Estimation of Air Mass Flow in Engines with Variable Valve Timing

Home , Connecting rod, Cylinder (engine), Exhaust manifold, Inlet manifold, Stroke (engine), Valve timing

Master of Science Thesis in Electrical Engineering Department of Electrical Engineering, Linköping University, 2018

Elina Fantenberg Master of Science Thesis in Electrical Engineering Estimation of Air Mass Flow in Engines with Variable Valve Timing Elina Fantenberg LiTH-ISY-EX--18/5116--SE

Supervisor: Christian Andersson Naesseth isy, Linköpings universitet Erik Höckerdal Scania CV AB Examiner: Martin Enqvist isy, Linköpings universitet

Division of Automatic Control Department of Electrical Engineering Linköping University SE-581 83 Linköping, Sweden

To control the combustion in an engine, an accurate estimation of the air mass flow is required. Due to strict emission legislation and high demands on fuel consumption from customers, a technology called variable valve timing is inves- tigated. This technology controls the amount of air inducted to the engine cylinder and the amount of gases pushed out of the cylinder, via the inlet and exhaust valves. The air mass flow is usually estimated by large look-up tables but when introducing variable valve timing, the air mass flow also depends on the angles of the inlet and exhaust valves causing these look-up tables to grow with two dimensions. To avoid this, models to estimate the air mass flow have been derived. This has been done with grey-box models, using physical equations together with unknown parameters estimated by solving a linear least-squares optimization problem. To be able to implement the models in the electronic control unit in the future, only sensors implemented in a commercial vehicle are used as much as possible. The work has been done using an inline 6-cylinder diesel engine with measurements from steady-state conditions. All four models derived in this project are based on the estimation methods in use today with fix cam phasing, and are derived from the ideal gas law together with a volumetric efficiency factor. The first three models derived in this work only include sensors provided in commercial engines. The measurements needed as input signals are engine rotational speed, crank angle resolved pressure in the intake manifold, intake and exhaust valve angles and intake manifold temperature. The fourth and last model is divided into three sub-models to model different parts of the four-stroke engine cycle. This model also includes crank angle resolved exhaust manifold pressure and exhaust manifold temperature, where the temperature is the only sensor used in this project that is not provided in a commercial engine. It has been concluded how influential it is to use correctly measured values for the input signals. Since the manifold pressure and the cylinder volume vary during one four-stroke cycle, it is essential that these signal measurements are taken at the right crank angle degree. With wrong crank angle degree, the estimation is worse than if the cylinder volume is constant for all operating points and the pressure signals are taken as a mean value over the whole four-stroke cycle. Fur- ther development to reach better estimation results with lower relative error is needed. However, for the work in this thesis, the model with best model fit is estimating the air mass flow well enough to use it as a basis for further control.

iii

Acknowledgments

First of all, I would like to thank my supervisor Erik Höckerdal at Scania for the guidance and for always having time for me. You have helped me with all kinds of questions and how to proceed the work. I would also like to thank my supervisor Christian Andersson Naesseth and my examiner Martin Enqvist at Linköping University. A big thank you to my family and friends without whom I wouldn’t have gotten this far. Last of all I would like to thank Pontus for all the support both during the past few years but most of all during this work.

Linköping, February 2018 Elina Fantenberg

Contents

Notation ix

1 Introduction 1 1.1 Problem formulation ...... 1 1.2 Method ...... 2 1.3 Related work ...... 2 1.4 Thesis outline ...... 3

2 System description 5 2.1 The four-stroke diesel engine ...... 5 2.2 Variable valve timing ...... 6 2.3 Valve timing strategies ...... 8 2.4 Experimental setup ...... 10 2.5 Assumptions ...... 11

3 Modeling 13 3.1 Parameter estimation ...... 13 3.2 Model validation ...... 13 3.3 Cylinder volume ...... 15 3.4 Gas law ...... 16 3.5 Volumetric eﬃciency ...... 17

4 Reference model 19 4.1 Validation with ﬁx valve timing ...... 19 4.2 Validation with variable valve timing ...... 21

5 The extended models 25 5.1 Model 1 – Dynamic IVC volume ...... 25 5.1.1 Modeling ...... 25 5.1.2 Result and discussion ...... 26 5.2 Model 2 – Cam phase angle augmentation ...... 28 5.2.1 Modeling ...... 28 5.2.2 Result and discussion ...... 28

vii viii Contents

5.3 Model 3 – Dynamic IVC pressure ...... 29 5.3.1 Modeling ...... 30 5.3.2 Result and discussion ...... 31

6 Model 4 – Division into sub-models 33 6.1 Total mass trapped in cylinder at IVC ...... 34 6.1.1 Assumptions ...... 34 6.1.2 Results ...... 34 6.2 Mass ﬂow during valve overlap ...... 36 6.2.1 Overlap factor ...... 36 6.2.2 Assumptions and limitations ...... 37 6.2.3 Results ...... 37 6.3 Total mass trapped in cylinder at EVC ...... 38 6.3.1 Assumptions ...... 38 6.3.2 Results ...... 39 6.4 Results and discussion ...... 40

7 Discussion and conclusions 43 7.1 Sensitivity analysis ...... 43 7.2 Discussion ...... 44 7.3 Future work ...... 46 7.4 Conclusions ...... 46

Bibliography 49 Notation

Abbrevation Meaning BDC Bottom dead center CAD Crank angle degree CI Compression ignition ECU Electronic control unit EVC Exhaust valve closing EVO Exhaust valve opening IVC Inlet valve closing IVO Inlet valve opening OF Overlap factor SI Spark ignition TDC Top dead center VVT Variable valve timing

Symbol Description Unit αe Exhaust valve angle ◦ αi Inlet valve angle ◦ ηvol Volumetric efficiency nc Number of cylinders Ne Engine rotational speed rpm pem Exhaust manifold pressure Pa pim Intake manifold pressure Pa Rspec,air Specific gas constant for air J/kgK Rspec,burned Specific gas constant for burned gases J/kgK Tem Exhaust manifold temperature K Tim Intake manifold temperature K 3 Vc Clearance volume m 3 Vd Displaced volume m

1 Introduction

Fuel consumption, emissions and performance largely depend on the amount of air in the engine cylinder. Measuring air mass flow into the cylinder directly is not cost effective and therefore accurate models are needed. To meet the increas- ingly strict emission legislations, high demands on fuel consumption and performance from customers, research on new technologies is an ongoing process. One of these technologies is called variable valve timing (VVT), which gives the opportunity to control the opening and closing of the inlet and exhaust valves. These valves control the amount of fresh air inducted into and the amount of gases ex- pelled out of the engine cylinder, respectively. VVT gives the opportunity to have good performance at all operating points. Even higher demands on the air mass flow estimation is required with VVT to be able to control the valves accurately. The air mass in the cylinder must also be known to control the amount of fuel injected to get optimal combustion. The goal of this work is therefore to estimate the air mass that flows through the engine with VVT.

1.1 Problem formulation

An accurate estimation of the engine air mass flow is vital to optimize engine operation with respect to emissions, fuel consumption and performance. The air mass flow into the cylinder is important for combustion and the mass flow out of the cylinder is important for after treatment. One example is to keep emissions within allowed limits (García-Nieto et al., 2009). One way to increase the performance of the engine is with VVT of the inlet and exhaust valves (Gray, 1988). This makes it possible to control the amount of air mass in the cylinder. However, this will add two dimensions to the now existing methods for estimating the air mass flow, which are based on large lookup tables that grow exponentially with each additional variable. Therefore, the pur-

1 2 1 Introduction pose of this work is to estimate the air mass ﬂow when VVT is present, as well as to reduce the model complexity. This will be done using grey-box models, combining physical insights with parameters learned from data.

