Research Papers

Transient Air-to-Fuel Ratio Control of an Spark Ignited Engine Using Linear Quadratic Tracking

[+] Author and Article Information
Stephen Pace

Electrical and Computer Engineering,
Michigan State University,
East Lansing, MI 48824
e-mail: paceste1@msu.edu

Guoming G. Zhu

Fellow ASME
Department of Mechanical Engineering,
Department of Electrical and
Computer Engineering,
Michigan State University,
1497 Engineering Research Court,
Room E148,
East Lansing, MI 48824
e-mail: zhug@egr.msu.edu

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received April 20, 2012; final manuscript received October 24, 2013; published online December 9, 2013. Assoc. Editor: Eric J. Barth.

J. Dyn. Sys., Meas., Control 136(2), 021008 (Dec 09, 2013) (11 pages) Paper No: DS-12-1114; doi: 10.1115/1.4025858 History: Received April 20, 2012; Revised October 24, 2013

Modern spark ignited (SI) internal combustion engines maintain their air-to-fuel ratio (AFR) at a desired level to maximize the three-way catalyst conversion efficiency and durability. However, maintaining the engine AFR during its transient operation is quite challenging due to rapid changes of driver demand or engine throttle. Conventional transient AFR control is based upon the inverse dynamics of the engine fueling dynamics and the measured mass air flow (MAF) rate to obtain the desired AFR of the gas mixture trapped in the cylinder. This paper develops a linear quadratic (LQ) tracking controller to regulate the transient AFR based upon a control-oriented model of the engine port fuel injection (PFI) wall wetting dynamics and the air intake dynamics from the measured airflow to the manifold pressure. The LQ tracking controller is designed to optimally track the desired AFR by minimizing the error between the trapped in-cylinder air mass and the product of the desired AFR and fuel mass over a given time interval. The performance of the optimal LQ tracking controller was compared with the conventional transient fueling control based on the inverse fueling dynamics through simulations and showed improvement over the baseline conventional inverse fueling dynamics controller. To validate the control strategy on an actual engine, a 0.4 l single cylinder direct-injection (DI) engine was used. The PFI wall wetting dynamics were simulated in the engine controller after the DI injector control signal. Engine load transition tests for the simulated PFI case were conducted on an engine dynamometer, and the results showed improvement over the baseline transient fueling controller based on the inverse fueling dynamics.

Copyright © 2014 by ASME
Your Session has timed out. Please sign back in to continue.


