Research Papers

Optimal Control of the Heat Release Rate of an Internal Combustion Engine With Pressure Gradient, Maximum Pressure, and Knock Constraints

[+] Author and Article Information
Florian Zurbriggen

Institute for Dynamic Systems and Control,
Department of Mechanical
and Process Engineering,
ETH Zurich,
Zurich 8092, Switzerland
e-mail: florianz@ethz.ch

Tobias Ott

Institute for Dynamic Systems and Control,
Department of Mechanical
and Process Engineering,
ETH Zurich,
Zurich 8092, Switzerland
e-mail: toott@ethz.ch

Christopher Onder

Institute for Dynamic Systems and Control,
Department of Mechanical
and Process Engineering,
ETH Zurich,
Zurich 8092, Switzerland
e-mail: onder@idsc.mavt.ethz.ch

Lino Guzzella

Institute for Dynamic Systems and Control,
Department of Mechanical
and Process Engineering,
ETH Zurich,
Zurich 8092, Switzerland
e-mail: lguzzella@ethz.ch

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received February 1, 2013; final manuscript received April 29, 2014; published online August 8, 2014. Assoc. Editor: Yang Shi.

J. Dyn. Sys., Meas., Control 136(6), 061006 (Aug 08, 2014) (9 pages) Paper No: DS-13-1051; doi: 10.1115/1.4027592 History: Received February 01, 2013; Revised April 29, 2014

In this paper, we present an analysis of the optimal burn rate in an internal combustion engine (ICE) considering pressure gradient, maximum pressure, and knocking. A zero-dimensional model with heat losses is used for that purpose. The working fluids are assumed to behave like ideal gases with temperature dependent gas properties. In the first part, it is assumed that the burn rate can be arbitrarily chosen at every time instance in order to maximize the mechanical work. This leads to an optimal control problem with constraints. In the second part, a Vibe type burn rate is assumed, where the center of combustion, the duration and the form factor can be chosen in order to maximize the mechanical work. This Vibe type burn rate is finally compared with the arbitrary combustion as the benchmark in order to evaluate the potential of the more realistic burn shape.

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Grahic Jump Location
Fig. 1

System boundaries (dashed) of the zero-dimensional model and the corresponding flows of energy and mass

Grahic Jump Location
Fig. 2

Efficiencies of Vibe combustion depending on center and duration of combustion if the constraints (24)(27) are not considered

Grahic Jump Location
Fig. 3

Results of DP comparing the influence of the constraints

Grahic Jump Location
Fig. 4

Maximum possible efficiencies depending on the parameters mv, φc, and φd. The gray area denotes the region, where no feasible configuration is possible due to knocking and pressure-gradient limitations (see Fig. 5).

Grahic Jump Location
Fig. 5

Efficiencies depending on center and duration of combustion for a form factor mv = 4

Grahic Jump Location
Fig. 6

Comparison between arbitrary and Vibe combustion for two engine speeds 2000 rpm and 5000 rpm




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