1.2 Method

Measurement data from the engine were provided by Scania CV AB. The approach was to ﬁrst do a reference model that corresponds to the mapping used in the electronic control unit (ECU) today. Then expanded models were devel- oped and validated. Finally another approach was used, where the estimation of the air mass ﬂow was divided into sub-models. Each model derived in this work includes several unknown parameters, which were trained with data by solving a linear least-squares optimization problem. Cross-validation was used to validate the models and several methods, e.g. relative error, were used to validate the accuracy of each model.

1.3 Related work

Most studies which estimate the air mass flow in an engine are done with fix cam phasing instead of VVT. Also, the studies regarding variable valve timing are often done on spark ignition (SI) engines instead of compression ignition (CI) engines, which is the engine used in this work. This is because there are higher benefits of variable valve timing on SI engines. In Wahlström and Eriksson (2011), a mean-value model of a diesel engine is determined, with the purpose to describe the dynamics of the gas flow in the engine. The unknown parameters in their model are estimated using both station- ary and dynamic measurements. The reference model in this work corresponds to the model that estimates the total mass flow in their work. Their article presents model derivation, estimation of the unknown parameters and model validation. One common method to estimate the cylinder mass is with the ∆p-method introduced by Akimoto et al. (1989), using the in-cylinder pressure. This method takes two points from the compression stroke, which is later described in the four- stroke cycle, and relates the increase of the in-cylinder pressure between these points to the mass trapped in the cylinder. The sensor measuring in-cylinder pressure is however not provided in commercial engines. A study that has adopted the ∆p-method is e.g. Desantes et al. (2010), which estimates the air mass flow on a diesel engine with fix cam phasing. Gray (1988) has done a review of variable valve timing on gasoline and diesel engines. Benefits of the two engine types are presented and although the benefits of gasoline engines are higher, improvements on diesel engines can still be done with VVT. Both Thomasson et al. (2018) and Leroy et al. (2009) model the fresh air inducted into the cylinder by dividing the model into several terms. Also both works are done on engines with variable valve timing actuators. Thomasson et al. (2018) use cylinder pressure to estimate cylinder charge in diesel engines with 1.4 Thesis outline 3

VVT. This is done by estimating different parts of the four-stroke cycle. This thesis has Thomasson et al. (2018) as a basis when deriving the last model. The models in that article are validated on the same data from the same engine as in this thesis work. Therefore, the model in their work is used as a reference when validating the sub-models in this work. Leroy et al. (2009) present a model for the fresh air that is inducted in the cylinder through the inlet valve of an SI engine with VVT. In this model, only sensors provided in commercial engines are used. The model is divided into three terms. The first term estimates the total mass in the cylinder, the second term models the mass flowing through the valves during overlap and the third term gives the amount of residual gases trapped in the cylinder from one four-stroke cycle to the next one. The analogy in Leroy et al. (2009) is used in this work when modeling the air mass flow, by dividing it into three similar terms. In Stefanopoulou et al. (1998), a third order polynomial is used to model the air mass flow into the cylinder, which depend on valve angle actuators, intake manifold pressure and engine speed. Their work is done on an SI engine with dual equal valve cam timing.

1.4 Thesis outline

The system is described in Chapter 2 together with an explanation and back- ground to variable valve timing. The experimental setup is also presented in this chapter. Chapter 3 describes how the models will be validated. Physical descriptions required to derive models to estimate the air mass flow are presented. In Chapter 4, the reference model, corresponding to the model to estimate the air mass flow in use today will be presented. First, model validation with fix cam phasing is presented, followed by validation with VVT. In Chapter 5 three different models, all extensions of the reference model, are derived. Results and discussion for each model will also be presented in this chapter. Chapter 6 presents a new approach to estimate the air mass flow. This is based on three sub-models, each estimating different parts of the four-stroke cycle. The chapter includes derivation of each sub-model together with validation and discussion as well as results for the final model. Chapter 7 first presents a sensitivity analysis of how different input signals influence the quality of a model dependent on inlet valve closing. Then all models are discussed and finally suggestions on how to proceed in the future are presented.

2 System description

This chapter gives an overview of the system used in this project. The system consists of the cylinders in a diesel engine, the intake and exhaust manifold together with actuators and sensors. First, a brief description of the diﬀerent strokes of a diesel engine are presented. Then variable valve timing (VVT) is described. Finally, the experimental setup is presented.

2.1 The four-stroke diesel engine

The diesel engine is a compression ignition (CI) engine and fuel is injected directly into the engine cylinder. The working process of a CI engine is well docu- mented by Heywood (1988). The engine used in this project follows a four-stroke operating cycle, see Figure 2.1. Top dead center (TDC) and bottom dead center (BDC) are deﬁned as the highest and lowest positions that the piston reaches, respectively. Therefore TDC and BDC corresponds to the smallest and largest cylinder volumes, respectively. When the piston is at TDC there is a small volume left in the cylinder, called the clearance volume, Vc. The four-stroke operating cycle is described by

(a) Intake stroke (TDC to BDC): When the inlet valve is open, air from the intake manifold ﬂows into the cylinder as the piston moves from TDC down to BDC.

(b) Compression stroke (BDC to TDC): Both valves are closed while the piston moves from BDC to TDC. This causes the air in the cylinder to compress, which results in high pressure and temperature inside the cylinder.

(c) Expansion stroke (TDC to BDC): Right before the piston reaches TDC, diesel fuel is injected into the cylinder. Due to the heat the fuel ignites, which

5 6 2 System description

causes a rapid increase of pressure and temperature. The gas is then expanded while pushing the piston down, from TDC to BDC.

(d) Exhaust stroke (BDC to TDC): The exhaust valve opens and the gas is pushed out of the cylinder, and into the exhaust manifold, as the piston moves back to TDC and the exhaust valve closes. If all gases are not pushed out, the remaining part in the cylinder when the valve closes is called residual gases. The cycle is complete and the next cycle starts with the inlet valve opening once again.

Figure 2.1: The four strokes of a four-stroke engine, image courtesy of Lars Eriksson (Eriksson and Nielsen, 2014).

The position of the piston is determined by the rotation of the crankshaft. The position of the crankshaft is deﬁned using crank angle degrees (CAD), ranging between -360 and 360 degrees over one four stroke cycle, where 0 degrees is TDC ﬁre.

2.2 Variable valve timing

One way to improve the engine performance is with variable valve timing (VVT). This gives freedom to control the amount of air mass and residual gases trapped in the cylinder. This affects for example emissions, fuel efficiency and output power. The valve timing is defined as the timing with respect to the crank angle at which the valves open and close, schematically shown in Figure 2.2. In the image, notation used for valve timing is inlet valve opening (IVO) and closing (IVC), and exhaust valve opening (EVO) and closing (EVC). With fix valve timing, a trade-off between performance at high and low loads must be done, as well as a trade-off between high and low engine speeds. There- fore, an optimization for different combinations of loads and engine speeds over a wide range can be done with VVT. This is done by the camshafts where one camshaft controls the inlet valves and one camshaft controls the exhaust valves. See Figure 2.3 for an overview of the camshaft, valves and crankshaft. 2.2 Variable valve timing 7

Figure 2.2: Valve timing diagram, where IVO and IVC are inlet valve opening and closing. EVO and EVC are exhaust valve opening and closing.

