Research Papers

Lyapunov-Based Nonlinear Feedback Control Design for Exhaust Gas Recirculation Loop of Gasoline Engines

[+] Author and Article Information
Weihai Jiang

Department of Engineering
and Applied Sciences,
Sophia University,
Tokyo 102-8554, Japan
e-mail: weihaijiang@eagle.sophia.ac.jp

Tielong Shen

Department of Engineering
and Applied Sciences,
Sophia University,
Tokyo 102-8554, Japan
e-mail: tetu-sin@sophia.ac.jp

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received July 9, 2018; final manuscript received November 28, 2018; published online January 14, 2019. Assoc. Editor: Fengjun Yan.

J. Dyn. Sys., Meas., Control 141(5), 051005 (Jan 14, 2019) (11 pages) Paper No: DS-18-1320; doi: 10.1115/1.4042146 History: Received July 09, 2018; Revised November 28, 2018

For gasoline engine with an exhaust gas recirculation loop, a challenging issue is how to achieve maximum brake efficiency while providing the desired torque. This paper presents a solution to this challenging issue via dynamical control approach which consists of two phases: optimal equilibrium point generation and feedback regulation of the optimized operating mode. First, a mean-value model is developed to represent the dynamical behavior of the intake manifold and exhaust manifold focused on gas mass flows. Then, the control scheme is constructed based on the control-oriented model. Mainly, the optimal set-points are designed by solving the optimal programming problem of maximizing the brake efficiency under demand torque constraint which is the first control design stage, and the dynamical model to the feedback stabilization regulation control for improving transient performance is at the second stage. Lyapunov-based design is used for the derivation of the state feedback law. Furthermore, the proposed exhaust manifold pressure estimator is also coupled into the controller to replace the cost prohibitive exhaust pressure sensor. Finally, experimental validations on the test bench are provided to evaluate the proposed controller.

Copyright © 2019 by ASME
Your Session has timed out. Please sign back in to continue.


