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Research Papers

Tracking Controller Design for MIMO Nonlinear Systems With Application to Automotive Cold Start Emission Reduction

[+] Author and Article Information
Selina Pan

Department of Mechanical Engineering,
Stanford University,
Stanford, CA 94305
e-mail: slpan@stanford.edu

J. Karl Hedrick

Department of Mechanical Engineering,
University of California, Berkeley,
Berkeley, CA 94720-1740
e-mail: khedrick@me.berkeley.edu

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received September 17, 2014; final manuscript received June 8, 2015; published online August 3, 2015. Assoc. Editor: Shankar Coimbatore Subramanian.

J. Dyn. Sys., Meas., Control 137(10), 101013 (Aug 03, 2015) (12 pages) Paper No: DS-14-1378; doi: 10.1115/1.4030868 History: Received September 17, 2014

The main contribution of this paper is the development of a nonlinear multiple-input, multiple-output (MIMO) tracking controller design using a discrete time sliding control approach. A Lyapunov stability analysis is used to prove the asymptotic stability of both the output errors as well as the parameter estimation errors. The application of the “New Invariance Principle” is key to the proof of the parameter error convergence. The developed approach is applied to the cold start emissions problem. The software design process for automotive powertrains on vehicles is growing increasingly complex. Verification and validation provides a systematic procedure to follow for the implementation of control algorithms on physical systems. However, errors can arise that prove costly if not mitigated early on in the verification and validation process. Therefore, the detection and mitigation of potential uncertainties early on in the design process is vital. In this work, the determination of the system model uncertainty is the focus of an adaptation algorithm designed in parallel with a discrete time, MIMO sliding controller. The unknown parameter representing the model uncertainty is updated online in order to decrease tracking error and control effort. The MIMO formulation allows for implementation of both coupled and decoupled frameworks, thus providing a basis for the algorithm to be utilized on a variety of complex vehicle systems. The control algorithms are implemented on a cold start emissions engine model as a case study. A matlab simulink environment is used for simulation results, and an engine test cell is used for experimental validation. Simulation results demonstrate that the algorithm drives tracking error to zero in a fraction of the run time and that the algorithm may be applied with equal efficacy to coupled and decoupled systems. Experimental results demonstrate the ability of the adaptation algorithm to estimate uncertainty in the engine and decrease tracking error.

