The polytropic volume method to detect engine events based on the measured cylinder pressure

Control Engineering Practice 20 (2012) 293–299

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Control Engineering Practice journal homepage: www.elsevier.com/locate/conengprac

The polytropic volume method to detect engine events based on the measured cylinder pressure T. Thurnheer, P. Soltic n ¨ Empa. Swiss Federal Laboratories for Materials Science and Technology, Internal Combustion Engines Laboratory, Uberlandstrasse 129, 8600 D¨ ubendorf, Switzerland

a r t i c l e i n f o

abstract

Article history: Received 13 May 2011 Accepted 13 November 2011 Available online 13 December 2011

Internal combustion engines deliver work using an intermittent thermodynamic process. For control and diagnosis purposes, it is useful to detect key events relative to the crank angle position. A new method to detect the intake valve closing (IVC), start of combustion (SOC), end of combustion (EOC) or exhaust valve opening (EVO), using the measured cylinder pressure as input, is described. The method is based on the observation that the compression and expansion processes are of polytropic nature. It is shown that the events can be detected by detecting the points where the real and the polytropic volume diverge. & 2011 Elsevier Ltd. All rights reserved.

Keywords: Internal combustion engines Combustion control and diagnosis Start of combustion End of combustion Valve timing Cylinder pressure based engine management

1. Introduction The measurement of the in-cylinder pressure of an internal combustion engine offers great potential for calibration, monitoring, diagnosis, validation of numerical modelling and closed-loopcontrol purposes (Held & Schubert, 1994; Leonhardt, Ludwig, & ¨ Schwarz, 1995; Leonhardt, Muller, & Isermann, 1999; Mladek, 2003; Powell, 1993). The measured in-cylinder pressure can be used to derive diverse engine parameters, e.g., the location of the cylinder peak pressure (Sellnau & Matekunas, 2000), indicated mean effective pressure (Corti, Moro, & Solieri, 2007), air–fuel ratio (Gilkey & Powell, 1985), estimated in-cylinder mass (Colin, Giansetti, Chamaillard, & Higelin, 2007) and SOC, perform thermodynamic analyses, such as heat release analysis (Krieger & Borman, 1966) and burn rate analysis (Brunt & Emtage, 1997; Rassweiler & Withrow, 1938; Shayler, Wiseman, & Ma, 1990). Many engine parameters can then be subsequently derived from the heat release or burn rate. The SOC is an important parameter to assess ignition delay in diffusion-controlled combustion concepts, flame kernel growth in spark-ignited concepts or success of combustion initiation in homogeneous charge compression ignition (HCCI) concepts. Different ways of detecting the SOC are described in the literature. Yoon, Lee, and Sunwoo (2007) detected the SOC by finding

n

Corresponding author. Tel.: þ41 58 765 4623; fax: þ 41 58 765 4041. E-mail address: [email protected] (P. Soltic).

0967-0661/$ - see front matter & 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.conengprac.2011.11.005

the crank angle position at which the difference pressure (the difference between the fired and motored pressure) reached 10 bar. Luja´n, Bermu´dez, Guardiola, and Abbad (2010) presented two methods of finding SOC, EOC and the peak heat release rate by analysing the first derivative of the cylinder pressure. The first method uses a time analysis of the signal, whereas the second is based on the instantaneous mean frequency variation. Both methods do not require pegging or filtering of the input signal. Assanis, Filipi, Fiveland, and Syrimis (2003) used the second derivative of the pressure signal to determine SOC, whereas Katraˇsnik, Trenc, and Opreˇsnik (2006) used the third derivative. Choi and Chen (2005) presented a fast method of predicting SOC using a combination of artificial neural networks and ignition delay model. The method was specifically designed for HCCI engines where SOC prediction is of great importance and showed reasonable accuracy. Ohyama (2001) transformed the in-cylinder pressure to a Fourier series to derive SOC. The SOC can also be detected by either analysing the heat release rate or burn rate, which is more complex as additional input parameters are needed. The EOC is usually identified by first calculating either the heat release or burn rate. The EOC is then found at the crank angle where either the cumulative heat release rate or the cumulative burn rate reaches a predefined value, e.g., 95%. IVC and EVO are normally not measured during engine operation because in most cases, the valve timing is constant (there are some exceptions with variable valve train though). This work describes an alternative approach for the detection of engine events during the high-pressure part of the working

