Engineering Engineers, Part D: Journal of Automobile

Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering http://pid.sagepub.com/

Estimation of effective compression ratio for engines utilizing flexible intake valve actuation Karla Stricker, Lyle Kocher, Ed Koeberlein, Dan Van Alstine and Gregory M Shaver Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering 2012 226: 1001 originally published online 29 February 2012 DOI: 10.1177/0954407012438024 The online version of this article can be found at: http://pid.sagepub.com/content/226/8/1001

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Original Article

Estimation of effective compression ratio for engines utilizing flexible intake valve actuation

Proc IMechE Part D: J Automobile Engineering 226(8) 1001–1015 Ó IMechE 2012 Reprints and permissions: sagepub.co.uk/journalsPermissions.nav DOI: 10.1177/0954407012438024 pid.sagepub.com

Karla Stricker, Lyle Kocher, Ed Koeberlein, Dan Van Alstine and Gregory M Shaver

Abstract Modulation of the effective compression ratio, a measure of the amount of compression of in-cylinder gases above intake manifold conditions, is a key enabler of advanced combustion strategies aimed at reducing emissions while maintaining efficiency, and is directly influenced by modulation of intake valve closing time. To date, the effective compression ratio has most commonly been calculated from in-cylinder pressure data, requiring reliable in-cylinder pressure sensors. These sensors are generally not found on production engines, and thus a method is needed to determine effective compression ratio without in-cylinder pressure data. The work presented here outlines an estimation scheme that combines a high-gain observer with a physically-based volumetric efficiency model to estimate effective compression ratio using only information available from stock engine sensors, including manifold pressures and temperatures and air flows. The estimation scheme is compared to experimental engine data from a unique multi-cylinder diesel engine test bed with flexible intake valve actuation. The effective compression ratio estimator was tested transiently at five engine operating points and demonstrates convergence within three engine cycles after a transient event has occurred, and exhibits steady-state errors of less than 3%.

Keywords Estimation, effective compression ratio, engines

Date received: 3 September 2011; accepted: 12 January 2012

Introduction Emissions regulations and demand for improved fuel economy drive the development of increasingly complex engine systems and control strategies. Understanding the dynamic interaction between engine subsystems and their impact on both the gas exchange and combustion processes is essential for incorporating new combustion strategies that target reduced emissions and increased efficiency. As shown in Figure 1, the gas exchange process of a modern diesel engine directly influences the combustion process, and vice versa. Conventional engine actuators, such as variable geometry turbochargers (VGTs) and exhaust gas recirculation (EGR) valves, allow manipulation of the outputs of the gas exchange process. The combustion process likewise affects the gas exchange process, most significantly in the form of exhaust gas enthalpy. Previous studies have well established the role conventional engine systems and actuators, VGT and EGR valves, play in reducing emissions, as well as understanding the importance of their effect on overall

engine performance.1–5 More recent engine development considers the additional capability of variable valve timing (VVT) or variable valve actuation (VVA), which allows flexibility in the valve train to modulate the valve events independently of piston position, such as intake and exhaust valve opening and closing times. Several studies have investigated the impact of this additional actuator on the gas exchange process and implications for advanced combustion strategies.

VVA and the gas exchange process Lancefield and Methley6 performed a simulation study to determine the effect of VVA, coupled with VGT and

Purdue University, West Lafayette, IN, USA Corresponding author: Gregory M Shaver, Purdue University, 585 Purdue Mall, West Lafayette, IN 47907, USA. Email: [email protected]

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Proc IMechE Part D: J Automobile Engineering 226(8)

EGR valve posion VGT nozzle posion

trapped mass

Gas Exchange Process

[O2] at IVC ECR Temp. at IVC

VVA (IVO, IVC, EVO,EVC)

“mixing” Injecon parameters Engine speed

Combuson Process

Torque

• Convenonal combuson

Emissions

• Advanced combuson strategies (i.e. PCCI, lied flame)

Fuel efficiency Exhaust enthalpy

Exhaust gas enthalpy

Figure 1. Gas exchange and combustion processes.

EGR, on engine performance and fuel consumption. Babajimopoulos et al.7 demonstrates that VVA is an effective tool to modulate EGR for use in control of homogeneous charge compression ignition combustion (HCCI). Leroy et al.8 presented a model for in-cylinder fresh air and EGR mass in a turbocharged sparkignition engine with VVT that considers the total charge mass in the cylinder, including mass trapped during valve overlap, and focused on independently phasing intake and exhaust valves. Milovanovic et al.9 showed that VVT has a strong influence on engine parameters and cylinder charge properties such as internal EGR, and that VVT has potential to be used to control these parameters at IVC and subsequently control the auto-ignition process in a gasoline engine. An experimental study by Widd et al.10 utilizes thermal management and VVA for HCCI combustion phasing control, which is key for emissions reductions. HCCI combustion timing is also targeted by Shaver et al.,11 in which the authors use their previous modeling work12 to develop a controller. In that study, the amount of compression is modulated via IVC timing. A simulation study by Yilmaz and Stefanopoulou13 investigates the use of exhaust valve timing modulation in charge dilution control for reduced nitrogen oxide emissions. The work of Deng and Stobart14 details the effect of various variable valve strategies on fuel efficiency, and results show an improvement in brake-specific fuel consumption with advanced IVC timing. Mahrous et al.15 showed a decrease in engine air flow and volumetric efficiency with either early or late intake valve closing when compared to a nominal closing time. One of the key characteristics of the gas exchange process that is affected by valve modulation is the effective compression ratio (ECR), a measure of the effective in-cylinder compression process above intake manifold conditions. Using conventional engine hardware and actuators, the compression ratio is generally fixed or has limited variability, however the work of Shaik et al.16 motivates a need for variable compression ratios in automobile engines for improved performance