There exist several forms of variable valve timing, were the form used in this project is called cam phasing. With cam phasing, the valves can open and close earlier or later due to forward or backward rotation of the camshaft relative to the crankshaft. However, in this project, only late opening and closing of the inlet valve and early opening and closing of the exhaust valve are possible. Also, in a cam phasing system, the lift and duration cannot be modified, i.e. the valve profiles will always look the same. For different operating points different camshaft positions, relative to the crankshaft position, gives optimum output for emissions, fuel efficiency or power.

Figure 2.3: Overview of the camshaft, valves and crankshaft. 8 2 System description

Valve overlap Valve overlap is when both intake and exhaust valves are open at the same time, i.e. IVO occurs before EVC, shown as the overlap period in Fig- ure 2.2. When there is an overlap between EVC and IVO, what happens depends on the diﬀerence between the intake manifold pressure, pim, and the exhaust manifold pressure, pem.

1) pim>pem causes air from the intake manifold to push out residual gases to the exhaust manifold. Fresh air from the intake manifold is capable of ﬂowing directly to the exhaust manifold, called scavenging. This results in less (or no) residual gases trapped in the cylinder to the next cycle.

2) pim

2.3 Valve timing strategies

The camshafts that operate the valves are dual independent, i.e. the inlet and exhaust camshafts can be rotated independently of each other in relation to the crankshaft. There are three strategies of valve timing that the models should be able to handle. Figure 2.4 shows the inlet and exhaust valve lifts for each case. The dashed lines correspond to the valve lift for an engine with cam phasers in the default position, also called pin position. Note that the lift profile is un- changed in height and duration, i.e. it is just shifted along the x-axis. (a) Valve overlap: This occurs when the inlet valve opens before the exhaust valve closes. Some characteristics for this is described in Section 2.2. The models must thus be able to estimate the mass that flows through the valves directly from intake to exhaust. The overlap can in the figure be seen by the intake valve opening slightly before 360 CAD and the exhaust valve closing slightly after -360 CAD. For this engine, valve overlap is the default setting. (b) Symmetric phasing: This is when the inlet and the exhaust valves are sym- metrically shifted. This gives the opportunity to change how much fresh air gets trapped in the cylinder. Symmetric cam phasing includes late opening and closing of the inlet valve which gives less air in the cylinder since air is pushed back into the intake manifold due to that the compression stroke begins before the valve is closed. Since it is symmetric phasing, the exhaust valve has already closed early from the previous cycle, resulting in residual gases remaining in the cylinder when the inlet valve opens, causing even less inducted fresh air. (c) Early exhaust: Early opening and closing of the exhaust valve causes higher gas temperatures since the valve is open before the expansion stroke is complete. This also results in more residual gases trapped in the cylinder to 2.3 Valve timing strategies 9

the next cycle due to closing of the exhaust valve before all the residual gases are fully pushed out. When the intake valve opens exhaust gases are breathed out into the intake manifold.

Intake Exhaust (def)

-360 -270 -180 -90 0 90 180 270 360

(a) Valve overlap

Intake Exhaust (def)

-360 -270 -180 -90 0 90 180 270 360

(b) Symmetric phasing

Intake Exhaust (def)

-360 -270 -180 -90 0 90 180 270 360

Figure 2.4: The plots show the inlet and exhaust valve lifts for the three valve timing strategies that the models should be able to handle. 10 2 System description

2.4 Experimental setup

The engine used in this work is an inline 6-cylinder, 13 l, diesel engine with fuel injected directly into the cylinder. Data is collected from the engine in a test cell at Scania CV AB during steady-state conditions. The data comes from a wide range of operating points of different engine speeds, engine loads and valve angle positions. A schematic overview of the engine showing pressure and temperature sensor locations is shown in Figure 2.5. The measured signals of interest are rotational engine speed, Ne, engine load, M, inlet- and exhaust valve angles, αi and αe, intake- and exhaust manifold temperatures, Tim and Tem, and crank angle resolved intake- and exhaust manifold pressures, pim and pem. The reason crank angle resolved pressure measurements are desired is that the pressure varies during the engine cycle. In the reference model, and other models in use today, the mean value of the pressure during one whole cycle is used. Pressure variations are due to pulsations caused by the opening and closing of the valves. The intake manifold temperature is given by the mean value of all six intake temperature sensors and with the mean value over one engine cycle. The exhaust manifold temperature is given by the mean value of all six exhaust temperature sensors and with the mean value over one engine cycle. A mass flow sensor is installed in the test cell to use as a reference, with over 99 % accuracy. The sensors implemented in the test engine but not provided in a commercial engine are the mass flow sensor and the exhaust manifold temperature sensors. Table 2.1 shows the symbols and units of the measured signals, including ranges of the controllable signals. Measurements have been used from Cylinder 6, which is placed furthest from the intake of fresh air.

Blank

Crank Angle resolved pim

Intake 6 5 4 3 2 1 Temperatures

Exhaust Temperatures

Crank Angle resolved pem

Figure 2.5: A schematic overview of the engine with pressure and temperature sensor locations, adapted from Nikkar (2017). 2.5 Assumptions 11

Table 2.1: Description of the measured signals of interest for this project with ranges of the controllable signals.

Symbol Description Unit Range Ne Rotational engine speed rpm 600 to 1450 M Load Nm -50 to 2500 αi Intake valve angle ◦ 0 to 60 αe Exhaust valve angle ◦ -70 to 0 Pim (CAD) Intake manifold pressure Pa Pem (CAD) Exhaust manifold pressure Pa Tim Intake manifold temperature K Tem Exhaust manifold temperature K

2.5 Assumptions

Several assumptions have been made to facilitate the work in this project. As- sumptions for speciﬁc models will be brought up in the corresponding section, but assumptions made for the whole system, regarding all models, will be presented here. As mentioned, the data is collected from an inline engine with six cylinders meaning that the six cylinders are mounted in a straight line, with Cylinder 1 closest to the fresh air intake and Cylinder 6 furthest away. The engine is not equipped with sensors for all cylinders and therefore the models are derived for one cylinder. The assumption is that the air mass ﬂow is equally distributed in the cylinders.

3 Modeling

In this chapter the parameter estimation method is brieﬂy presented and the model validation process is described. The physical description required to derive a model to estimate the air mass ﬂow will also be presented.

3.1 Parameter estimation

Each model contains a set of unknown parameters which are estimated from data by solving a linear least-squares optimization problem. This minimizes the squared difference between the estimated and measured air mass flow. A limitation when using the linear least squares method is that the input signals are assumed to be free from error. Since the input signals come from sensors, this is not true. If the signals contain significant errors this approach might give inaccurate results.

3.2 Model validation

To mitigate overﬁtting, cross-validation is used and the measurements are divided into estimation and validation data. The estimation data consists of 2/3 of the samples and were used when estimating the unknown parameters. The validation data consists of the remaining 1/3 part. The split is done using every third sample as validation data to get as much information as possible in both data sets. Every third sample was used, rather than random samples, since the measurements were done with varying engine speed and load. See Figure 3.1 for the variation in the engine speed and the split of estimation and validation data on all data.

13 14 3 Modeling

1500

1400

1300

1200

1100

1000

900

800

700

600

500 0 20 40 60 80 100 120 140 160

Figure 3.1: Engine speed divided in 2/3 to estimation data and 1/3 to validation data.