Song, D. , Jia, N. , Guo, X. , Ma, X. , Ma, Z. , Gao, D. , Li, K. , Lai, H. , and Zhang, C. , 2014, “ Low Pressure Cooled EGR for Improved Fuel Economy on a Turbocharged PFI Gasoline Engine,” SAE Paper No. 2014-01-1240.
Alger, T. , Gingrich, J. , Roberts, C. , and Mangold, B. , 2011, “ Cooled Exhaust-Gas Recirculation for Fuel Economy and Emissions Improvement in Gasoline Engines,” Int. J. Engine Res., 12(3), pp. 252–264. [CrossRef]
Teodosio, L. , De Bellis, V. , and Bozza, F. , 2015, “ Fuel Economy Improvement and Knock Tendency Reduction of a Downsized Turbocharged Engine at Full Load Operations Through a Low-Pressure EGR System,” SAE Paper No. 2015-01-1244.
Liu, F. , Pfeiffer, J. , Caudle, R. , Marshall, P. , and Olin, P. , 2016, “ Low Pressure Cooled EGR Transient Estimation and Measurement for an Turbocharged SI Engine,” SAE Paper No. 2016-01-0618.
Hong, S. , Park, I. , Shin, J. , and Sunwoo, M. , 2017, “ Simplified Decoupler-Based Multivariable Controller With a Gain Scheduling Strategy for the Exhaust Gas Recirculation and Variable Geometry Turbocharger Systems in Diesel Engines,” ASME J. Dyn. Syst. Meas. Control, 139(5), p. 051006. [CrossRef]
Nieuwstadt, M. , Kolmanovsky, I. , Moraal, P. , Stefanopoulou, A. , and Jankovic, M. , 2000, “ EGR-VGT Control Schemes: Experimental Comparison for a High-Speed Diesel Engine,” IEEE Control Syst. Mag., 20(3), pp. 63–79. [CrossRef]
Jung, M. , Glover, K. , and Christen, U. , 2005, “ Comparison of Uncertainty Parameterisations for H-Infinity Robust Control of Turbocharged Diesel Engines,” Control Eng. Pract., 13(1), pp. 15–25. [CrossRef]
Stefanopoulou, A. , Kolmanovsky, I. , and Freudenberg, J. , 2000, “ Control of Variable Geometry Turbocharged Diesel Engines for Reduced Emissions,” IEEE Trans. Control Syst. Technol., 8(4), pp. 733–745. [CrossRef]
Upadhyay, D. , 2001, “ Modeling and Model Based Control Design of the VGT-EGR System for Intake Flow Regulation in Diesel Engines,” Ph.D. thesis, The Ohio State University, Columbus, OH.
Wahlström, J. , and Eriksson, L. , 2013, “ Output Selection and Its Implications for MPC of EGR and VGT in Diesel Engines,” IEEE Trans. Control Syst. Technol., 21(3), pp. 932–940. [CrossRef]
Jankovic, M. , and Kolmanovsky, I. , 2000, “ Constructive Lyapunov Control Design for Turbocharged Diesel Engine,” IEEE Trans. Control Syst. Technol., 8(2), pp. 288–299. [CrossRef]
Kim, S. , Choi, S. , and Jin, H. , 2016, “ Pressure Model Based Coordinated Control of VGT and Dual-Loop EGR in a Diesel Engine Air-Path System,” Int. J. Automot. Technol., 17(2), pp. 193–203. [CrossRef]
Chen, P. , and Wang, J. , 2015, “ Nonlinear Model Predictive Control of Integrated Diesel Engine and Selective Catalytic Reduction System for Simultaneous Fuel Economy Improvement and Emissions Reduction,” ASME J. Dyn. Syst. Meas. Control, 137(8), p. 081008. [CrossRef]
Nielsen, K. V. , Blanke, M. , Eriksson, L. , and Vejlgaard-Laursen, M. , 2017, “ Control-Oriented Model of Molar Scavenge Oxygen Fraction for Exhaust Recirculation in Large Diesel Engines,” ASME J. Dyn. Syst. Meas. Control, 139(2), p. 021007. [CrossRef]
Matsuo, S. , Ikeda, E. , Ito, Y. , and Nishiura, H. , 2016, “ The New Toyota Inline 4 Cylinder 1.8L ESTEC 2ZR-FXE Gasoline Engine for Hybrid Car,” SAE Paper No. 2016-01-0684.
Powell, M. , 1978, “ A Fast Algorithm for Nonlinearly Constrained Optimization Calculations,” Numerical Analysis, Vol. 630, G. A. Watson, ed., Springer, Berlin, pp. 144–157.
Wang, Y.-Y. , and Haskara, I. , 2012, “ Exhaust Pressure Estimation and Its Application to Detection and Isolation of Turbocharger System Faults for Internal Combustion Engines,” ASME J. Dyn. Syst. Meas. Control, 134(2), p. 021002. [CrossRef]
Olin, P. , 2008, “ A Mean-Value Model for Estimating Exhaust Manifold Pressure in Production Engine Applications,” SAE Paper No. 2008-01-1004.
Zentner, S. , 2014, “ Contributions to Model-Based Control of Diesel Engines,” Ph.D. thesis, Swiss Federal Institute of Technology Zurich, Zurich, Switzerland. https://www.research-collection.ethz.ch/handle/20.500.11850/84326
Chauvin, J. , Petit, N. , and Rouchon, P. , 2006, “ Air Path Estimation on Diesel HCCI Engine,” SAE Paper No. 2006-01-1085.
Grondin, O. , Moulin, P. , and Chauvin, J. , 2009, “ Control of a Turbocharged Diesel Engine Fitted With High Pressure and Low Pressure Exhaust Gas Recirculation Systems,” Joint 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference, Shanghai, China, Dec. 16–18, pp. 6582–6589.
Wahlström, J. , and Eriksson, L. , 2011, “ Modelling Diesel Engines With a Variable-Geometry Turbocharger and Exhaust Gas Recirculation by Optimization of Model Parameters for Capturing Non-Linear System Dynamics,” Proc. Inst. Mech. Eng., 225(7), pp. 960–986. [CrossRef]
Heywood, J. B. , 1988, Internal Combustion Engine Fundamentals, McGraw-Hill, New York.
Eriksson, L. , and Nielsen, L. , 2014, Modeling and Control of Engines and Drivelines, Wiley, Chichester, UK.
Kao, M. , and Moskwa, J. , 1994, “ Model-Based Engine Fault Detection Using Cylinder Pressure Estimates From Nonlinear Observers,” 33rd IEEE Conference on Decision and Control, Lake Buena Vista, FL, Dec. 14–16, pp. 2742–2747.
Hong, M. , Shen, T. , Ouyang, M. , and Kako, J. , 2011, “ Torque Observers Design for Spark Ignition Engines With Different Intake Air Measurement Sensors,” IEEE Trans. Control Syst. Technol., 19(1), pp. 229–237.


Grahic Jump Location
Fig. 1

The system schematic of the gasoline engine

Grahic Jump Location
Fig. 2

The EGR system of the gasoline engine

Grahic Jump Location
Fig. 3

The general structure of the proposed optimal control scheme

Grahic Jump Location
Fig. 4

The observer-based pem estimator

Grahic Jump Location
Fig. 5

The engine test bench

Grahic Jump Location
Fig. 6

The validation of torque modeling

Grahic Jump Location
Fig. 7

The validation of dynamic pim and pem modeling

Grahic Jump Location
Fig. 8

Set-point map (pim*, pem*, Ta*, EGR*) by solving the stationary optimization problem under different operating conditions: (a) optimal map of throttle angle, (b)optimal map of EGR step, (c) optimal map of pim, and (d) optimal map of pem

Grahic Jump Location
Fig. 9

The experimental validation of the proposed PI observer

Grahic Jump Location
Fig. 10

The experimental validation of the proposed controller by using the measured pem

Grahic Jump Location
Fig. 11

The experimental validation of the proposed controller by using the estimated pem



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In