through implementation of advanced combustion strategies, such as homogeneous charge compression ignition. Rychter et al.17 detail a theoretical study in which variation of the compression ratio allows a reduction in both fuel consumption and combustion noise. Experimental studies by Gerard et al.18 and Pesic et al.19 also show the benefits of varying the compression ratio to reduce emissions and improve fuel economy. Haraldsson et al.20 target optimal HCCI combustion timing in a gasoline engine using exhaust cam-phasing as well as a variable compression ratio, realized by tilting the engine. While these studies accomplish variable compression ratios through hardware modifications, several other efforts leverage valve modulation as a method for effectively varying an engine’s compression ratio. Using VVA, Helmantel et al.21 discuss the role ECR plays in controlling combustion phasing in order to reduce NOx emissions. He and Durrett22 describe the effect of late IVC timing on the ECR and reducing cylinder temperature, as well as confirming a reduction in volumetric efficiency. Modiyani et al.23 also showed a direct link between IVC timing and ECR and, more specifically, that the same reduction in ECR may be achieved by either an early or late IVC timing. The study also showed the effect this reduction in ECR has on the entire gas exchange process, in that lowering the ECR reduces volumetric efficiency, and subsequently the charge flow through the engine. While this is generally undesirable, lower ECRs are beneficial when considering advanced-mode combustion strategies such as PCCI, or premixed charge compression ignition. Kulkarni et al.24 showed that ECR reductions via early intake valve closure, coupled with early fuel injection and modest amounts of EGR, lead to large reductions in NOx emissions without penalties on fuel economy. Several other efforts report similar results of lower NOx emissions through use of reduced ECR, via either early or late IVC modulation.21,25–28 It is evident that careful coordination of valve events and the ECR is key for closed-loop targeting of advanced combustion strategies, and implementing

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these strategies real-time requires knowledge of the ECR.

Compression ratio estimation

in most cases does not occur exactly when the piston is at bottom dead center. Thus, a geometric ECR (GECR) is defined as GECR =

Historically, methods for determining the compression ratio of an engine rely heavily on the availability of accurate in-cylinder pressure measurements. Several efforts estimate variations in desired compression ratio for diagnostics or control purposes. For example, Hountalas et al.29 detail an experimental investigation to determine compression conditions using in-cylinder pressure traces in a geometrically variable compression ratio engine. The work includes experimental tests at only one operating point and uses portions of the incylinder pressure trace to determine effects of different parameters (i.e. inlet pressure, blowby) on the compression process. Lamaris and Hountalas30 build on the work in Hountalas et al.29 to validate a diagnostic method for variations in compression conditions (i.e. reductions in compression ratio) using a thermodynamic compression model coupled with cylinder pressure traces. Similarly, Watzenig et al.31 outline a thermodynamic model-based approach to estimate compression ratio using in-cylinder pressure traces for fault diagnostic purposes. Klein et al.32–35 present various methods for estimating compression ratio, using either a polytropic compression model or a heat release model, both in simulation and experiment. Each of the estimation methods use in-cylinder pressure data, and estimates of the compression ratio are used for diagnostic and control purposes in a SAAB variable compression engine, in which the compression ratio can be varied by tilting the mono-head of the engine. As stated, these methods for estimating the compression ratio of an engine all depend on the availability of in-cylinder pressure data. However, accurate in-cylinder pressure measurements are not commonly available in production engines, motivating the need for a real-time estimation scheme for ECR using only information available from stock engine sensors. The work presented here includes an estimation scheme for effective compression ratio, relying not on in-cylinder pressure measurements, but instead on knowledge from typical production-viable on-engine sensors, including manifold temperatures and pressures, fresh air and exhaust gas flows.