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cycle. Above all, the approach described here directly incorporates the physics of the combustion and expansion processes which is well known to be polytropic (Heywood, 1988; Rassweiler & Withrow, 1938). Other approaches described in the literature just interpret the pressure signals (e.g., detecting fast changes looking at derivatives or the like), or use the measured in-cylinder pressure as input for further calculations. The authors experienced that the parametrisation of these other known approaches depends heavily on the engine and also on the operating point. Some are even not able to detect SOC accurately in difficult cases such as low engine load situations. Therefore, the approach described here is based on the physics of the gas trapped inside the cylinder, and events such as IVC, SOC, EOC or EVO can be detected as points, where the state of the gases inside the combustion chamber diverges from a polytropic change of state. The knowledge of SOC and EOC can be used, e.g., for closed-loop combustion control, injection- or ignition system fault analysis or fuel quality detection. The detection of IVC and EVO can be used for closed-loop control or diagnosis of valve actuation (e.g., when using cam-phasing or more flexible valve actuation systems such as electrohydraulic or electromagnetic valve trains).

2. Polytropic cylinder volume model The most intuitive and easily accessible measure of a reciprocating engine is the cylinder volume versus the crank position. Strictly speaking, the cylinder volume is only well-defined when all gas exchange valves are closed (i.e., during compression, combustion and expansion). However, the cylinder volume during gas exchange phases is normally defined as if the valves were always closed. For a reciprocating engine, the cylinder volume Vc versus crank angle f is given by  qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  E1 ðl þ 1cos f R2 sin2 fÞ V c ðfÞ ¼ V c,TDC 1þ ð1Þ 2 where V c,TDC denotes the cylinder volume at TDC (also known as clearance volume), E ¼ V c,BDC =V c,TDC is the compression ratio, R is the crank radius and l is the ratio of connecting rod length l to crank radius R. Fig. 1 depicts the definitions graphically. A detailed derivation of Eq. (1) can be found in Heywood (1988). Assuming that the change of state is polytropic whenever the valves are closed, no combustion occurs, and the trapped gas is ideal, and thus the cylinder volume Vc versus cylinder pressure p

follows the equation p  V nc ¼ constant

ð2Þ

where n denotes the polytropic exponent (Heywood, 1988). Assuming that the pressure pðfÞ is perfectly known and the change of state is polytropic during compression and expansion, the cylinder volume V c ðfÞ can be estimated as  1=ni pðfref,i Þ V c,est,i ðfÞ ¼ V c ðfref,i Þ 8f A i ð3Þ pðfÞ where i either stands for the compression or expansion process (thus, i ¼ compression or i ¼ expansion, and 8f A i consequently refers to all crank angles during the compression or expansion process), and fref,i denotes the respective reference crank angle with known states for the compression or expansion process (typically, one would choose the start of compression or the start of expansion as a reference). The polytropic exponent ni differs slightly for compression and expansion because the gas properties change due to combustion. Let us define a polytropic cylinder volume V p,i ðfÞ – with i ¼ compression or i ¼ expansion – not only during compression or expansion but throughout the whole engine cycle (i.e., a 360 1CA period for two-stroke- and 720 1CA for four-stroke-engines)  1=ni pðfref,i Þ 8f ð4Þ V p,i ðfÞ ¼ V c ðfref,i Þ pðfÞ Thus, all crank angles f where the polytropic cylinder volume V p,i ðfÞ is not equal to the real cylinder volume V c ðfÞ do not belong to the compression process (if i¼compression) or expansion process (if i ¼expansion) of the engine cycle. All experimental results presented here refer to the experiments performed with a spark ignited passenger car engine running at low speed and low load, even though the approach proved to work very well also on many other engines (e.g., large diesel engines). The operating conditions in this natural gas engine showed to be the most challenging ones since it was a stoichiometrically operated engine (i.e., high combustion temperatures and therefore high thermal shocks of the pressure transducer) using methane as a fuel (i.e., slow combustion) at very low engine load (i.e., low pressure levels and therefore high measurement noise). Fig. 2 shows the real cylinder volume Vc and the polytropic cylinder volumes computed from experimental cylinder pressure data for the spark ignited natural gas-fired passenger car engine running at 2000 min  1 and 2 bar brake mean effective pressure. The points where the intake valve closes

bore

Vc,TDC

TDC

Vc (ϕ)

Vc,BDC BDC

l

BDC

ϕ

stroke = 2 R

TDC

Fig. 1. Geometry of a reciprocating piston engine.