The relative error (3.1) is one way to validate the model. Here yi is the measured air mass ﬂow, m˙ air , in sample i and yˆi is the estimated m˙ air .

y yˆ RE(i) = i − i (3.1) yi The air mass ﬂow varies depending on the operating point, and this method of evaluation will give higher error on small air mass ﬂows. However, it is important to know the error at each operating point since the estimation should be accurate everywhere. A second way to validate the models is with absolute error, given by

AE(i) = y yˆ . (3.2) i − i The reason for this is that for very small air mass flows, the relative error will be very high while the difference in air mass flow is in fact very low. This equation shows a more reasonable value in that case. The third way to validate the performance of each model is with normalized mean-square error (NMSE) and normalized root mean-square error (NRMSE). The model fit based on NMSE and NRMSE is given by ! y yˆ 2 NMSE model fit = 100 1 || − || (3.3) − y y¯ 2 || − || ! y yˆ NRMSE model fit = 100 1 || − || (3.4) − y y¯ || − || where · indicates the L2-norm of a vector. k k 3.3 Cylinder volume 15

A model fit of 100 % corresponds to perfect fit, and 0 % means that the model does not estimate the air mass flow better than a constant. If the model fit is negative, the model is worse at estimating the air mass flow than a constant. As mentioned before, 2/3 of the data is used as estimation data and 1/3 is used as validation data. This is illustrated in Figure 3.1, where every third sample is taken as validation data, giving 110 estimation data points and 56 validation data points. An evaluation has been done on taking the first, second or third sample as the starting point of the validation data. The difference in model quality when estimating the air mass flow using the different divisions has been marginal.

3.3 Cylinder volume

In order to properly model the air mass ﬂow, the displacement volume in the cylinder is needed. Figure 3.2 below shows the engine geometry over one cylinder and Table 3.1 explains the dimension parameters in the ﬁgure (Eriksson and Nielsen, 2014).

Figure 3.2: The geometry of an engine cylinder where B is bore, Vc is the clearance volume, Vd is the displacement volume and θ is the crank angle deﬁned as 0 when the piston is at TDC. Note that L = 2a. 16 3 Modeling

Table 3.1: Engine parameters.

Parameter Deﬁned as B Cylinder bore l Connecting rod length a Crank radius L Piston stroke θ Crank angle Vc Clearance volume Vd Displaced volume

The volume for each cylinder, Vcyl, is given by

Vcyl = Vc + Vd, (3.5) where the clearance volume, Vc, is constant and corresponds to the volume in the cylinder when the piston is at TDC and is the smallest cylinder volume. The displacement volume is given by

πB2 V = (l + a s(θ)), (3.6) d 4 − where q s(θ) = a cos(θ) + l2 a2 sin2(θ). (3.7) − The largest displacement volume is when θ = π and is then given by

πB2 · L V = , (3.8) d,max 4 where L = 2a.

3.4 Gas law

The ideal gas law states that pV = nRT , where p is pressure, V is volume, n is the amount of gaseous substance in moles, R is the ideal gas constant and T is temperature of the gas. With m n = , (3.9) M where m is mass and M is molar mass, the ideal gas law can be written as

R pV = m T (3.10) M instead, where 3.5 Volumetric eﬃciency 17

R = R (3.11) M spec and Rspec is the speciﬁc gas constant. This results in

pV = mRspecT. (3.12) Assuming the same pressure and temperature in the intake manifold as in the cylinder, the total air mass in one cylinder is

pimVd ma = , (3.13) Rspec,air Tim where ma is the air mass in the cylinder, pim is the intake manifold pressure, Vd is the displaced volume, Rspec,air is the speciﬁc gas constant for air and Tim is intake manifold temperature. From this equation, a model to predict the theoretical air mass ﬂow, m˙ a, is given by

pimVd ncNe m˙ a = , (3.14) 120Rspec,air Tim where Ne is engine speed and nc is number of cylinders. 120 originates from 2 · 60, were 2 represents that air intake occurs once every 2 revolutions for a four-stroke cycle and 60 to translate rpm to revolutions per second.

3.5 Volumetric efﬁciency

A volumetric efficiency factor, denoted by ηvol, is used to describe the ratio between the actual amount of air mass inducted to the cylinder during the intake stroke and the displaced volume Vd. The volumetric efficiency is defined as

120m˙ air Rspec,air Tim ηvol = , (3.15) pimNeVd nc where m˙ air is the actual air mass flow. The volumetric efficiency can be calculated using the air mass flow sensor, if measurements are done at steady-state over a wide operating range. With fix valve timing, measurements over a wide range of operating points shows that the volumetric efficiency is highly dependent on engine speed and inlet manifold pressure. This dependency appears to have a square root behavior, as discussed in Eriksson and Nielsen (2014). This is valid when not including cam phasing, resulting in modeling ηvol as p ηvol = c0 + c1√pim + c2 Ne, (3.16) where c0, c1 and c2 are the unknown parameters. This approach, other black-box models, as well as physical models are described by Eriksson and Nielsen (2014). However, when including VVT, the volumetric efficiency will depend on the cam phase angles as well.

4 Reference model

Today at Scania, commercial vehicles have fix cam phasing and the air mass flow is estimated in the ECU using look-up tables, which is good enough in this case. However, with variable valve timing, the look-up tables do not take opening and closing of the inlet and exhaust valves into consideration. This chapter describes a reference model corresponding to these look-up tables. Results on how well this model estimates the air mass flow with fix valve timing as well as with variable valve timing will be presented. From (3.14) and (3.16) in Section 3.4 and 3.5 a parametric model

pimNeVd nc m˙ air = ηvol (4.1) 120Rspec,air Tim for the air mass ﬂow in the cylinder was derived. Here Vd is constant and calculated as in (3.8) with θ = π. The intake manifold pressure, pim is given as a mean value over one whole engine cycle.

4.1 Validation with ﬁx valve timing

This section shows how accurately the reference model estimates the air mass flow with fix valve timing. No measurements with fix valve timing, i.e. αi = αe = 0, are available, therefore only operating points with small valve angles are considered. The valve angles at each operating point can be seen in Figure 4.1. Angles are considered small if αi < 10◦ and αe > -10◦. Table 4.1 below shows the validation result for the reference model with the parameters c0, c1 and c2 estimated when only small valve angles are considered and the model fit is good. The reference model has a very low mean absolute relative error and the largest absolute relative error is also very small.

19 20 4 Reference model

-2

-4

-6

-8

-10 0 2 4 6 8 10 12 14 16 18

Figure 4.1: Valve angles in the validation data, only considering small angles.

Table 4.1: Validation results for the reference model for small valve angles.

ﬁt NRMSE ﬁt NMSE Mean |RE| Max |RE| Model [%] [%] [%] [%] Reference model 95.94 99.84 1.08 9.06

In Figure 4.2 a comparison between the reference model and measurements of the air mass flow on validation data for small valve angles can be seen. The lower right plot shows relative errors for the predicted air mass flow and note that the relative error axis is not centered around 0 %. The relative error is negative if the measured air mass flow is lower than the predicted air mass flow and positive if the measured air mass flow higher than the predicted air mass flow. The reference model has a very low mean absolute relative error and can estimate the air mass flow well in each operating point. 4.2 Validation with variable valve timing 21

0.5

0.4

0.3

0.5 0.2

0.45 0.1

0.4 0 0 0.1 0.2 0.3 0.4 0.5 0.35

0.3 2 0.25 0 0.2 -2

0.15 -4

0.1 -6

0.05 -8

0 -10 0 2 4 6 8 10 12 14 16 18 0 0.1 0.2 0.3 0.4 0.5

Figure 4.2: Results for the reference model on validation data for small valve angles. The left plot shows a comparison between the reference model output and measurements for each sample. The right top plot shows measured against predicted air mass ﬂow. The bottom right plot shows the relative error for the reference model.