Vivc Vtdc

where Vivc is the volume in the combustion chamber at the time of intake valve closing. This definition, however, does not account for both piston-induced and gas momentum-induced compression, each of which contribute to the overall compression process. As such, a more accurate approach for characterizing the effective compression process is desired for implementation in models predicting engine performance and emissions. A commonly used method for calculating the ECR that more accurately captures the effective compression process is the pressure-based method.22,23,36 The pressure-based method for calculating ECR relies on measurements of in-cylinder pressure to generate a log P–log V diagram (see Figure 2). The compression stroke is linearly extrapolated assuming polytropic compression, and the slope of this line on a log–log scale is the polytropic coefficient. A horizontal line is plotted at the intake manifold pressure, averaged over the intake stroke. Where this IMP line intersects the extrapolated polytropic compression line is termed the effective volume at intake valve closing. The ECR is then defined as ECR =

Vivceff Vtdc

The geometric compression ratio of an engine is defined as the ratio of in-cylinder volume when the piston is at bottom dead center (Vbdc ) to the in-cylinder volume when the piston is at top dead center (Vtdc ) Vbdc Vtdc

ð1Þ

The actual compression process, however, does not effectively start until after the intake valve closes, which

ð3Þ

This method of calculating ECR is more accurate than using a GECR (equation (2)) since it takes into account the effect of flow momentum on compression of the incylinder mass, as well as piston-motion-induced compression.22 However, this accuracy comes at the cost of requiring a reliable method for measuring in-cylinder pressure. Additionally, this method of calculating ECR relies on data from a previous engine cycle, and cannot

ECR defined

GCR =

ð2Þ

Figure 2. Pressure-based method to calculate ECR.36

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necessarily be considered a real-time measurement. Generating a reliable and accurate estimation scheme for ECR, without the need for in-cylinder pressure measurements, would be greatly beneficial for developing advanced-mode combustion strategies. In the following sections, a high-gain observer for ECR is outlined and validated.

Development of a high-gain observer for ECR estimation Several classical observer design strategies exist, including high gain, Kalman, Luenberger, sliding mode, and dirty derivative filters. Several of the charge flow estimation schemes developed have been based on Luenberger estimation techniques.37–39 For estimation of a slowly varying variable, the system state vector may be augmented to include that variable, with its time derivative assumed to be zero. In many cases, a Luenberger or Kalman filter is then sufficient to estimate the system states, including the ‘slowly’ varying variable. However, there are certain instances when the rate of change of the variable of interest is of the same order of magnitude as the other system states, as is the case with ECR where it would be varied and estimated on a cycle-tocycle basis. In these cases, the assumption of a zero rate of change is no longer acceptable, and a different approach must be taken to estimate the desired variable. For the current application, a high-gain observer is developed for the unknown variable, ECR. High-gain observers have been used for numerous nonlinear control applications,40–44 including input estimation techniques and estimation of uncertain system variables, and are generally considered more desirable than classical estimation techniques for real-time implementation.

High-gain observer In this section, a high-gain observer for an unknown system variable is outlined using a strategy considered by Stotsky and Kolmanovsky,44 and is also similar to those presented by Khalil41 and Saberi and Sannuti.43 Consider a first-order dynamic system described by z_ = y + x

ð4Þ

where z and y are measured signals and x is the unknown variable to be estimated. The variable x is not assumed to be slowly varying. The observer is described in terms of an auxiliary variable e satisfying _ ke + ky + k2 z e[

ð5Þ

where k is a positive observer gain. Estimate of the unknown variable x is given by x^[kz e

ð6Þ

It can be shown that x^ ! x for large gain k. Consider the error between x^ and x

e = x^ x = kz e x

ð7Þ

Now assuming that x_ is bounded, as _ j4b1 supjx(t)

ð8Þ

t

a transient bound is obtained for the estimation error rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi b2 ð9Þ je(t)j4 (e(0))2 exp ( kt) + 12 k This transient bound implies that by choosing a sufficiently large gain k, the upper bound on the estimation error can be made arbitrarily small. Hence, e in equation (7) tends to zero and x^ ! x. The proof is presented in Appendix 2.

Estimation of volumetric efficiency and charge flow The high-gain observer described in the previous section is now applied to estimation of volumetric efficiency as well as flow through an engine, or charge flow, in order to estimate the ECR. Consider intake manifold pressure (pim ) dynamics, described by the commonly used manifold filling dynamics45–47 p_ im =

g im Rim (Wegr Tegr + Wcomp Tcac We Tim ) Vim

ð10Þ

Here, Wcomp and Tcac are the measured values of fresh air flow through the compressor and the gas temperature of the fresh air at the charge air cooler outlet, respectively. Charge flow We is to be estimated. Rim and g im are the gas constant and ratio of specific heats of the air in the intake manifold, respectively, both taken at ambient conditions. Vim is the volume of the intake manifold, considered to be the volume between the compressor outlet and the cylinders. EGR flow can be determined using standard orifice flow equations45 8 pj pi pffiffiffiffiffiffi > C if pj \ pi CA eff > pi RTi > > > > < if pj = pi Wegr = 0 > > > > pi j > ppffiffiffiffiffiffi if pj . pi > ð11Þ : CAeff RTj C pj where the pressure ratio correction factor, C is given by 8 pffiffiffi 2 ((g + 1)=2(g1)) > > > > g g+1 > > g=(g1) > > pi 2 > > if 4 > g+1 < pj pi ffi C = sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi (g + 1)=g 2=g > pj > pi pi 2g > pj > pj g1 > > > > > g=(g1) > > : if pi . 2 pj g+1 ð12Þ