R

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1400 Vc

1200

Vp,compression Vp.expansion

V [cm3]

1000 800 600 400

IVC

EVO

200 EOC

SOC

0 0

90

180

270

360 φ [°]

450

540

630

720

Fig. 2. Real cylinder volume Vc and polytropic cylinder volumes V p,i with points IVC, SOC, EOC and EVO. The dotted vertical grid shows ignition events of all four cylinders where the spark discharge affected the pressure measurement.

295

an affine relationship) needs to be referenced to a known pressure ~ fÞ þ Dp. This procedure is using a pressure bias Dp: pðfÞ ¼ pð called pegging. There are several pegging techniques, such as setting cylinder pressure at inlet bottom dead centre equal to measured intake manifold absolute pressure, setting average cylinder pressure during the exhaust stroke equal to the measured exhaust back pressure, forcing a polytropic compression with a fixed or variable polytropic coefficient or using a second pressure transducer (Randolph, 1990). A different pegging technique was used here: The real cylinder volume Vc was known and from the measured cylinder pressure, the polytropic cylinder volume Vp could be calculated by evaluating Eq. (4). If the pegging pressure difference Dp is set correctly, these two volumes closely match. Therefore, the pegging pressure difference Dp was chosen such that the integrated absolute difference between real and polytropic cylinder volume was minimised during the compression, i.e., ! Z 345 1CA

Dp ¼ min

Dp A R

9V c ðfÞV p ðf, DpÞ9 df

ð5Þ

250 1CA

The resulting polytropic exponents were found using a linear least squares fit for logðpÞ versus logðVÞ data (because logðpÞ ¼ logðconstantÞn  logðVÞ according to Eq. (2)). Note that the used pegging technique is considered to be very accurate but more commonly used pegging techniques are computationally cheaper. Therefore, the use of a commonly used pegging technique, such as the pressure adjustment around TDC position with an absolute pressure sensor in the engine’s intake, could be necessary. However, the sensitivity of the results to pegging level errors and other uncertainties is discussed in detail in Section 5.

3. Detection of events To detect the events where the polytropic volume diverges from the real cylinder volume, the volume difference can be considered:

DV i ¼ V c V p,i Fig. 3. Experimental set-up (Horiba Dynas3 250LI test bench, water cooled Kistler 6041 pressure transducers flush mounted in the combustion chambers, and Kistler 2614A crank angle encoder).

(IVC), where combustion starts (SOC), where combustion ends (EOC) and where the exhaust valve opens (EVO) can be seen clearly by the naked eye. The experimental cylinder pressure data were recorded using a water-cooled piezo-electric transducer (Kistler 6041). Fig. 3 shows a picture of the experimental set-up. Although the incylinder pressure can be measured with different measurement ¨ principles, e.g., piezo-resistive (Muller et al., 2000), fibre opticbased (Roth, Sobiesiak, Robertson, & Yates, 2002) or non-intrusive pressure sensors (Mobley, 1999), piezo-electric pressure transducers are most commonly used (Asad, Kumar, Han, & Zheng, 2011). Piezo-electric pressure transducers are very well suited for incylinder pressure measurements because they are accurate, small and have a high frequency response (Randolph, 1990). However, they suffer from two main design flaws. First, heat flux to the sensor induced by the approaching flame front causes a temperature gradient across the pressure sensor (Davis & Patterson, 2006), which can lead to a shift of the sensor output that is not related to a change in in-cylinder pressure. This phenomenon is called thermal shock, and its effect on the pressure trace cannot ¨ be completely prevented (Putter & Eisele, 1986). Second, the ~ fÞ (usually a charge converted to pressure transducer output pð a voltage by a charge amplifier and converted to a pressure using

or written out in full  qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  E1 ðl þ 1cos f R2 sin2 fÞ DV i ðfÞ ¼ V c,TDC 1 þ 2  1=ni pðfref,i Þ V c ðfref,i Þ pðfÞ

