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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

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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Engine speed tracking (coupled)

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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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