh, Atmika; Kaul, Brian C.
  • IEEE Transactions on Neural Networks, Vol. 18, Issue 4
  • DOI: 10.1109/TNN.2007.899199

Output Feedback Controller for Operation of Spark Ignition Engines at Lean Conditions Using Neural Networks
journal, March 2008

  • Vance, J. B.; Kaul, B. C.; Jagannathan, S.
  • IEEE Transactions on Control Systems Technology, Vol. 16, Issue 2
  • DOI: 10.1109/TCST.2007.903368

Linear Stochastic Modeling and Control of Diluted Combustion for SI Engines
journal, January 2018


Statsmodels: Econometric and Statistical Modeling with Python
conference, January 2010


Cross-Validation and the Estimation of Conditional Probability Densities
journal, December 2004

  • Hall, Peter; Racine, Jeff; Li, Qi
  • Journal of the American Statistical Association, Vol. 99, Issue 468
  • DOI: 10.1198/016214504000000548

Stochastic Feedback Combustion Control at High Dilution Limit
conference, June 2018

  • Maldonado, Bryan P.; Freudenberg, James S.; Stefanopoulou, Anna G.
  • 2018 Annual American Control Conference (ACC)
  • DOI: 10.23919/ACC.2018.8431020

Analysis of Cyclic Variability of Heat Release for High-EGR GDI Engine Operation with Observations on Implications for Effective Control
journal, April 2013

  • Kaul, Brian; Wagner, Robert; Green, Johney
  • SAE International Journal of Engines, Vol. 6, Issue 1
  • DOI: 10.4271/2013-01-0270

Online Control of Process Variance Using Feedback
conference, July 2020


Invited Review: A review of deterministic effects in cyclic variability of internal combustion engines
journal, February 2015

  • Finney, Charles EA; Kaul, Brian C.; Daw, C. Stuart
  • International Journal of Engine Research, Vol. 16, Issue 3
  • DOI: 10.1177/1468087415572033

Non-Equiprobable Statistical Analysis of Misfires and Partial Burns for Cycle-to-Cycle Control of Combustion Variability
conference, January 2019

  • Maldonado, Bryan P.; Stefanopoulou, Anna G.
  • ASME 2018 Internal Combustion Engine Division Fall Technical Conference, Volume 2: Emissions Control Systems; Instrumentation, Controls, and Hybrids; Numerical Simulation; Engine Design and Mechanical Development
  • DOI: 10.1115/ICEF2018-9540

Characteristics of Cycle-to-Cycle Combustion Variability at Partial-Burn Limited and Misfire Limited Spark Timing Under Highly Diluted Conditions
conference, December 2019

  • Maldonado, Bryan; Stefanopoulou, Anna; Scarcelli, Riccardo
  • ASME 2019 Internal Combustion Engine Division Fall Technical Conference
  • DOI: 10.1115/ICEF2019-7256

Cyclic dynamics of misfires and partial burns in a dilute spark-ignition engine
journal, October 2020

  • Stiffler, Rachel; Kaul, Brian; Drallmeier, James
  • Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, Vol. 235, Issue 2-3
  • DOI: 10.1177/0954407020964004

Effects of Ignition and Injection Perturbation under Lean and Dilute GDI Engine Operation
conference, September 2015

  • Wallner, Thomas; Sevik, James M.; Scarcelli, Riccardo
  • JSAE/SAE 2015 International Powertrains, Fuels & Lubricants Meeting, SAE Technical Paper Series
  • DOI: 10.4271/2015-01-1871

Closed-Loop Ignition Timing Control for SI Engines Using Ionization Current Feedback
journal, May 2007

  • Zhu, Guoming G.; Haskara, Ibrahim; Winkelman, Jim
  • IEEE Transactions on Control Systems Technology, Vol. 15, Issue 3
  • DOI: 10.1109/TCST.2007.894634

Model-Based Control-Oriented Combustion Phasing Feedback for Fast CA50 Estimation
journal, January 2015