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with g corresponding to the ratio of specific heats of the exhaust gas. The pressure ratio is determined from pressure drop across a calibrated orifice, measured on engine, and intake manifold pressure, pim , where pim corresponds to the downstream pressure pj in equation (11). The upstream temperature, Ti , corresponds to the temperature of the recirculated exhaust gas, Tegr , and is taken to be the on-engine temperature measurement of the calibrated orifice. C is the discharge coefficient associated with the valve opening and Aeff is the effective flow area, which is a function of the EGR valve position. Charge flow, We , can be described by the speeddensity equation48 We =

1 r h Vd N 2 im v

ð13Þ

where Vd is the displacement volume of the engine, and N is the engine speed in revolutions per minute. The gas density in the intake manifold, rim , can be written in terms of intake manifold temperature and pressure via the ideal gas law. Charge flow is then written as We =

pim h Vd N 2Rim Tim v

ð14Þ

and the pim dynamic equation (equation (10)) can be written as g Rim g pim (Wegr Tegr + Wcomp Tcac ) im hv Vd N p_ im = im Vim 2Vim ð15Þ

From the observer derived in the previous section, z, y and x are chosen as z = pim g Rim y = im Wegr Tegr + Wcomp Tcac Vim g pim x = im hv Vd N 2Vim

ð16Þ

With these assignments, it is seen that equation (15) becomes exactly the first-order system described by equation (4). We can then combine equations (4) and (6) with equations (5) and (16) to derive an estimate for hv h ^v =

2Vim (e kpim ) gim pim Vd N

ð17Þ

with e given by e_ = k2 pim ke + k

gim Rim (Wegr Tegr + Wcomp Tcac ) Vim ð18Þ

Again, with the choices of z, y and x defined in equation (16), equations (15), (17) and (18) correspond to equations (4), (5) and (6). The estimated volumetric efficiency in equation (17) can then be used in the speed-density equation (equation (14)) to estimate charge flow

ê = W

pim h ^ Vd N 2Rim Tim v

ð19Þ

Estimation of ECR Once an estimate for volumetric efficiency is obtained via equation (17), it is used to estimate the ECR. A static volumetric efficiency equation developed in Kocher et al.36 is given by equation (20). This volumetric efficiency model is physically-based and requires no tuning parameters, and was extensively experimentally validated against an advanced multi-cylinder diesel engine equipped with a VVA system. The experimental data spans the operating range of the engine, including stock air-handling actuator sweeps (e.g. EGR and VGT position sweeps) as well as IVC timing sweeps using the VVA system, for a total of 286 operating conditions. Kocher et al.36 report model predictions within 2.2% RMS (root mean square) error pim hv =

k

Vtdc ECR Vivc

c

Vivc cRv pem Vivo cRv pem (Vevc Vivo ) Rp c

pim Vd Rp

+

ht pim (Vtdc ECR Vivo ) + 1000 (Twall Tim )(SA) cp pim Vd R

ð20Þ

In the model (equation (20)), Vivo , Vevo and Vevc are the respective in-cylinder combustion chamber volumes at the time the intake valve opens, the time the exhaust valve opens, and the time the exhaust valve closes. cp , cv and R are specific heats and gas constant of the gas in the intake manifold, and pem is the exhaust manifold pressure, a stock measurement typically found on production diesel engines. The polytropic compression coefficient, k, is taken to be 1.35, a typical value for directinjection diesel engines.48 The heat transfer coefficient, ht, is a function of engine speed (N), intake manifold temperature and pressure (Tim , pim ). SA is the integrated surface area, and is a function of intake valve open and close time ( IVO, IVC), exhaust valve close time (EVC), and engine speed. The temperature of the cylinder walls, Twall is taken as the average of the exhaust temperature (Tem ) and the engine coolant temperature (Tclt ). The estimate of ECR is converged upon numerically using the model in equation (20), as it cannot be inverted analytically to solve directly for ECR. Estimator inputs and constants are listed in Table 1, as well as shown in a block diagram of the estimation scheme in Figure 3. As shown, the ECR estimation scheme does not require in-cylinder pressure data and uses only measurements readily available on production engines. The overall estimation scheme is given by solving equations (21) to (24) e_ = k2 pim ke + k

gim Rim (Wegr Tegr + Wcomp Tcac ) Vim ð21Þ

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Proc IMechE Part D: J Automobile Engineering 226(8) Table 1. ECR estimator inputs and constants.

N, IVC inputs

Wegr , Tegr , Wcomp , Tcac , Pim , Tim , Pem

Inputs

ECR Esmator ECR

Wegr Tegr Wcomp Tcac pim Tim pem Tclt IVO IVC EVC N

ε

measurements

Figure 3. Estimation scheme block diagram.

Figure 4. Engine schematic.