4.2 Validation with variable valve timing

This section includes validation of the reference model on all validation data to show how accurately it predicts the air mass ﬂow with variable valve timing. Fig- ure 4.3 shows the valve angles in each operating point for the validation data. Sample 1 to 11 correspond to strategy (c) Early exhaust, sample 12 to 56 correspond to strategy (b) Symmetric phasing and sample 19 to 46 correspond to strategy (a) Valve overlap. 22 4 Reference model

-20

-40

-60

-80 0 10 20 30 40 50 60

Figure 4.3: Valve angles in the complete validation data set, where αi and αe are the inlet valve and the exhaust valve angles, respectively.

Table 4.2 below shows the validation of the reference model with the parameters c0, c1 and c2 estimated when valve angles are dual independent. The validation shows that the reference model has a poor model ﬁt and the largest absolute value of the relative error is over 100 %.

Table 4.2: Model validation results for the reference model when valve angles are dual independent.

Validation Reference model Fit NRMSE [%] 78.83 Fit NMSE [%] 95.52 Mean |RE| [%] 25.73 Max |RE| [%] 139 Max positive AE [kg/s] 0.0422 Max negative AE [kg/s] -0.0521

Figure 4.4 shows a comparison between the reference model and measurements of the air mass flow on validation data. The lower right plot shows relative errors for the predicted air mass flow and note that the relative error axis is not centered around 0 %. In the left plot in Figure 4.4, the predicted and measured air mass flow start to differ significantly in sample 12. If looking at Figure 4.3, from sample 11 to sample 12, the inlet valve angle has increased from 6◦ to 45◦. Here αi=45◦ corresponds to very late intake valve opening and closing, causing less fresh air in the cylinder, described in Section 2.3 as (b) Symmetric phasing. Together with early closing of the exhaust valve, trapping residuals in the cylinder, even less air flows into the cylinder. Therefore, the measured air mass flow is very low, 4.2 Validation with variable valve timing 23

while the estimated air mass ﬂow does not change as much since no regard is taken to the cam phasing in the reference model. Sample 12 to 18 have the worst estimated air mass ﬂow, which also can be seen in the lower, right plot, with a cluster with relative error between -86 % and -139 %.

0.6

0.5

0.4

0.3 0.6 0.2

0.1 0.5 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.4

25 0.3 0 -25 0.2 -50 -75

0.1 -100 -125

0 -150 0 10 20 30 40 50 60 0 0.1 0.2 0.3 0.4 0.5 0.6

Figure 4.4: Results for the reference model on validation data. The left plot shows a comparison between the reference model output and measurements for each sample. The right top plot shows measured against predicted air mass ﬂow. The bottom right plot shows the relative error for the reference model.

The relative error has an absolute value over 100 %, meaning that the difference between the measured and the estimated air mass flow is greater than the measured air mass flow. This is due to the very low measured air mass flow and much higher estimated air mass flow. If it was the other way around, the absolute value of the relative error would not exceed 100 %. When the predicted air mass flow is lower than the measured air mass flow this could be because of overlap. The air mass flow sensor registers all air mass, and some might flow directly from the intake manifold to the exhaust manifold, earlier referred to as scavenging. The results show that with variable valve timing better models to estimate the air mass flow are needed.

5 The extended models

This chapter includes three models which are all extensions of the reference model. Each section in this chapter presents derivation of a model together with results and a discussion.

5.1 Model 1 – Dynamic IVC volume

In chapter 4 it was verified that the reference model estimates of the air mass flow are inaccurate when dual independent variable valve timing is present and therefore better models are needed. In this section a first model is derived to estimate the air mass flow more accurately than the reference model. Validation and a discussion of the results are presented.

5.1.1 Modeling

First of all, the reference model includes the displaced volume, Vd, in the cylinder as constant. This is true when the valve angles are ﬁxed, because then the valves always open and close at the same points in the engine cycle. However, with VVT the volume in the cylinder, and therefore how much air that is inducted into the cylinder, depends on when the inlet valve is closing. Therefore, Vd is replaced by Vd,IV C which is the displaced volume at intake valve closing (IVC). Using the reference model from (4.1) with the substituted displaced volume, the model, which is referred to as Model 1, becomes

pimNeVd,IV C nc p m˙ air = (c01 + c11√pim + c21 Ne). (5.1) 120Rspec,air Tim

Here, Vd,IV C is calculated using (3.6) with θ = θIVC + αi, where θIVC is the default CAD at IVC for zero cam phasing.

25 26 5 The extended models

Figure 5.1 shows the volume in the cylinder, according to (3.5) and (3.6), and the valve lift for the intake and exhaust valves during one engine cycle, here for an operating point with strategy (b) Symmetric phasing. The black circle in the upper plot shows which cylinder volume that corresponds to IVC. The ﬁgure shows how the cylinder volume changes during one engine cycle, and how the volume depends on when IVC occur.

0 -360 -270 -180 -90 0 90 180 270 360

15 Intake 10 Exhaust (def) 5

0 -360 -270 -180 -90 0 90 180 270 360 CAD

Figure 5.1: The upper plot shows the cylinder volume, Vcyl, during one cycle and the black circle corresponds to Vcyl at IVC, from (3.5). The lower plot shows the intake and exhaust valve lift during one cycle.

5.1.2 Result and discussion Table 5.1 shows the validation results for Model 1 with the estimated parameters c01, c11 and c21 in (5.1), when valve angles are dual independent. The model ﬁt for Model 1 is better than the ﬁt of the reference model. However, the absolute value of the relative error is still large.

Table 5.1: Model 1 validation results when valve angles are dual independent.

Validation Model 1 Fit NRMSE [%] 84.96 Fit NMSE [%] 97.74 Mean |RE| [%] 18.20 Max |RE| [%] 69.75 Max positive AE [kg/s] 0.0304 Max negative AE [kg/s] -0.0333 5.1 Model 1 – Dynamic IVC volume 27

Figure 5.2 shows a comparison between Model 1 outputs and measurements of the air mass ﬂow on validation data. The lower right plot shows relative errors for the predicted air mass ﬂow. Again, note that the relative error axis is not centered around 0 %.

0.5

0.4

0.3

0.5 0.2

0.45 0.1

0.4 0 0 0.1 0.2 0.3 0.4 0.5 0.35

0.3 20 0.25 0 0.2 -20 0.15 -40 0.1 -60 0.05

0 -80 0 10 20 30 40 50 60 0 0.1 0.2 0.3 0.4 0.5

Figure 5.2: Results for Model 1 for dual independent valve angles on validation data. The left plot shows a comparison between the output from Model 1 and measurements for each sample. The right top plot shows measured against predicted air mass ﬂow. The bottom right plot shows the relative error for Model 1.