ð6Þ

ð7Þ

with i ¼ compression or i ¼ expansion. Fig. 4 depicts DV i for the signals discussed in Fig. 2. The most straightforward method to detect the characteristic crank angle of the events IVC, SOC, EOC and EVO is to look at a certain threshold of the volume differences DV i . However, this approach is not sufficiently sensitive for reliable detection. The next approach would be to look at first or higher order derivatives of the volume difference with respect to the crank angle. This approach is feasible, but it is sensitive to noise. An alternative method, which was used here and is able to detect characteristic points in signals, is the wavelet transformation (Jaffard, Meyer, & Ryan, 2001) which allows for a flexible choice of filtering. Note that the use of the wavelet transformation led to good results with the data used but interested users of the polytropic volume method may find other well suited methods. The wavelet transformation computes the inner product of a function f ðfÞ (in this case, the volume difference) with a translated, compressed and stretched analysing function CðfÞ (the wavelet):   Z 1 1 fb df Cða,bÞ ¼ pffiffiffi f ðfÞC ð8Þ a a 1

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100 ΔV [cm3]

400 200 IVC

SOC

EVO

0 EOC

0 −50

−400

0

500 1000 crank angle index = φ [°] / 0.1 [°]

0

200 400 600 downsampled index = crank angle index / 2

0

200 400 600 downsampled index = crank angle index / 2

1500

200

−600 l.f.coeff.

ΔV [cm3]

−200

50

−800 −1000

Vc−Vp,compression

−1200

Vc−Vp,expansion

100 0 −100

−1400 90

180

270

360 φ [°]

450

540

630

720

Fig. 4. Real minus polytropic cylinder volumes DV i ¼ V c V p,i .

where a and b are parameters for wavelet dilation and shifting. A wavelet function has to fulfil numerous requirements, but only one is mentioned here Z 1 CðfÞ df ¼ 0 ð9Þ

0.1 h.f.coeff.

0

0 −0.1 −0.2

Fig. 5. Original signal and wavelet coefficients (low- and high-frequency parts) after a single level discrete wavelet transformation using the Haar wavelet.

1

In practice, measured data that have to be transformed are available in sampled form and have a finite length. As an alternative to calculating the inner product for the whole (a,b) parameter space, the discrete wavelet transformation (Mallat, 1989) is numerically much cheaper (Misiti, Misiti, Oppenheim, & Poggi, 2011). Instead of dilating the wavelet, the signal it passed to a low- and a high-pass filter and the resulting two signals are downsampled by two (i.e., only the even indexed elements remain). For a complete discrete wavelet transformation, this process is repeated for the remaining low-frequency signal as many times as the remaining low-frequency signal has a useful length. In the case studied here, a single level discrete wavelet decomposition (using the Haar wavelet described above) proved to be sufficient to detect the drifting points of the volume difference DV. However, no information is lost in the discrete wavelet transformation process of any level, and the original signal can always be reconstructed perfectly. Fig. 5 depicts the result of such a single level discrete wavelet transformation using the Haar wavelet for the DV signal in the crank angle range of 270–420 1CA. This range contains 1500 samples because the cylinder pressure was sampled at a resolution of 0.1 1CA. As Fig. 5 shows, the high-frequency coefficients (sometimes also called detail coefficients) allow for the detection of the runaway point by using a threshold level ( 0.02 in the example) that is undershot for a certain duration. For signals with

0.4 1st level high frequency coefficient

The wavelet transformation has the advantage that it can provide information on the scale (something like a frequency) of the signal by looking at the dilation factor a. Unlike the well-known Fourier transformation, which implies an infinite periodicity, the wavelet transformation can also provide information on when a characteristic of a signal changes by looking at the shifting parameter b. For the problem to detect the drifting points of the volume difference DV, the Haar wavelet proved to provide good results for the application studied here. The Haar wavelet is defined as 8 0 r x o 12 > < 1, CðxÞ ¼ 1, 12 rx o 1 ð10Þ > : 0 else