2Vim (e kpim ) ð22Þ gim pim Vd N ^ e = pim h W ^ Vd N ð23Þ 2Rim Tim v k ^ c ECR pim VtdcVivc Vivc cRv pem Vivo cRv pem (Vevc Vivo ) Rp h ^v = c pim Vd Rp h ^v =

+

ht ^ pim (Vtdc ECR Vivo ) + 1000 (Twall Tim )(SA) cp pim Vd R

ð24Þ

Experimental set-up The experimental engine used to validate the ECR estimation scheme is a 2008 Cummins ISB engine, a schematic of which is shown in Figure 4. The engine is a 6.7 liter, 350 horsepower, in-line six-cylinder directinjection diesel engine with a 17.3:1 geometric compression ratio. The engine cylinder head has a four-valve design, with two exhaust and two intake valves per cylinder. The engine is also outfitted with a Bosch common rail fuel injection system with multi-pulse injection capability, a variable-geometry turbocharger and cooled EGR with an electronic EGR valve for control of fresh charge and EGR flow to the cylinder. Pressure measurements in the EGR loop and standard orifice equations are used to determine EGR flow on-engine,

Constants EGR flow [kg/min] EGR gas temperature [K] Fresh air flow [kg/min] CAC outlet temperature [K] Intake pressure [kPa] Intake temperature [K] Exhaust pressure [kPa] Coolant temperature [K] Intake valve open time [CAD] Intake valve close time [CAD] Exhaust valve close time [CAD] Engine speed [rpm]

k k cp cv Rim gim Vtdc Vd Vivo Vim Vevc

30 s1 1.35 1.005 0.7179 0.287 1.3994 4.1297e-4 m3 0.067m3 6.9530e-4 m3 0.04m3 9.9703e-4 m3

denoted by Wegr in Figure 4. The engine additionally has stock sensors for intake and exhaust manifold pressures, used as inputs to the estimation scheme. CO2 measurements in the intake and exhaust manifolds via fast Cambustion CO/CO2 emissions analyzers are also used with fresh air flow via a laminar flow element (LFE) to determine a lab-grade measurement of total charge flow. The LFE measurement of fresh air flow through the compressor and charge air cooler (Wcomp ) effectively emulates a mass air flow (MAF) sensor. A water-cooled in-cylinder pressure transducer is also installed in the engine for cylinder pressure measurements, from which the engine ECR data is calculated using the pressure-based method described in the earlier section ECR defined, and is compared to results of the ECR estimator. The engine is also equipped with a fully flexible VVA system, manufactured by Team Corporation. The VVA system adds the capability to modify valve events, including opening and closing times, lifts, and ramp rates, on a cylinder-independent, cycle-to-cycle basis. In this study, the VVA system is used to actuate pairs of intake valves; the exhaust valves remain cam-driven in the conventional manner. A basic schematic of the VVA system is shown in Figure 5, and is operated as follows. A hydraulic power supply sends high-pressure hydraulic oil to a servo valve, which shuttles the oil to one side of a piston actuator which, in turn, presses on an intake valve crosshead connecting a pair of intake valves. Depending on which side of the piston actuator the high-pressure oil is on, the actuator moves up or down, opening and closing the pair of intake valves.

Estimator comparison with engine data The most direct way to vary the ECR is modulation of the intake valve closing time, as indicated in Shaver et al.,11 Helmantel et al.,21 He and Durrett,22 Modiyani et al.,23 Murata et al.25 and Nevin et al.26 To determine estimator performance, transient tests were carried out, during which IVC timing was modulated. Two different IVC times, noted in Table 2, were used during these

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1007 Table 3. Engine operating points. Case

Speed (rpm)

Torque (N-m)

1 2 3 4 5

2300 1850 1000 1200 1500

520 410 200 540 610

Torque−Speed Curve 900 800

Torque [N−m]

700

Figure 5. Schematic of VVA system.

Table 2. ECR timing and transient test nomenclature. Name

IVC time (CAD)

Test

Step change from

IVC1 IVC2

510 565 (nominal)

Jump1 Jump2

IVC1 to IVC2 IVC2 to IVC1

600 500 400 300 Case 1 Case 2 Case 3 Case 4 Case 5

200 100 0

1000

1500

2000

2500

3000

Engine Speed [rpm]

Figure 7. Engine operating points on a torque-speed map. 9 IVC1 IVC2

8

Valve Lift [mm]

7 6 5 4 3

Estimated charge flow

2 1 0 300

previously. As per Figure 3, inputs to the estimator included engine speed, intake manifold temperature, EGR cooler and CAC outlet temperature, and EGR flow, each of which are measured using the stock engine sensors. EGR flow, as previously noted, is also measured using emissions analyzers.