In the lower right plot, the cluster of the worst relative error, between -29 % and -70 %, corresponds to samples between 1 and 18 in the left plot. As can be seen in Figure 4.3, sample 1 to 11 correspond to strategy (c) and sample 12 to 18 correspond to (b), with large inlet and exhaust cam phase angles. The latter corresponds to very early opening and closing of the exhaust valve together with very late opening and closing of the inlet valve. As for the reference model, the poor estimation could depend on the residual gases remaining in the cylinder from early closing of the exhaust valve, causing less air to be inducted. The difference between strategy (b) and (c) is that for (c) exhausts are breathed out into the intake manifold causing fresh air together with exhaust gases to be drawn into the cylinder next cycle. Model 1 estimates the air mass flow better than the reference model but improvements are still needed since the maximum and mean relative errors are still too large. Also, it is important to estimate the air mass flow accurately for all three strategies, not only an overall good performance. 28 5 The extended models

5.2 Model 2 – Cam phase angle augmentation

Although Model 1 estimates the air mass ﬂow better than the reference model it still has too poor performance for strategy (c) and large cam phase angles for strategy (b). Another model is made, called Model 2, which extends the reference model with the valve angles. This section includes the derivation of Model 2 together with model validation, results and discussion.

5.2.1 Modeling

The volumetric efficiency, ηvol, described in Section 3.5, only depends on intake manifold pressure, pim, and rotational engine speed, Ne. With variable valve timing, ηvol will also be dependent on the angles of the inlet valve, αi, and the exhaust valve, αe. Since the volumetric efficiency is a ratio between the amount of air mass that flows in through the inlet valve and the displaced volume, e.g. the amount of residuals trapped in the cylinder will have an effect. Therefore a second approach will include these angles according to

pimNeVd nc p m˙ air = (c02 + c12√pim + c22 Ne + c32αi + c42αe) (5.2) 120Rspec,air Tim

Note that in this model, Vd is constant, as in the reference model. This is to see how much the accuracy of the estimated air mass ﬂow increases when only including the inlet and the exhaust valve angles.

5.2.2 Result and discussion

The estimated parameters in Model 2 are c02, c12, c22, c32 and c42 in (5.2). Table 5.2 shows the validation results for Model 2 when valve angles are dual independent. Model 2 has a good model ﬁt and a low mean relative error.

Table 5.2: Model 2 validation results when valve angles are dual independent.

Validation Model 2 Fit NRMSE [%] 95.07 Fit NMSE [%] 99.76 Mean |RE| [%] 5.25 Max |RE| [%] 29.26 Max positive AE [kg/s] 0.0178 Max negative AE [kg/s] -0.0110

A comparison between Model 2 outputs and measurements of the air mass ﬂow is shown in Figure 5.3. The lower right plot shows relative errors for the predicted air mass ﬂow. 5.3 Model 3 – Dynamic IVC pressure 29

0.5

0.4

0.3

0.5 0.2

0.45 0.1

0.4 0 0 0.1 0.2 0.3 0.4 0.5 0.35

0.3

0.25 10

0.2 0 0.15 -10 0.1 -20 0.05

0 -30 0 10 20 30 40 50 60 0 0.1 0.2 0.3 0.4 0.5

Figure 5.3: Results for Model 2 for dual independent valve angles on validation data. The left plot shows a comparison between the output from Model 2 and measurements for each sample. The right top plot shows measured against predicted air mass ﬂow. The bottom right plot shows the relative error for Model 2.

In the lower right plot, the cluster of the worst relative error, between approx- imately -14 % and -29 %, corresponds to samples between 12 and 18 in the left plot. Model 2 has difficulties to estimate the air mass flow in operating points with very large inlet and exhaust cam phase angles, corresponding to strategy (b) Symmetric phasing, as can be seen in Figure 4.3. Model 2 is however able to estimate the air mass flow for strategy (c), early opening and closing of the exhaust valve.

5.3 Model 3 – Dynamic IVC pressure

This section describes a third model, called Model 3, which is based on Model 1 and Model 2. The model includes the valve angles, like Model 2, as well as an inlet valve angle dependent cylinder volume, like Model 1. Model 3 also includes an intake manifold pressure dependent on inlet valve angles. The third model is derived because physical insight implies that VVT has a larger eﬀect on the air mass ﬂow than previously captured by the models. Model derivation, validation and discussion are presented. 30 5 The extended models

5.3.1 Modeling The pressure in the intake manifold changes over one four-stroke cycle due to pulsations caused by opening and closing of the valves. These pulsations are dependent on for example the engine speed. When variable valve timing is included, these pulsations vary even more, depending on the valve angles. Therefore the mean intake manifold pressure, pim, which is a mean value of one whole cycle, has been replaced by a mean value over a small interval around IVC in Model 3. In Figure 5.4, the lower plot shows the pressure pulsations over one cycle and the black circle corresponds to the pressure in the intake manifold at IVC.

0 -360 -270 -180 -90 0 90 180 270 360

15 Intake 10 Exhaust (def) 5

0 -360 -270 -180 -90 0 90 180 270 360 CAD

1.1

1.05

0.95 -360 -270 -180 -90 0 90 180 270 360

Figure 5.4: The upper plot shows the cylinder volume, Vcyl, during one cycle and the black circle corresponds to Vcyl at IVC. The middle plot shows the intake and exhaust valve lift during one cycle. The black circle in the lower plot corresponds to the pressure in the intake manifold at IVC.

Model 3 is deﬁned by

pim,IV C NeVd,IV C nc p m˙ air = (c03 + c13√pim,IV C + c23 Ne + c33αi + c43αe), (5.3) 120Rspec,air Tim where pim,IV C and Vd,IV C are the intake manifold pressure and the displaced volume at inlet valve closing, respectively. 5.3 Model 3 – Dynamic IVC pressure 31

5.3.2 Result and discussion

The estimated parameters in Model 3 are c03, c13, c23, c33 and c43 in (5.3). Table 5.3 shows the validation results for Model 3 when valve angles are dual independent. The model ﬁt is good and the mean relative error is quite small.

Table 5.3: Model 3 validation results when valve angles are dual independent.

Validation Model 3 Fit NRMSE [%] 94.41 Fit NMSE [%] 99.69 Mean |RE| [%] 6.38 Max |RE| [%] 35.28 Max positive AE [kg/s] 0.0184 Max negative AE [kg/s] -0.0136

Figure 5.5 shows a comparison between Model 3 outputs and measurements of the air mass ﬂow. The lower right plot shows relative errors for the predicted air mass ﬂow.

0.5

0.4

0.3

0.5 0.2

0.45 0.1

0.4 0 0 0.1 0.2 0.3 0.4 0.5 0.35

0.3 10 0.25 0 0.2 -10 0.15 -20 0.1 -30 0.05

0 -40 0 10 20 30 40 50 60 0 0.1 0.2 0.3 0.4 0.5

Figure 5.5: Results for Model 3 for dual independent valve angles on validation data. The left plot shows a comparison between the output from Model 3 and measurements for each sample. The right top plot shows measured against predicted air mass ﬂow. The bottom right plot shows the relative error for Model 3. 32 5 The extended models

In the lower right plot, the cluster of the worst relative error, between -18 % and -35 %, corresponds to samples between 12 and 18 in the left plot. This model should be able to estimate the air mass ﬂow better than Model 2, due to taking both the intake manifold pressure as well as the displaced volume at IVC. How- ever, the model ﬁt is slightly worse for Model 3 than for Model 2, even though it is marginal. 6 Model 4 – Division into sub-models