0.2 SOC EOC 0 −0.2

EVO

−0.4 for ΔVcompression

−0.6

for ΔVexpansion

−0.8 −1 180

IVC 270

360 φ [°]

450

540

Fig. 6. High-frequency parts of the single level discrete transformation for the DV signals. The detected events IVC, SOC, EOC and EVO are marked.

more noise, the signals may require more filtering (i.e., a higher level transformation or another wavelet shape may be necessary). Fig. 6 shows the detection of the events IVC, SOC, EOC and EVO based on the high-frequency signals of DV for compression and expansion. The events SOC, EOC and EVO could easily be detected using threshold values. Because the DV signal is very noisy around the IVC event, the detection of the first level frequency coefficient’s minimum proved to be a robust method for the data used (the proposed way of detecting IVC might not be suitable for different engine types or operating points). Note that in case of an exceptionally high combustion duration or even misfire, the detection of EOC and EVO could be problematic, particularly if the exhaust valve opens when combustion is not yet completed. However, if ordinary combustion durations are considered, the events EOC and EVO can clearly be distinguished. Fig. 7 depicts the p(V) data in a double logarithmic plot. This representation has the advantage that a polytropic change of state leads to a straight line with slope  n, as described earlier. It can

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60 40 20

1.7%

0

100

320

330

340

350

99%

97.4%

360 φ [°]

370

EOC (polytropic volume method)

EVO

80

ignition

EOC

101

released heat (%)

cylinder pressure [bar]

SOC

SOC (polytropic volume method)

100

IVC

297

380

390

400

Fig. 9. Released heat (detailed modelling using ‘‘WEG’’) and detected events SOC and EOC using the polytropic volume method.

102 cylinder volume [cm3] Fig. 7. Detected events in double logarithmic p(V) plot.

550 500

φ [°]

450 400 350 IVC SOC EOC EVO

300 250 200 0

50

100

150

cycle # Fig. 8. Detected events for 144 consecutive cycles.

clearly be seen with the naked eye that the events are correctly detected with the method described above. Fig. 8 depicts the events IVC, SOC, EOC and EVO not only for one but for all 144 consecutive cycles that were recorded for this example. The method proved to be robust. Not very surprisingly, the detection of the IVC event can give some outliers because measurement noise or real pressure oscillation phenomena have their largest influence on the polytropic volume at low pressure intervals. Note that the approach presented here is capable of detecting engine events not only during steady-state but also during transient engine operation since every engine cycle is analysed individually.

4. Polytropic volume method results versus reality 4.1. SOC and EOC compared with detailed heat release analysis In the previous section, the events SOC and EOC were detected according to the polytropic volume method. In this section, these events are compared with results of a detailed, and hence computationally intensive, heat release analysis, which represents the real heat release rate as closely as possible. In detailed heat release analysis, all relevant processes (gas properties, heat

transfer, blow-by processes, etc.) are modelled, and the heat release is calculated using the measured cylinder pressure as an input. To do so, the software package ‘‘WEG’’ of the Aerothermochemistry and Combustion Systems Laboratory of ETH Zurich was used (Obrecht, 2011). Fig. 9 depicts the calculated released heat using ‘‘WEG’’ and the events SOC and EOC detected by the polytropic volume method described above. The released heat is expressed as percents of the total chemical energy of the fuel present in the combustion chamber using the lower heating value of the fuel (50 MJ/kg in this case because the engine was fired with pure methane). The heat release analysis gives a final released heat of 99%, i.e., about 1% of the fuel is detected to leave the combustion chamber unburned via the exhaust valves. As Fig. 9 shows, the polytropic volume method detected the SOC as the point where 1.7% of the energy of the fuel was released. EOC was detected as the point where 97.4% of the heat was released or, in other words, as the point before 1.6% of the final heat was released. This analysis shows that the polytropic volume method is able to detect the SOC and EOC events as events very close to the start of end of the real heat release. 4.2. IVC and EVO compared to the valve lifts The engine whose data was used to describe the polytropic volume method has a conventional camshaft driven valve train with a cam phasing device on the intake side. In the operating point discussed here, the intake camshaft phase was set to the latest possible position. Fig. 10 depicts the valve lift curves provided by the engine manufacturer for the used intake cam phasing setting. Because the effective valve lift curves were not measured on this particular engine, the curves given by the manufacturer were assumed to comply with the real valve lift curves. In Fig. 10, the detected events IVC and EVO using the polytropic method are plotted on the valve lift curves. IVC was detected at basically zero intake valve lift. EVO was detected at a small lift of 0.18 mm. Therefore, it can be said that the polytropic method proves to be very well suited to detect IVC and EVO very close to the zero valve lift points.