350

400

450

500

550

600

650

700

Crank Angle [deg]

Figure 6. Intake valve lift profiles.

transient IVC tests. Intake valve profiles corresponding to these two closing times are shown in Figure 6. Note that the intake valve opening time and lift stays the same for both of the intake valve closing times. The transient IVC tests consisted of step changes between these two IVC times, also indicated in Table 2, where the IVC time was changed within in a single engine cycle. The engine (described in the previous section) was run at five operating conditions, listed in Table 3, and shown on the torque-speed map in Figure 7. The estimation scheme developed in the previous section was compared to experimental engine data as described

Figure 8 shows transient test results for charge flow for Case 1. Each subfigure is labeled with the transient test carried out, as per Table 2. Figures 9 to 12 show similar test results for Cases 2–5. Engine data is shown in blue, and estimator results using stock pressure measurements and standard orifice equations to determine EGR flow are shown in dashed red. In all cases, the estimator tracks transient engine behavior extremely well, and is fast enough to capture the transient events with little to no delay, and steady-state errors of less than 6%. These small steady-state offsets can typically be mitigated through use of feedback. One transient event to note is Jump 2 of Case 4. The particular operating condition of Case 4 lies very close to the compressor surge region, and in snapping back to IVC1 from IVC2, conditions crossed into the surge region, resulting in the flow oscillations seen in Figure 11(b). As air flow measurements are an input to the observer, the estimated charge flow follows the oscillatory nature of compressor surge. After roughly one


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Estimated ECR Figures 13 to 17 show estimator results for ECR compared to engine data. In all cases, the estimator tracks the trends in engine behavior well. The change in ECR is a cycle-to-cycle event, since IVC timing directly impacts ECR. Any change in IVC timing is immediately seen in the next engine cycle through a change in ECR. In most cases, the estimator takes no more than three engine cycles, at 720CAD per cycle, to converge. Depending on the operation condition (i.e. engine speed), this ranges between 0.15 and 0.36 seconds, which is sufficiently fast for real-time control synthesis.

Similar to charge flow results for Case 4, Jump 2, oscillations are seen in the estimate of ECR. Since the estimation scheme relies on fresh air flow measurements, the oscillatory behavior during compressor surge propagates through the ECR calculations. The oscillations die out within about one second as compressor flow stabilizes. Additionally, for some cases (see Figures 14(b) and 17(b)), the sudden step change in IVC timing results in an undershoot of the ECR in excess of 1 ECR. However, these transients also settle quickly, within one second. In either case (compressor surge or estimator undershoot), this convergence time is still adequate for real-time operation. As in the charge flow estimation results, the estimator shows good agreement with the experimental data. Steady-state errors in estimated ECR are, on average, roughly 3% or less as compared to engine data, shown


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Time [s]

(a) Jump1

(b) Jump2

20

20

18

18

16

16

14

14

12

12

ECR [−]

ECR [−]

Figure 13. Estimation of ECR for Case 1.

10 8 6

8 6

4


2 0 0

10

2

4

6

8


2 0 0

10

2

4

Time [s]

6

8

10

Time [s]

(b) Jump2

(a) Jump1

20

20

18

18

16

16

14

14

12

12

ECR [−]

ECR [−]


10 8

10 8

6

6

4


2 0 0

2

4

6

Time [s]

(a) Jump1 Figure 15. Estimation of ECR for Case 3.

8


2 10

0 0

2

4

6

Time [s]

(b) Jump2

8

10

1011

20

20

18

18

16

16

14

14

12

12

ECR [−]

ECR [−]

Stricker et al.

10 8 6

10 8 6

4


2 0 0

2

4

6

8


2 0 0

10

2

4

Time [s]

6

8

10

Time [s]

(b) Jump2

(a) Jump1

20

20

18

18

16

16

14

14

12

12

ECR [−]

ECR [−]


10 8

10 8 6

6

4


2 0 0

2

4

6

8


2 10

0 0

2

4

6

8

10

Time [s]

Time [s]

(a) Jump1

(b) Jump2


Table 4. ECR steady state error (%). Case

Test

Maximum

Minimum

Average

1 1 2 2 3 3 4 4 5 5

Jump1 Jump2 Jump1 Jump2 Jump1 Jump2 Jump1 Jump2 Jump1 Jump2

5.3420 7.5525 4.3806 4.7387 5.0276 2.5031 4.0748 4.8541 4.8789 7.2801

0.0290 0.0255 0.0007 0.1409 0.0000 0.0000 0.0011 0.0000 0.0233 0.5906

2.0924 2.2884 1.6737 1.6514 1.4671 1.1274 1.6861 1.3343 1.6304 3.0868

in Table 4. Some of the factors that may contribute to the steady-state errors in ECR estimation include sensitivity in flow and temperature measurements and

calculations. There is also inherent uncertainty in the static relationship between volumetric efficiency and ECR, given in equation (20), which could account for a portion of the steady-state error in ECR. Although steady-state errors can be mitigated through use of feedback, it is essential to have accurate estimates in order to effectively implement additional control algorithms.