Yildiz, Y., Annaswamy, A., Yanakiev, D., and Kolmanovsky, I., 2008, “Adaptive Air Fuel Ratio Control for Internal Combustion Engines,” Proceedings of American Control Conference, pp. 2058–2063. [CrossRef]
Pace, S., and Zhu, G., 2009, “Sliding Mode Control of a Dual-Fuel System Internal Combustion Engine,” Proceedings of ASME Dynamic Systems and Control Conference, pp. 881–887. [CrossRef]
White, A., Choi, J., Nagamune, R., and Zhu, G., 2010, “Gain-Scheduling Control of Port-Fuel-Injection Processes,” IFAC J. Control Prac., 19, pp. 380–394. [CrossRef]
Kyung-ho, A., Stefanopoulou, A., and Jankovic, M., 2010, “Puddle Dynamics and Air-to-Fuel Ratio Compensation for Gasoline-Ethanol Blends in Flex-Fuel Engines” IEEE Trans. Control Syst. Technol., 18(6), pp. 1241–1253. [CrossRef]
Stivender, D. L., 1978, “Engine Air Control—Basis of a Vehicular Systems Control Hierarchy,” SAE Technical Paper No. 780346.
Aquino, C., 1981, “Transient A/F Control Characteristics of the 5 Liter Central Fuel Injection,” SAE Technical Paper No. 810494.
Hires, S., and Overington, M., 1981, “Transient Mixture Strength Excursions—An Investigation of Their Causes and the Development of a Constant Mixture Strength Fuelling Strategy,” SAE Technical Paper No. 800054.
Rose, D., Ladommatos, N., and Stone, R., 1994, “In-Cylinder Mixture Excursions in a Port-Injected Engine During Fast Throttle Opening,” SAE Technical Paper No. 940382.
Ladommatos, N., and Rose, D., 1998, “Measurements of In-Cylinder Mixture Strength and Fuel Accumulation in the Inlet Port of a Gasoline-Injected Engine During Very Rapid Throttle Openings,” IMechE J. Autom. Eng., 212(D2), pp. 103–108. [CrossRef]
Ladommatos, N., and Rose, D., 1996, “On the Causes of In-Cylinder Air-Fuel Ratio Excusions During Load and Fuelling Transients in Port-Injected Spark-Ignition Engines,” SAE Technical Paper No. 960466.
Xu, H., 1999, “Control of A/F Ratio During Engine Transients,” SAE Technical Paper No. 1999-01-1484.
Ye, Z., 2003, “A Simple Linear Approach for Transient Fuel Control,” SAE Technical Paper No. 2003-01-8407.
Yao, J., 2009, “Research on Transient Air Fuel Ratio Control of Gasoline Engines,” Int. Forum Info. Technol. App., 1, pp. 610–613. [CrossRef]
Grizzle, J., Cook, J., and Milam, W., 1994, “Improved Cylinder Air Charge Estimation for Transient Air Fuel Ratio Control,” American Controls Conference, pp. 1568–1573. [CrossRef]
Osburn, A., and Franchek, M., 2004, “Transient Air/Fuel Ratio Controller Identification Using Repetitive Control,” ASME J. Dyn. Syst., Meas. Control, 126(4), pp. 781–789. [CrossRef]
Cipollone, R., and Sughayyer, M., 2002, “Transient Air/Fuel ratio control in SI Engines,” ASME Journal of Internal Combustion Engine, 39, pp. 527–535. [CrossRef]
Fiengo, G., Grizzle, J., Cook, J., and Karnik, A., 2005, “Dual-UEGO Active Catalyst Control for Emissions Reduction: Design and Experimental Validation,” IEEE Trans. Control Syst. Technol., 13(5), pp. 722–736. [CrossRef]
Zhang, F., Grigoriadis, K., Franchek, M., and Makki, I., 2006, “Transient Lean Burn Air-Fuel Ratio Control Using Input Shaping Method Combined With Linear Parameter-Varying Control” American Controls Conference, pp. 3290–3295. [CrossRef]
Chang, C., Fekete, N., Amstutz, A., and Powell, J., 1995, “Air-Fuel Ratio Control in Spark-Ignition Engines Using Estimation Theory” IEEE Trans. Control Syst. Technol., 3(1), pp. 22–31. [CrossRef]
ZhaiY., and Vu, D., 2008, “Radial-Basis-Function-Based Feedforward-Feedback Control for Air-Fuel Ratio of Spark Ignition Engines,” Proc. Inst. Mech. Eng., Part D (J. Autom. Eng.), 222(3), pp. 415–428. [CrossRef]
Pace, S., and Zhu, G., 2011, “Optimal LQ Transient Air-to-fuel Ratio Control of an Internal Combustion Engine,” 2011 ASME Dynamic Systems and Control Conference, Arlington, VA.
Heywood, J., 1988, Internal Combustion Engine Fundamentals. McGraw-Hill, Inc., New York.
Yang, X., and Zhu, G., 2010, “A Mixed Mean-Value and Crank-Based Model of a Dual-Stage Turbocharged SI Engine for Hardware-in-the-Loop Simulation,” American Control Conference, pp. 3791–3796. Available at: http://www.dcsc.tudelft.nl/~bdeschutter/private_20100705_acc_2010/data/papers/0270.pdf
Guzzella, L., and Onder, C., 2004, Introduction to Modeling and Control of Internal Combustion Engine Systems, Springer, New York.
Naidu, D., 2003, Optimal Control Systems, CRC Press, Boca Raton, FL.
Luenberger, D. G., 1966, “Observers for Multivariable Systems,” IEEE Trans. Autom. Control, AC-11, pp. 190–197. [CrossRef]


Grahic Jump Location
Fig. 1

Mean-value engine model architecture

Grahic Jump Location
Fig. 2

Schematic of AFR control problem

Grahic Jump Location
Fig. 3

LQ tracking controller with state estimator

Grahic Jump Location
Fig. 5

Schematic of baseline inverse fueling controller

Grahic Jump Location
Fig. 4

Reference buffer formation

Grahic Jump Location
Fig. 8

Single cylinder engine setup

Grahic Jump Location
Fig. 11

Response of LQ tracking controller with state estimator

Grahic Jump Location
Fig. 12

Response of LQ tracking controller with new wall wetting parameters

Grahic Jump Location
Fig. 9

Throttle dynamics model validation

Grahic Jump Location
Fig. 10

Intake manifold filling dynamics model validation

Grahic Jump Location
Fig. 7

Response of simulation 2

Grahic Jump Location
Fig. 6

Response of simulation 1

Grahic Jump Location
Fig. 14

Response of LQ tracking with PID feedback control

Grahic Jump Location
Fig. 13

Response of inverse fueling dynamics feedforward controller



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