Another approach to estimate the air mass flow, also studied by both Leroy et al. (2009) and by Thomasson et al. (2018), is to divide the estimation of the air mass flow into several parts, each predicting different parts of the four-stroke cycle. Leroy et al. (2009) use physical models together with parameter estimation to model in-cylinder air mass on a spark ignition engine with only commercial sensors. Thomasson et al. (2018) use physical models together with in-cylinder pressure which is measured with a sensor not provided in commercial engines. The approach studied in Thomasson et al. (2018) is used as a reference to validate the three sub-models derived in this work and is referred to when mentioning a reference in Section 6.1 to Section 6.3. By following the principles in Thomasson et al. (2018), the air mass flow estimation is divided into three terms. The first term models the total mass trapped in the cylinder at IVC. The second term describes the mass that flows through the valves during the valve overlap. The third term estimates the total mass trapped in the cylinder at EVC. These three terms together describe the air mass in one cylinder as

m = m + m m , (6.1) air IVC ol − EVC where the direction of mol is defined positive if the mass flows from the intake manifold to the exhaust manifold and negative if flowing from the exhaust manifold to the intake manifold. The division is partly done because the inlet and exhaust cam phase angles should still affect the air mass flow more than previously modeled, i.e. more than intake manifold pressure and displaced volume. Another benefit is in knowing each of these masses individually. The mass trapped in the cylinder at IVC, mIVC, influences combustion and engine out emissions. The masses mEVC and mol together give the amount of residual gases that remain in the cylinder from the

33 34 6 Model 4 – Division into sub-models previous cycle. These residual gases are important for, for example, after treatment, such as selective catalytic reduction (SCR) to reduce emission of nitrogen oxides (NOx) (Eriksson and Nielsen, 2014). Conversion from air mass to air mass ﬂow results in

m n N m˙ = air c e . (6.2) air 120

6.1 Total mass trapped in cylinder at IVC

The first term, mIVC, in (6.1) describes the total mass trapped in the cylinder at IVC. In the same way as the reference model is based on the ideal gas law together with the volumetric efficiency to model the air mass that flows through the inlet valve, the total in-cylinder mass at IVC can be written as

pim,IV C VIVC p mIVC = (c0 + c1√pim,IV C + c2 Ne), (6.3) Rspec,air Tim | {z } ηvol where VIVC is the cylinder volume at IVC (previously Vd,IV C has been used, which is the displaced volume at IVC). The parenthesis in (6.3) looks like (3.16), if changing pim,IV C to pim.

6.1.1 Assumptions Depending on the cam phase angles, the ratio between residual gases and fresh air in the cylinder changes. The model uses Rspec,air , and therefore assumes that only air is trapped in the cylinder at IVC. However, the speciﬁc gas constants for air and residual gases are almost the same and should not inﬂuence the estimation that much. Because no sensors inside the cylinder are available, the model assumes that, at IVC, the intake manifold pressure equals the in-cylinder pressure and that the intake manifold temperature equals the in-cylinder temperature. Because no CAD resolved temperature measurements are available, Tim is given as a mean value over one whole four-stroke cycle. Therefore, Tim will not correspond to the in-cylinder temperature at IVC.

6.1.2 Results Table 6.1 shows the validation results when the model (6.3) is used to estimate the mass trapped in the cylinder at IVC, with the estimated parameters c0, c1 and c2. The mean relative error is small and the model ﬁt is good. A comparison between the estimated in-cylinder mass at IVC using (6.3) and the reference can be seen in Figure 6.1. The model has diﬃculties estimating the mass for strategy (c) Early exhaust. For this case, gases are pushed out into the intake manifold from the cylinder when the inlet valve is open, and residual gases remain in the cylinder. 6.1 Total mass trapped in cylinder at IVC 35

Table 6.1: Model validation results when the model (6.3) is used to estimate the total mass trapped at inlet valve closing.

Validation Model mIVC Fit NRMSE [%] 92.60 Fit NMSE [%] 99.45 Mean |RE| [%] 4.19 Max |RE| [%] 23.33

The reason why the mass is estimated higher than the reference could be that the in-cylinder temperature is higher than Tim; the mass in the cylinder is proportional to the inverse of the temperature from the ideal gas law. Also, residual gases ﬂow back into the intake manifold when the inlet valve opens and then re-enter the cylinder. This means that a mixture of residual gases and fresh air is inducted into the cylinder while the model assumes that all mass trapped in the cylinder is air. For strategy (b) Symmetric phasing with large cam phase angles, the model estimates a lower mass than the reference. This could be because of higher in- cylinder pressure than pim,IV C since the mass in the cylinder is proportional to the pressure.

10-3 8 7 6 5

10-3 4 8 3 2 7 1 0 6 0 1 2 3 4 5 6 7 8 10-3

5 10 4 0

3 -10

2 -20

1 -30 0 10 20 30 40 50 60 0 1 2 3 4 5 6 7 8 10-3

Figure 6.1: Results for model (6.3) for dual independent valve angles on validation data. The left plot shows a comparison between predicted mIVC using (6.3) and a reference for each sample. The right top plot shows a reference against predicted mIVC. The bottom right plot shows the relative error. 36 6 Model 4 – Division into sub-models

6.2 Mass ﬂow during valve overlap

The second term in (6.1) predicts the mass that flows through the valves during valve overlap. The mass can flow either from the intake to the exhaust manifold or vice versa, depending on the pressure difference, and this term is defined positive for the flow direction from the intake to the exhaust manifold. The pressure difference is taken at the crankshaft angle where the intake and exhaust valve opening areas are equal, denoted IV = EV where IV is inlet valve and EV is exhaust valve. To describe the amount of mass that passes through the valves during the overlap period an overlap factor (OF), defined in Section 6.2.1, is included in the model. The amount of mass transferred during the overlap period is also proportional to the inverse of the engine speed, Ne, because this describes the time that the overlap is present. The model is thus given by   OF (c + c (p p )) if p > p at IV=EV  Ne 0 1 im,(IV =EV ) em,(IV =EV ) im em mol =  OF − (6.4)  (c0 + c1(pim,(IV =EV ) pem,(IV =EV ))) if pim < pem at IV=EV, − Ne − where pim,(IV =EV ) and pem,(IV =EV ) are the pressures in the intake and exhaust manifolds, at the CAD when intake and exhaust opening areas are equal, respectively.

6.2.1 Overlap factor To describe the amount of mass that passes through the valves during the overlap period an overlap factor (OF) can be deﬁned as in Leroy et al. (2009),

IVZ=EV EVCZ OF = Aint dθ + Aexhdθ, (6.5) IVO IV =EV where Aint and Aexh are the areas under the valve area/crank angle curves, i.e. the eﬀective opening areas of the intake and exhaust valves, respectively, see Fig- ure 6.2.

Figure 6.2: Valve overlap (Leroy et al., 2009). 6.2 Mass ﬂow during valve overlap 37

The overlap factor is equal to zero if the exhaust valve closes before the inlet valve opens.

6.2.2 Assumptions and limitations The assumption for this model is that the crank angle where the inlet and the exhaust opening areas are equal, IV = EV, is in the middle of IVO and EVC, as can be seen in Figure 6.2. One limitation is that only measurements with ﬂow from intake manifold to exhaust manifold were available in this work.

6.2.3 Results

Table 6.2 shows the validation of model mol in (6.4), with the estimated parameters c0 and c1. The mean relative error is not so small but the model ﬁt is good.

Table 6.2: Model validation results when the model (6.4) is used to estimate the mass transferred during valve overlap.