Conclusions and future work A high-gain observer was developed for the estimation of intake manifold pressure, charge flow, and ultimately ECR. This design used only those measurements available from stock engine sensors (including intake and exhaust manifold pressures and temperatures, EGR flow, and fresh air flow, as shown in Table 1 and

1012 Figure 3), and did not require in-cylinder pressure measurements. The estimation scheme was tested against experimental engine data, and successfully tracked the behavior of intake manifold pressure, charge flow, and ECR during transients. The ECR estimation scheme developed here takes at most three engine cycles to converge once a transient event takes place. Additionally, average steady-state ECR errors fell within 3% of experimental engine data. Contributing factors to these steady-state errors may include sensitivity in sensor measurements. The estimation strategy presented here assumed accurate measurements of fresh air flow through the charge air cooler. While the experimental engine is equipped with a reliable laminar flow element to measure fresh air flow to emulate a mass air flow sensor, not all production engines use, or are equipped with, MAF sensors. Hence, a modification to the estimation scheme may be investigated in order to obviate the need for MAF measurements. Future work includes examining the factors impacting estimator accuracy, including sensitivity of the estimator to the various inputs and flow and temperature measurements. The estimator ultimately will be leveraged for closed-loop control strategies of the gas exchange process in multi-cylinder diesel engines. Funding This material is based upon work supported by the Department of Energy under Award Number DEEE0003403. Acknowledgements Special thanks to Cummins, Inc. for providing the engine and other experimental equipment, as well as technical support, especially from the following researchers at Cummins Technical Center in Columbus, Indiana: Ray Shute, Tim Frazier, Cheryl Klepser, Don Stanton, Phanindra Garimella and Rajani Modiyani. Special thanks, also, to AVL North America, Inc. for providing use of an AVL 621 Indimodul for the collection and analysis of in-cylinder pressure transducer data. The authors also wish to thank the Technical Services staff at the Ray W. Herric Laboratories for their assistance: Fritz Peacock, Bob Brown, Gil Gordon and Frank Lee. Disclaimer This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by

Proc IMechE Part D: J Automobile Engineering 226(8) trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof. References 1. Kolmanovsky I, Moraal P, van Nieuwstadt M and Stefanopoulou A. Issues in modelling and control of intake flow in variable geometry turbocharged engines. In: 8th IFIP conference on system modeling and optimization, 1997, p.436. 2. Wijetunge RS, Brace CJ, Hawley JG and Vaughn ND. Dynamic behavior of a high speed direct injection diesel engine. SAE paper 1999-01-0829, 1999. 3. Filipi Z, Wang Y and Assanis D. Effect of variable geometry turbine (VGT) on diesel engine and vehicle system transient response. SAE paper 2001-01-1247, 2001. 4. Zheng M, Reader GT and Hawley JG. Diesel engine exhaust gas recirculation – a review on advanced and novel concepts. Energy Convers Manage 2004; 45: 883–900. 5. Buchwald R, Lautrich G, Maiwald O and Sommer A. Boost and EGR system for highly premixed diesel combustion. SAE paper 2006-01-0204, 2006. 6. Lancefield T and Methley I. The application of variable event valve timing to a modern diesel engine. SAE paper 2000-01-1229, 2000. 7. Babajimopoulos A, Assanis DN and Fiveland SB. An approach for modeling the effects of gas exchange processes on HCCI combustion and its application in evaluating variable valve timing control strategies. SAE paper 2002-01-2823, 2002. 8. Leroy T, Aix G, Chauvin J, Duparchy A and Le Berr F. Modelling fresh air charge and residual gas fraction on a dual independent variable valve timing SI engine. SAE paper 2008-01-0983, 2008. 9. Milovanovic N, Chen R and Turner J. Influence of variable valve timings on the gas exchange process in a controlled auto-ignition engine. Proc IMechE Part D: J Automobile Engineering 2004; 218: 567–583. 10. Widd A, Ekholm K, Tunestal P and Johansson R. Experimental evaluation of predictive combustion phasing control in an HCCI engine using fast thermal management and VVA. In: 18th IEEE international conference on control applications, 2009, pp. 334–339. 11. Shaver GM, Gerdes JC and Roelle MJ. Physics-based modeling and control of residual-affected HCCI engines. ASME J Dynam Syst Meas Contr 2009; 131: 021002. 12. Shaver GM, Gerdes JC, Roelle MJ, Caton PA and Edwards CF. Dynamic modeling of residual-affected homogeneous charge compression ignition engine with variable valve actuation. ASME J Dynam Syst Meas Contr 2005; 127: 374–381. 13. Yilmaz H and Stefanopoulou A. Control of charge dilution in turbocharged diesel engines via exhaust valve timing. ASME J Dynam Syst Meas Contr 2005; 127: 363–373. 14. Deng J and Stobart R. BSFC investigation using variable valve timing in a heavy duty diesel engine. SAE paper 2009-01-1525, 2009.