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References

Cho, D. , and Hedrick, J. K. , 1989, “Automotive Powertrain Modeling for Control,” ASME J. Dyn. Syst. Meas. Control, 111(4), pp. 568–576. [CrossRef]
Dabney, J. B. , Barber, G. , and Ohi, D. , 2006, “Estimating Direct Return on Investment of Independent Verification and Validation Using COCOMO-II,” 10th IASTED International Conference on Software Engineering and Applications, pp. 394–399.
Shahbakhti, M. , Li, J. , and Hedrick, J. K. , 2012, “Early Model-Based Verification of Automotive Control System Implementation,” American Control Conference (ACC), Montreal, Canada, June 27–29, pp. 3587–3592.
Edelberg, K. , Pan, S. , and Hedrick, J. K. , 2013, “A Discrete-Time Sliding Mode Formulation for Automotive Cold-Start Emission Control,” Conference on Decision and Control, pp. 6818–6823.
Edelberg, K. , Pan, S. , and Hedrick, J. K. , 2013, “Design of Automotive Control Systems Robust to Hardware Imprecision,” ASME Paper No. DSCC2013-3900.
Khalil, H. K. , and Grizzle, J. , 2002, Nonlinear Systems, Vol. 3, Prentice Hall, Upper Saddle River, NJ.
Furuta, K. , 1990, “Sliding Mode Control of a Discrete System,” Syst. Control Lett., 14(2), pp. 145–152. [CrossRef]
Niu, Y. , Ho, D. W. , and Wang, Z. , 2010, “Improved Sliding Mode Control for Discrete-Time Systems Via Reaching Law,” IET Control Theory Appl., 4(11), pp. 2245–2251. [CrossRef]
Bartoszewicz, A. , 1998, “Discrete-Time Quasi-Sliding-Mode Control Strategies,” IEEE Trans. Ind. Electron., 45(4), pp. 633–637. [CrossRef]
Misawa, E. , 1997, “Discrete-Time Sliding Mode Control for Nonlinear Systems With Unmatched Uncertainties and Uncertain Control Vector,” ASME J. Dyn. Syst. Meas. Control, 119(3), pp. 503–512. [CrossRef]
Slotine, J.-J. E. , and Li, W. , 1991, Applied Nonlinear Control, Prentice Hall, Upper Saddle River, NJ.
Acary, V. , and Brogliato, B. , 2010, “Implicit Euler Numerical Scheme and Chattering-Free Implementation of Sliding Mode Systems,” Syst. Control Lett., 59(5), pp. 284–293. [CrossRef]
Chan, C. , 1997, “Discrete Adaptive Sliding-Mode Tracking Controller,” Automatica, 33(5), pp. 999–1002. [CrossRef]
Muñoz, D. , and Sbarbaro, D. , 2000, “An Adaptive Sliding-Mode Controller for Discrete Nonlinear Systems,” IEEE Trans. Ind. Electron., 47(3), pp. 574–581. [CrossRef]
Fang, Y. , Chow, T. , and Li, X. , 1999, “Use of a Recurrent Neural Network in Discrete Sliding-Mode Control,” Control Theory and Applications, Vol. 146(1), pp. 84–90. [CrossRef]
Pan, S. , Edelberg, K. , and Hedrick, J. K. , 2014, “Discrete Adaptive Sliding Control of Automotive Powertrains,” American Control Conference (ACC), Portland, OR, June 4–6, pp. 202–207.
Edelberg, K. , Shahbakhti, M. , and Hedrick, J. K. , 2013, “Incorporation of Implementation Imprecision in Automotive Control Design,” American Control Conference (ACC), Washington, DC, June 17–19, pp. 2854–2859.
Edelberg, K. D. , 2013, “Model-Based Approaches to Powertrain Control Design,” Master's thesis, University of California, Berkeley, Berkeley, CA.
Shaw, B. T., II , 2002, “Modelling and Control of Automotive Coldstart Hydrocarbon Emissions,” Ph.D. thesis, University of California, Berkeley, Berkeley, CA.
Barkana, I. , 2014, “Defending the Beauty of the Invariance Principle,” Int. J. Control, 87(1), pp. 186–206. [CrossRef]
Pan, S. , and Hedrick, J. K. , “Sliding Control With Adaptation in the Discrete Time Domain,” (unpublished).
Sanketi, P. R. , 2009, “Coldstart Modeling and Optimal Control Design for Automotive SI Engines,” Ph.D. thesis, University of California, Berkeley, Berkeley, CA.
Zhou, Q. , Sun, J. , and Qiu, J. , 2010, “Development of Control Strategy for SI Engine Cold Start,” International Conference on Information and Automation (ICIA), Harbin, June 20–23, pp. 1618–1621.
Shaw, B. , and Hedrick, J. K. , 2002, “Coldstart Engine Combustion Modelling to Control Hydrocarbon Emissions,” 15th Triennial World Congress of the International Federation of Automatic Control, July 21–26, Barcelona, Spain, p. 1515.
Heywood, J. B. , 1988, Internal Combustion Engine Fundamentals, Vol. 930, McGraw-Hill, New York.
Andrianov, D. , Brear, M. , and Manzie, C. , 2012, “A Physics-Based Integrated Model of a Spark Ignition Engine and a Three-Way Catalyst,” Combust. Sci. Technol., 184(9), pp. 1269–1301. [CrossRef]
Guzzella, L. , and Onder, C. H. , 2004, Introduction to Modeling and Control of Internal Combustion Engine Systems, Springer, Berlin, Heidelberg.
Pozniak, D. J. , 1976, “A Spark Ignition, Lean-Homogeneous Combustion, Engine Emission Control System for a Small Vehicle,” SAE Paper No. 760225.
Russ, S. , Thiel, M. , and Lavoie, G. , 1999, “SI Engine Operation With Retarded Ignition: Part 2—HC Emissions and Oxidation,” SAE Paper No. 1999-01-3507.
Ueno, M. , Akazaki, S. , Yasui, Y. , and Iwaki, Y. , 2000, “A Quick Warm-Up System During Engine Start-Up Period Using Adaptive Control of Intake Air and Ignition Timing,” SAE Paper No. 2000-01-0551.
Sanketi, P. , Zavala, J. , Wilcutts, M. , Kaga, T. , and Hedrick, J. , 2007, “MIMO Control for Automotive Coldstart,” 5th IFAC Symposium on Advances in Automotive Control.
Sun, J. , and Sivashankar, N. , 1998, “Issues in Cold Start Emission Control for Automotive IC Engines,” American Control Conference, Philadelphia, PA, June 21–26, Vol. 3, pp. 1372–1376.
Pan, S. , 2014, “Discrete Sliding Control for the Dynamics of Engine Cold Start,” Ph.D. thesis, University of California, Berkeley, Berkeley, CA.

Figures

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Fig. 1

Exhaust temperature tracking

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Fig. 3

Engine speed tracking

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Fig. 4

Intake air tracking

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Fig. 5

Adaptation for uncertainty in the exhaust temperature state

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Fig. 6

Adaptation for uncertainty in the AFR state

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Fig. 7

Adaptation for uncertainty in the engine speed state

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Fig. 8

Adaptation for uncertainty in the intake air state

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Fig. 9

Exhaust temperature tracking (coupled)

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Fig. 10

AFR tracking (coupled)

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Fig. 11

Engine speed tracking (coupled)

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Fig. 12

Intake air tracking (coupled)

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Fig. 13

Adaptation for uncertainty in the exhaust temperature state (coupled)

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Fig. 14

Adaptation for uncertainty in the AFR state (coupled)

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Fig. 15

Adaptation for uncertainty in the engine speed state (coupled)

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Fig. 16

Adaptation for uncertainty in the intake air state (coupled)

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Fig. 17

Control inputs of spark timing and fuel injection rate

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Fig. 18

Control inputs of mass of air and intake air flow rate

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Fig. 19

Complete engine test cell with heat exchanger and dynamometer

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Fig. 20

Tracking results via incremental adaptation for engine speed as implemented on engine test cell

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Fig. 21

Closeup view of tracking results via incremental adaptation for engine speed as implemented on engine test cell

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Fig. 22

Tracking results via incremental adaptation for intake air as implemented on engine test cell

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Fig. 23

Adaptation parameter estimation results via incremental adaptation for engine speed as implemented on engine test cell

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Fig. 24

Adaptation parameter estimation results via incremental adaptation for intake air as implemented on engine test cell

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