  • Zhu, Qilun; Wang, Shu; Prucka, Robert
  • SAE International Journal of Engines, Vol. 8, Issue 3
  • DOI: 10.4271/2015-01-0868

Spark Ignition Feedback Control by Means of Combustion Phase Indicators on Steady and Transient Operation
journal, July 2014

  • Emiliano, Pipitone
  • Journal of Dynamic Systems, Measurement, and Control, Vol. 136, Issue 5
  • DOI: 10.1115/1.4026966

Prediction of Flame Burning Velocity at Early Flame Development Time With High Exhaust Gas Recirculation and Spark Advance
journal, March 2017

  • Lian, H.; Martz, J. B.; Maldonado, B. P.
  • Journal of Engineering for Gas Turbines and Power, Vol. 139, Issue 8
  • DOI: 10.1115/1.4035849

The effect of exhaust gas recirculation (EGR) on combustion stability, engine performance and exhaust emissions in a gasoline engine
journal, October 2001

  • Cha, Jinyoung; Kwon, Junhong; Cho, Youngjin
  • KSME International Journal, Vol. 15, Issue 10
  • DOI: 10.1007/BF03185686

Controlling Cyclic Combustion Variations in Lean-Fueled Spark-Ignition Engines
conference, January 2002

  • Daw, C. S.
  • EXPERIMENTAL CHAOS: 6th Experimental Chaos Conference, AIP Conference Proceedings
  • DOI: 10.1063/1.1487542

Artificial-intelligence-based prediction and control of combustion instabilities in spark-ignition engines
book, January 2022

  • Maldonado, Bryan; Stefanopoulou, Anna; Kaul, Brian
  • Artificial Intelligence and Data Driven Optimization of Internal Combustion Engines
  • DOI: 10.1016/B978-0-323-88457-0.00006-0

Closed-Loop Control of Combustion Initiation and Combustion Duration
journal, May 2020

  • Maldonado, Bryan P.; Zaseck, Kevin; Kitagawa, Eiki
  • IEEE Transactions on Control Systems Technology, Vol. 28, Issue 3
  • DOI: 10.1109/TCST.2019.2898849

Numerical Prediction of Cyclic Variability in a Spark Ignition Engine Using a Parallel Large Eddy Simulation Approach
journal, March 2018

  • Ameen, Muhsin M.; Mirzaeian, Mohsen; Millo, Federico
  • Journal of Energy Resources Technology, Vol. 140, Issue 5
  • DOI: 10.1115/1.4039549

Low Size, Weight, and Power Neuromorphic Computing to Improve Combustion Engine Efficiency
conference, October 2020

  • Schuman, Catherine D.; Young, Steven R.; Mitchell, J. Parker
  • 2020 11th International Green and Sustainable Computing Workshops (IGSC)
  • DOI: 10.1109/IGSC51522.2020.9291228

Control-Oriented Modeling of Cycle-to-Cycle Combustion Variability at the Misfire Limit in SI Engines
conference, January 2021

  • Maldonado, Bryan P.; Kaul, Brian C.
  • ASME 2020 Dynamic Systems and Control Conference, Volume 2: Intelligent Transportation/Vehicles; Manufacturing; Mechatronics; Engine/After-Treatment Systems; Soft Actuators/Manipulators; Modeling/Validation; Motion/Vibration Control Applications; Multi-Agent/Networked Systems; Path Planning/Motion Control; Renewable/Smart Energy Systems; Security/Privacy of Cyber-Physical Systems; Sensors/Actuators; Tracking Control Systems; Unmanned Ground/Aerial Vehicles; Vehicle Dynamics, Estimation, Control; Vibration/Control Systems; Vibrations
  • DOI: 10.1115/DSCC2020-3255

Evaluation of residual gas fraction estimation methods for cycle-to-cycle combustion variability analysis and modeling
journal, January 2021


Self-tuning gross heat release computation for internal combustion engines
journal, April 2009