5. Robustness of the method In this section, the sensitivity of the method against errors (pegging level, crank angle reference and compression ratio) is shown. The sensitivity analysis was particularly carried out with

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IVC (polytropic volume method)

valve lift [mm]

8

6

4

2

0

intake valves exhaust valves

0.18 mm

0.00013 mm 90

180

EVO (polytropic volume method)

5.2. Sensitivity to crank angle reference errors

10

270

360 φ [°]

450

540

630

Fig. 10. Valve lift curves and detected events SOC and EOC using the polytropic volume method.

Table 1 Pegging level influence on mean value and standard deviation of the detected events. Event location/Standard deviation

 0.2 bar offset

Reference pegging

þ0.2 bar offset

fIVC (1CA) sðfIVC Þ (1CA)

222.51 3.68

223.06 2.23

223.06 2.25

fSOC (1CA) sðfSOC Þ (1CA)

353.79 1.03

353.57 1.04

353.36 1.04

fEOC (1CA) sðfEOC Þ (1CA)

383.71 2.30

382.60 2.26

382.00 2.22

fEVO (1CA) sðfEVO Þ (1CA)

498.12 2.48

499.15 2.39

499.90 2.39

real measured engine data as described earlier instead of, e.g., using modelled data, in order for the findings to be uninfluenced by the choice of models and their parametrisation. 5.1. Sensitivity to pegging level errors Up to now, the pegging of the cylinder pressure signal was done such that the absolute difference between the real and the polytropic cylinder volume was minimised (see Eq. (5)). This approach is computationally intensive. For that reason, it is barely feasible for real-time applications. Therefore, the feasibility of the polytropic volume approach was studied by allowing a certain degree of pegging level uncertainty. To do so, the pegging level was additionally de-tuned as follows. 1. Negative mistuning: the smallest absolute pressure of the correctly pegged signal over all 144 cycles is about 0.3 bar. The pressure level is additively lowered by 0.2 bar, so the smallest absolute pressure is about 0.1 bar. 2. Positive mistuning: The correct pressure level is additively elevated by 0.2 bar. Table 1 lists the detected crank angles f and their standard deviations sðfÞ over 144 consecutive engine cycles already discussed above. The pegging level has only a rather small impact on the events IVC, SOC, EOC and EVO using the unchanged detection method and unchanged threshold levels (according to Fig. 6). The polytropic volume method is fairly insensitive to pegging errors.

