Cold start modelling of spark ignition engines

https://doi.org/10.1016/j.conengprac.2011.05.005Get rights and content

Abstract

The ability of mean value models to replicate the key characteristics of automotive powertrains has been well established over the past four decades. There has been considerable success in the application of these models to controller design, with improved emissions and performance of the primary benefits. However, these low order models typically must make certain assumptions about the engine—with constant temperature operation a standard approximation. As economy and emissions at every point in the drive cycle become scrutinised, the cold start operation of the engine becomes more critical and the constant temperature assumption is limiting. This paper seeks to develop a model framework for capturing the temperature transients and gaseous concentrations throughout the engine. A methodology for calibrating the model is also presented, and uses a combination of steady state and transient testing. Finally, certain states in the full model are eliminated to produce a family of reduced order models, with the intention of outlining the minimum complexity required for control and optimisation studies with differing objectives.

Introduction

The use of mathematical models is now widespread in the design and development of automotive engine management systems, however the development of automotive engine models that empirically approximate the indicated torque in terms of engine operating and control variables began in the 1970s with the work of Hazell and Flower (1971), Flower and Hazell (1971), Prabhakar, Citron, and Goodson (1977) and Cassidy, Athans, and Lee, (1980). These ‘black box’ models were largely based around extensive static maps, and as a result suffered from the cost of extensive calibration experiments required and a lack of portability between engine variants. Consequently there was, and still is, significant motivation to reduce the storage and calibration requirements of black box approaches by including some physical processes within the model. Naturally, this also promotes greater portability of the model between engines.

It was not until the 1980s that the potential to use mixed static and dynamic models as an effective simulation and control tool became apparent in work conducted by Dobner, 1980, Dobner, 1983, Cho and Hedrick (1989), Moskwa and Hedrick, 1990, Moskwa and Hedrick, 1992 and Moskwa and Weeks (1995). This approach to modelling was based on simple physical approaches with typical approximations including continuous flows through volumes, constant temperature and gas properties, and the approach was termed a mean value engine model (MVEM) by Hendricks (1986). The approach has been extended to cope with more complex powertrains including components such as external exhaust gas recirculation and turbochargers by researchers including (Eriksson et al., 2002, Muller et al., 1999).

The success of these models in dealing with various powertrain control strategies is well established with a multitude of examples in the literature including work by Jankovic and Kolmanovsky (2000), Eriksson, Frei, Onder, and Guzzella (2002), Choi and Hedrick (1998) and Sun and Sivashankar (1997). However, the absence of temperature dynamics in the models limits their application to warmed engine operation. Meanwhile, the performance of engines following a cold start is growing in importance due to the increased fuel consumption and emissions relative to a warm engine, and the high proportion of driving time conducted with the engine not completely warm—an average urban journey duration of less than 10 miles was reported in one US study by Hu and Reuscher (2004), while average trip durations of less than 20 min have also been noted by the Australian Bureau of Statistics (2008). Hybrid-electric vehicles, with continual engine stop–start operation in urban conditions, may also be subject to more frequent periods of cold start operation. To address these issues, Sandoval and Heywood (2003) noted the mean value model must be augmented to include temperature-dependant frictional effects for torque and fuel based studies, while it is also apparent that the exhaust gas temperature is required for catalyst light-off and emission based problems.

There exist mathematical models that give a good insight into the engine thermal processes of major engine components and demonstrate good correlation with experimental data, with much of the pioneering work done by Kaplan and Heywood (1991), Shayler, Christian, and Ma (1993), Veshagh and Chen (1993), and Cortona and Onder (2000). The common approach is the amount of the heat transferred from the exhaust gases to the cooling system is treated as the input to the model. Given the amount of heat rejection, it is possible to find the portion of fuel energy that is transferred to the engine block, coolant and oil. Kaplan and Heywood (1991) assume a constant amount of heat rejection and exhaust gas temperature, while Cortona and Onder (2000) required a static map of cycle-averaged total heat transferred through the cylinder walls. Both cases require extensive calibration to map adequate heat rejection characteristics in terms of the engine operating variables. Other approaches at thermal modelling have investigated heat transfer at the exhaust gas side, where exhaust gas temperature, mixture composition and various coefficients of heat transfer are required. Previous attempts in this regard have typically been of high order and cycle-by-cycle combustion model such as in Bohac, Baker, and Assanis (1996), or are phenomenologically based as in Fiengo, Glielmo, Santini, and Serra (2003). Importantly, all of these thermal models do not capture the effect of variations with engine control variables (such as spark advance or air fuel ratio) which makes model based control and optimisation difficult at best.

Initial progress at incorporating engine warm up into mean value type models for two different powertrains has been described in Manzie, Keynejad, Andrianov, Dingli, and Voice (2009) and Roeth and Guzzella (2010). This paper builds on these works by not only presenting a complete, validated MVEM with thermal dynamics and the influence of species concentrations (an important characteristic for emissions studies), but also includes validation over a drive cycle. Furthermore, a model reduction procedure is undertaken to provide families of models suited to different control and optimisation problems. In all cases, there is a high emphasis on physics-based aspects in the model to retain portability of the approach.

Section snippets

Engine model

The automotive engine can be split into three interconnected physical domains—the mechanical domain where the dynamics of engine speed are considered; the thermal domain describing the temperature dynamics of, and heat transfer between, the fluids flowing throughout the engine system; and the thermodynamic domain containing both the combustion process and the gaseous pressure and temperature dynamics within the various control volumes in the engine. The overall system being modelled is

Model calibration procedure

The test engine used was a 4.0 l, Ford Falcon BF inline six cylinder engine with 10.3:1 compression ratio, and was mounted on a 460 kW transient AC dynamometer. Aside from the standard engine sensors and dynamometer load feedback, an additional thermocouple was mounted at the exhaust port to measure Tcyl, and in-cylinder pressure was recorded to measure indicated mean effective pressure. External exhaust gas recirculation was disabled in the engine.

From manufacturer data and CAD drawings, most of

Validation

The model from Section 2 with parameters identified in Section 3 was then produced in the Dymola–Modelica simulation environment. The calibration data consisted of largely steady state engine operating conditions, with temperature transients used in the calibration of the thermal domain and temperature-dependant friction model.

To measure the fidelity of the model for unseen data, the cold engine was run over the NEDC cycle starting until the thermostat opened. The engine speed was obtained from

Model reduction

The model described in 2 Engine model, 3 Model calibration procedure is based on physical relationships using lumped approximations for each body, and as many physical parameters as possible to reduce the model calibration requirements. However the total number of states present in the model (if Assumption 8 is utilised, there are five states in the intake and exhaust manifolds, nine temperatures and one mechanical state), requires 17 s with a Pentium(R) 4 CPU, 3.2 GHz processor, and 2G RAM to

Conclusions

A physics-based, control-oriented engine model that encompasses the cold start operation has been presented in this paper, along with a set of assumptions under which the model is valid. The model is able to make use of detailed knowledge about the engine's physical parameters in specifying the system. For the remaining unknown model parameters, a model calibration procedure is presented based on steady state speed-load conditions covering the warm-up period.

The model was found to have very

Acknowledgments

The authors would like to acknowledge the ARC funding of Linkage Project LP0453768 and the in-kind support provided by the Ford Motor Company of Australia. Furthermore, the resources and facilities within the ACART research centre (http://www.acart.com.au) were instrumental in conducting the experimental work. The comments of the anonymous reviewers were also very helpful in refining the final manuscript.

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