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1014


Appendix 1

Ilya Kolmanovsky at the University of Michigan. As a reminder, consider a first-order system

Notation Aeff cp cv C k N pem pim Rim Tcac Tclt Tegr Tim Twall Vd Vevc Vim Vivc Vivo Vtdc Wcomp We Wegr x y, z g e hv k r

effective flow area (m3) specific heat at constant pressure (kJ/kg-K) specific heat at constant volume (kJ/kg-K) discharge coefficient polytropic compression constant engine speed (rpm) exhaust manifold pressure (kPa) intake manifold pressure (kPa) gas constant of intake manifold gas (kJ/kg-K) gas temperature at charge-aircooler exit (K) Engine coolant temperature (K) recirculated exhaust gas temperature (K) intake manifold temperature (K) cylinder wall temperature (K) displacement volume (m3) cylinder volume at EVC (m3) intake manifold volume (m3) cylinder volume at IVC (m3) cylinder volume at IVO (m3) cylinder volume at top-deadcenter (m3) fresh air flow through compressor (kg/min) engine charge flow (kg/min) EGR flow (kg/min) estimator quantity to be estimated estimator measured quantities ratio of specific heats estimator auxiliary variable (kPa/s) volumetric efficiency estimator gain (1/s) gas density (kg/m3)

Acronyms ECR EVC GCR GECR IVC IVO

effective compression ratio exhaust valve closing time (CAD) geometric compression ratio geometric effective compression ratio Intake valve closing time (CAD) intake valve opening time (CAD)

Appendix 2 In the following section, the transient bound for the estimation error given in equation (9) is shown. This proof was developed in correspondence with Professor

z_ = y + x

ð25Þ

where z and y are measured or known, x is to be estimated. The estimate of x is given by x^ = k z e

ð26Þ

where k is the observer gain and e satisfies e_ = ke + ky + k2 z

ð27Þ

To show x^ is a good approximation for x, consider the error between the two, given by e as e = x^ x = kz e x

ð28Þ

Taking the derivative of equation (28), together with equations (25) and (27), yields e_ = kz_ e_ x_ = ke x_

ð29Þ

For a physical system, the dynamics of the unknown variable x may be bounded, that is, for some constant b1 . 0 _ sup jx(t)j4b 1

ð30Þ

t

Multiplying equation (29) by 2e yields 2ee_ = 2ke2 2ex_

ð31Þ

Consider the last term in the above equation. The following inequality holds true _ _ 2xe4j2 xej

ð32Þ

Considering this along with the derivative of e2 , equation (31) becomes d(e2 ) _ 2ke2 + j2xej _ = 2ee_ = 2ke2 2ex4 dt d(e2 ) _ 4 2ke2 + j2xej ) dt

ð33Þ

_ in equation (33). Now a bound must be put on j2xej Consider the following. For any two real numbers u and w, and any real number c . 0, the following inequality holds ðjuj cjwjÞ2 50

ð34Þ

Expanding this inequality and rearranging terms yields 04ðjuj cjwjÞ2 = juj2 cjuwj cjuwj + c2 jwj2 04u2 2cjuwj + c2 w2

) +

2cjuwj4u2 + c2 w2

Solving for juwj yields the following inequality juwj4

u2 c2 w2 u2 cw2 + = + 2c 2c 2c 2

ð35Þ

Stricker et al.

)

1015

u2 cw2 juwj4 + 2c 2

ð36Þ

In the context of the high-gain observer problem, make the following assignments for u, w and c u = x_ w = 2e k c= 2

ð37Þ

Substituting these assignments into equation (36) yields k ð2eÞ2 4ke2 x_ 2 x_ 2 k + 2 _ = + jx(2e)j4 2 k 4 2 2 )

_ j2xej4

x_ 2 + ke2 k

ð38Þ

Now equation (38) is substituted into equation (33) and the bound given in equation (30) is included to yield d(e2 ) b2 _ 4 2ke2 + j2xej4 2ke2 + 1 + ke2 dt k 2 2 d(e ) b 4 ke2 + 1 ) dt k

ð39Þ

Separation of variables results in d(e2 ) b2 b2 4 ke2 + 1 = k e2 12 dt k k

d(e ) e2

b21 k2

4 kdt

Both sides of this inequality are then integrated ð ð d(e2 ) 4 kdt b2 e2 k12

ð41Þ

To solve for e, the error between the estimate x^ and true value x, the exponential of both sides is taken and rearranged as e2

b21 4 exp ( kt + a1 ) k2

+ b21 4a2 exp ( kt) k2 rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi b2 ) je(t)j4 a2 exp ( kt) + 12 k

e2

ð42Þ

Solving for a2 by considering initial conditions rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi b2 b2 ð43Þ je(0)j4 a2 exp (0) + 12 = a2 + 12 k k qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2ffi pffiffiffiffiffi pffiffiffiffiffi b Choosing je(0)j = a2 , since a2 \ a2 + k12 , results in a2 = je(0)j2 = e(0)2 = e20

ð44Þ

Thus, equation (42) becomes

2

)

)

2 b21 ln e 2 4 kt + a1 k

ð40Þ

rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi b2 je(t)j4 e20 exp ( kt) + 12 k

ð45Þ

Then it is easy to see that in equation (28), for t . 0, the error in estimation of x becomes arbitrarily small for large k, and as e ! 0, x^ ! x.