For engine cylinder pressure measurement in R&D, a crank angle encoder is attached at the engine’s crankshaft. For the measurements discussed here, a Kistler 2614A crank angle encoder was used. Such encoders usually provide high-resolution pulses for the data acquisition system, triggering 0.1 1CA in this case, plus one reference pulse per revolution. Often, the angle between the reference pulse and the engine’s TDC position is not exactly known but has to be estimated, e.g., using motored pressure data, detailed heat release analysis or a capacitive TDC sensor mounted through the spark- or glow plug bore. In this case, the angle between real TDC and the encoder’s reference pulse was detected such that the spark discharge noise seen in the cylinder pressure signal fitted exactly with the ignition timing given by the engine control unit (see Fig. 2) and corrected for the crank angle reference assignment used so far. The question addressed in this section is what results gives the polytropic volume method if the TDC position is shifted at a certain angle. Ideally, the detected events would be shifted at the same angle. To quantify the sensitivity to crank angle reference errors, the TDC position was shifted by 72 1CA. Table 2 lists the resulting differences. The results show that a TDC mistuning is rather critical, especially for EOC detection. Towards the end of combustion, the pressure drops rapidly due to the fast moving piston, which makes it difficult to detect pressure rise due to the quenching flame. However, not only the polytropic volume method but all heat release- or burn rate analysis approaches are sensitive to TDC position errors, and thus it is recommended to pay special attention to correct TDC settings in any case. 5.3. Sensitivity to compression ratio errors The compression ratio of a given production engine can vary due to tolerances of the piston, the connecting rod, the cylinder head gasket and the cylinder roof shape. In research and development, the real compression ratio of the engine being tested is often experimentally determined by measuring the dead volume at TDC. As the cylinder’s displacement is perfectly known due to the high precision in crankshaft and bore manufacturing, the real compression ratio can easily be calculated using the measured dead volume at TDC. For production engines, the authors have the experience that the real compression ratio differs from the nominal by 0.5 in worst cases. Therefore, the compression ratio was mistuned by 70.5, i.e., the real compression ratio of 9.6 (which was experimentally measured by oil filling) was set to 9.1 and 10.1, respectively. Table 3 lists the resulting differences. Table 2 Effect of a TDC position error of 7 2 1CA on event detection. Event

f2 1CA fref

f þ 2 1CA fref

IVC (1CA) SOC (1CA) EOC (1CA) EVO (1CA)

 1.6  1.2  4.6  2.4

3.2 1.6 5.6 1.4

Table 3 Effect of a compression ratio error of 7 0.5 on event detection. Event

fE ¼ 10:1 fE ¼ 9:6

fE ¼ 9:1 fE ¼ 9:6

IVC (1CA) SOC (1CA) EOC (1CA) EVO (1CA)

0.0 0.0  0.6  0.2

0.0 0.2 0.8 0.0

T. Thurnheer, P. Soltic / Control Engineering Practice 20 (2012) 293–299

It can be seen, that the method is rather insensitive to the mistuning of the compression ratio, the errors in the detection of the events lies always well below 71 1CA for the case discussed here.

6. Conclusion A polytropic volume method, capable of detecting engine valve and combustion events, was presented and studied in this paper. The method is based on the well-known observation that the compression and expansion processes in an internal combustion engine are polytropic. Using the measured cylinder pressure, a hypothetical ‘‘polytropic volume’’ can be calculated. As long as compression and expansion occur, the polytropic volume corresponds to the real cylinder volume. Points at which the polytropic volume drifts away from the real cylinder volume can be detected as IVC, SOC, EOC and EVO. It could be shown that this detection can be performed using the simplest possible fast wavelet transformation at the first level. Comparing the detected events with real heat release and valve lift curves led to the conclusion that the polytropic method is capable of detecting the events in a meaningful way. SOC and EOC are detected at less than 2% of the start or end of the released heat, and the valve lift events are detected very close to zero valve lift. The method proved to be robust regarding pegging level errors, but it is relatively sensitive to crank angle mistuning. Given the access to a cylinder pressure signal of adequate quality, the authors believe that the polytropic volume method is a useful approach to gain feedback information for the control and diagnosis of engine operation.

Acknowledgements The authors are grateful for the financial support by the ETH Domain’s Swiss Competence for Energy and Mobility for research on cylinder based engine management (Project no. 705, CELaDE). Gratitude is expressed to Empa’s engine laboratory crew, namely to David Mauke for performing the test bench set-ups and the experiments. References Asad, U., Kumar, R., Han, X., & Zheng, M. (2011). Precise instrumentation of a diesel single-cylinder research engine. Measurement, 44, 1261–1278. Assanis, D. N., Filipi, Z. S., Fiveland, S. B., & Syrimis, M. (2003). A predictive ignition delay correlation under steady-state and transient operation of a direct injection diesel engine. Journal of Engineering for Gas Turbines and Power, 125, 450–457. Brunt, M. F. J., & Emtage, A. L. (1997). Evaluation of burn rate routines and analysis errors. SAE Technical Paper, 970037. Choi, Y., & Chen, J.-Y. (2005). Fast prediction of start-of-combustion in HCCI with combined artificial neural networks and ignition delay model. Proceedings of the Combustion Institute, 30, 2711–2718.

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