A Polytopic System Approach for the Hybrid Control of a Diesel Engine Using VGT/EGR

Sorin Bengea; Ray DeCarlo; Martin Corless; Giorgio Rizzoni

doi:10.1115/1.1876473

Journal of Dynamic Systems, Measurement, and Control | Volume 127 | Issue 1 | TECHNICAL PAPERS

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TECHNICAL PAPERS

A Polytopic System Approach for the Hybrid Control of a Diesel Engine Using VGT/EGR

Sorin Bengea, Ray DeCarlo, Martin Corless and Giorgio Rizzoni

[+] Author and Article Information

Sorin Bengea

Eaton Innovation Center Eden Prairie, MNsorinBengea@eaton.com

Ray DeCarlo

School of ECE Purdue University W. Lafayette, INdecarlo@purdue.edu

Martin Corless

School of AAE Purdue University W. Lafayette, INcorless@purdue.edu

Giorgio Rizzoni

CAR-IT Ohio State University Columbus, OHRizzoni.1@osu.edu

J. Dyn. Sys., Meas., Control 127(1), 13-21 (Apr 25, 2004) (9 pages) doi:10.1115/1.1876473 History: Received January 28, 2003; Revised April 25, 2004

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Abstract

This paper develops a hybrid/gain scheduled controller for moving the state of a diesel engine through a driving profile represented as a sequence of operating points in the seven-dimensional state space of a mean value breathing nonlinear engine state model. The calculations for the control design are based on a third-order (reduced) model of the diesel engine, on whose state space the operating points are projected. About each operating point, we generate a third-order nonlinear error model in polytopic form. Using the polytopic error model at each operating point, a control design is set forth as a system of LMIs. The solution of each system of LMIs produces a norm bounded controller guaranteeing that $x_{i - 1}^{d} \to x_{i}^{d}$ where $x_{i}^{d}$ is the $i th$ desired operating point in the three-dimensional state space. The control performance is then evaluated on the seventh order model.

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References

Guzzella, L., and Amstutz, A., 1998, “Control of Diesel Engines,” IEEE Control Syst. Mag. [CrossRef], 18 (5), pp. 53–71.

van Nieuwstadt, M. J., Kolmanovsky, I. V., Moraal, P. E., Stefanopoulou, A., and Jankovic, M., 2000, “EGR-VGT Control Schemes: Experimental Comparison for a High-Speed Diesel Engine,” IEEE Control Syst. Mag. [CrossRef], 20 (3), pp. 63–79.

McClamroch, N. H., and Kolmanovsky, I., 2000, “Performance benefits of hybrid control design for linear and nonlinear systems,” Proc. IEEE [CrossRef], 88 (7), pp. 1083–1096.

Guckenheimer, J., 1995, “A robust hybrid stabilization strategy for equilibria,” IEEE Trans. Autom. Control [CrossRef], 40 , pp. 321–326.

Jankovic, M., Jankovic, M., and Kolmanovsky, I., 1998, “Robust nonlinear controller for turbocharged diesel engines,” "Proceedings of the 1998 American Control Conference", Philadelphia, PA, June, pp. 1389–1394.

Kolmanovsky, I, Moraal, P., van Nieuwstadt, M., and Stefanopoulou, A., 1999 “Issues in Modeling and Control of Intake Flow in Variable Geometry Turbocharged Engines,” "Proceedings of 18th IFIP Conference on System Modeling and Optimization", Detroit, July, 1997; published in "System Modeling and Optimization", edited by M.P.Polis, A.L.Dontchev, P.Kall, I.Lasiecka, and A.W.Olbrot, Chapman and Hall/CRC Research Notes in Mathematics, February 1999, pp. 436–445.

Kolmanovsky, I, Nieuwstadt, M., and Moraal, P., 1999, “Optimal control of variable geometry turbocharged diesel engines with exhaust gas recirculation,” DSC-Vol. 67 , "Proceedings of the 1999 ASME Congress and Exposition", ASME, November, pp. 265–273.

Utkin, V., Chang, H.-C, Kolmanovski, I., and CookJ., 2000, “Sliding Mode Control for the Variable Geometry Turbocharged Diesel Engines,” "Proceedings of the 2000 American Control Conference", Chicago, June, pp. 584–588.

Upadhyay, D., 2001, Modeling and Model based Control Design of the VGT-EGR System for Intake Flow Regulation in Diesel Engines, Ph.D. dissertation, Ohio State University, Columbus Ohio.

Bengea, S., DeCarlo, R., Corless, M., and Rizzoni, G., 2002, “A Polytopic System Approach for the Hybrid Control of a Diesel Engine using VGT/EGR,” Technical Report, Purdue University, July.

Landau, I. D., 2001, “Identification in Closed Loop: A Powerful Design Tool (Better Design Models, Simpler Controllers),” "Control Engineering Practice", Pergamon, New York, Vol 9 , pp. 51–65.

Khalil, H., 1996, "Nonlinear Systems", Prentice-Hall, Upper Saddle River, NJ.

Boyd, S., El Ghaoui, L., Feron, E., and Balakrishnan, V., 1994, "Linear Matrix Inequalities in System and Control Theory", SIAM, Philadelphia.

Jankovic, M., Jankovic, M., and Kolmanovsky, I., 2000, “Constructive Lyapunov Control Design for Turbocharged Diesel Engines,” IEEE Trans. Control Syst. Technol. [CrossRef], 8 (2), pp. 288–299.

Stefanopoulou, A. G., Kolmanovsky, I. V., and Freudenberg, J. S., 1998, “Control of variable geometry turbocharged diesel engines for reduced emissions,” "Proceedings of the American Control Conference", Philadelphia, June, pp. 1383–1388

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Figure 8

Second set of simulations: plots of the desired driving profiles (dotted) and of the simulated driving profile (solid)

Desired trajectory (dashed), the trajectory from the first set of simulations (solid), and the trajectory from the second set of simulations (dotted)

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Figure 9

Desired trajectory (dashed), the trajectory from the first set of simulations (solid), and the trajectory from the second set of simulations (dotted)

Schematic diagram of a VGT/EGR diesel engine

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Figure 1

Schematic diagram of a VGT/EGR diesel engine

Sketch showing the concept of polytopic controller design for hybrid systems

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Figure 2

Sketch showing the concept of polytopic controller design for hybrid systems

First set of simulations: plot of the simulated value of the partial state. (p1 and p2 are represented by the solid and dashed curves, respectively)

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Figure 3

First set of simulations: plot of the simulated value of the partial state. (p1 and p2 are represented by the solid and dashed curves, respectively)

First set of simulations: plots of the input flows through EGR and VGT

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Figure 4

First set of simulations: plots of the input flows through EGR and VGT

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Figure 5

First set of simulations: plots of the desired driving profiles (dotted) and of the simulated driving profile (solid)

Second set of simulations: plot of the simulated value of the partial state (p1 and p2 are represented by the solid and dashed curves, respectively)

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Figure 6

Second set of simulations: plot of the simulated value of the partial state (p1 and p2 are represented by the solid and dashed curves, respectively)

Second set of simulations: plots of the input flows through EGR and VGT

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Figure 7

Second set of simulations: plots of the input flows through EGR and VGT

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Bengea S, DeCarlo R, Corless M, Rizzoni G. A Polytopic System Approach for the Hybrid Control of a Diesel Engine Using VGT/EGR. ASME. J. Dyn. Sys., Meas., Control. 2004;127(1):13-21. doi:10.1115/1.1876473.

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A Polytopic System Approach for the Hybrid Control of a Diesel Engine Using VGT/EGR

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