Validation Model mol Fit NRMSE [%] 92.53 Fit NMSE [%] 99.44 Mean |RE| [%] 10.38 Max |RE| [%] 28.57

Figure 6.3 shows a comparison between the estimated mass, that ﬂows through the valves during valve overlap using (6.4), and a reference. Note that the mass transferred during overlap is very small, a tenfold less than the mass trapped in the cylinder at IVC. This should thus not inﬂuence the air mass estimation that much. This model estimates the mass well over all. However, in the lower right plot showing relative error, the error is large for very small masses. 38 6 Model 4 – Division into sub-models

10-4 2.5

1.5 10-4 3 1

0.5 2.5 0 0 0.5 1 1.5 2 2.5 2 10-4

30 1.5 20 10 1 0 -10 0.5 -20 -30 0 0 10 20 30 40 50 60 0 0.5 1 1.5 2 2.5 10-4

Figure 6.3: Results for model (6.4) for dual independent valve angles on validation data. The left plot shows a comparison between predicted mol using (6.4) and a reference for each sample. The right top plot shows a reference against predicted mol. The bottom right plot shows relative error.

6.3 Total mass trapped in cylinder at EVC

The third term in (6.1) is included to estimate the mass trapped in the cylinder at EVC. It is assumed that the in-cylinder pressure and exhaust manifold pressure are equal at EVC and that in-cylinder temperature and exhaust manifold temperature are equal at EVC. Then the total mass trapped in the in-cylinder can be derived from the ideal gas law, together with the volumetric eﬃciency as

pem,EV C VEVC p mEVC = c0 + c1√pem,EV C + c2 Ne , (6.6) Rspec,burned Tem

where pem,EV C is exhaust manifold pressure at EVC, VEVC is cylinder volume at EVC, Rspec,burned is the speciﬁc gas constant for burned gases and Tem is exhaust manifold temperature. Tem is taken as the mean value over a whole engine cycle. The residual gases that are trapped in the cylinder at EVC are important for knowing how much air that is trapped in the cylinder. The start of the ignition depends on the temperature of the gas in the cylinder which is dependent on the mixture of residual gases and fresh air in the cylinder at IVC.

6.3.1 Assumptions An assumption for the model (6.6) to estimate the mass trapped in the cylinder at EVC is that the temperature in the exhaust manifold, Tem, is known. Sensors 6.3 Total mass trapped in cylinder at EVC 39 measuring the exhaust temperature only exists in the test cell, not in commercial engines. To calculate Tem knowing the air mass ﬂow is required (i.e. one of the reasons of this work and calculating Tem is a separate study). Furthermore, Tem is given as a mean value over one four-stroke cycle and not at EVC. Because Rspec,burned is a constant for burned gases, no consideration is taken to that the mass trapped in the cylinder at EVC is not only burned gases. In reality, the remaining gases after the compression stroke consists of both burned gases and air. Also, in case of valve overlap and pim > pem, fresh air is injected into the cylinder before EVC, causing less burned gases in the cylinder.

6.3.2 Results

The estimated parameters for model mEVC in (6.6) are c0, c1 and c2 and table 6.3 shows the validation results. The relative error is very large, both the mean and max relative error. The model ﬁt is not so good.

Table 6.3: Model validation results when the model (6.6) is used to estimate the mass trapped in the cylinder at EVC.

Validation Model mEVC Fit NRMSE [%] 78.43 Fit NMSE [%] 95.35 Mean |RE| [%] 19.10 Max |RE| [%] 56.76

See Figure 6.4 for a comparison between the estimated mass using (6.6) that is trapped in the cylinder at EVC and a reference. Note that this mass is very small, a tenfold less than the mass trapped in the cylinder at IVC. The model has difficulties to estimate the mass trapped in the cylinder at EVC in several parts. Mainly the estimation accuracy is poor for periods of valve overlap. The model does not consider overlap, it assumes that all gases trapped in the cylinder at EVC are burned gases. Because Tem comes from sensor measurements and is the mean value during one whole cycle this could be far from the temperature in the cylinder at EVC. Samples between 20 to 45 correspond to strategy (a) Valve overlap, where the biggest overlap occurs from sample 20 to 30, where the estimation is worst. This should be because more mass flows through the valves during the overlap in this region and therefore the model has difficulties in estimating the mass trapped at EVC. 40 6 Model 4 – Division into sub-models

10-4 9 8 7 6 5 10-4 9 4 3 8 2 1 7 0 0 1 2 3 4 5 6 7 8 9 6 10-4

5 60

4 40 20 3 0

2 -20

1 -40 -60 0 0 10 20 30 40 50 60 0 1 2 3 4 5 6 7 8 9 10-4

Figure 6.4: Results for model (6.6) for dual independent valve angles on validation data. The left plot shows a comparison between predicted mEVC using (6.6) and a reference for each sample. The right top plot shows a reference against predicted mEVC. The bottom right plot shows relative error.

6.4 Results and discussion

In this section the validation of the air mass ﬂow will be presented. This model, which comes from (6.1) and (6.2) containing the three sub-models from Section 6.1 to 6.3, is called Model 4. Table 6.4 shows validation results for Model 4. The mean relative error is not so large and the model ﬁt is good.

Table 6.4: Model 4 validation results when estimating the air mass ﬂow when valve angles are dual independent.

Validation Model 4 Fit NRMSE [%] 94.24 Fit NMSE [%] 99.67 Mean |RE| [%] 6.24 Max |RE| [%] 30.53 Max positive AE [kg/s] 0.0126 Max negative AE [kg/s] -0.0267

Figure 6.5 shows a comparison between the estimated and measured air mass ﬂow. This model estimates the air mass ﬂow quite well in the whole region. How- 6.4 Results and discussion 41

ever, the validation results for Model 4 is almost equal to the validation results for Model 2 and Model 3.

0.5

0.4

0.3

0.5 0.2

0.45 0.1

0.4 0 0 0.1 0.2 0.3 0.4 0.5 0.35

0.3

0.25 20 10 0.2 0 0.15 -10 0.1 -20 0.05 -30 0 0 10 20 30 40 50 60 0 0.1 0.2 0.3 0.4 0.5

Figure 6.5: Results for Model 4 for dual independent valve angles on validation data. The left plot shows a comparison between the output from Model 4 and measurements for each sample. The right top plot shows measured against predicted air mass ﬂow. The bottom right plot shows the relative error for Model 4.

Since the mass trapped in the cylinder at IVC is much larger than the mass that flows through the valves during overlap and the mass trapped in the cylinder at EVC, mIVC using (6.3) will have the largest influence on Model 4. Therefore Model 4 overestimates the air mass flow from sample 1 to 11 corresponding to strategy (c) Early exhaust and underestimates the air mass between sample 12 to 18 corresponding to strategy (b) Symmetric phasing.

7 Discussion and conclusions

This chapter includes a sensitivity analysis, a summarized discussion for all models derived, and suggestions on how to proceed with the work on estimation of the air mass ﬂow.

7.1 Sensitivity analysis

Opening and closing angles of the intake and exhaust valves, respectively, are defined as an offset together with a valve clearance. For the intake valve, the valve clearance is defined as 0.45 mm and for the exhaust valve it is defined as 0.7 mm. The offset however, is defined differently depending on the manufacturer. In this project, the offset is set to 0.4 mm, from investigations looking at where the mass flow into and out of the cylinder actually can be seen. However, a common value for the offset is 1 mm. The models that include signals with respect to valve closing or opening will be affected due to that the offset gives different IVC, IVO, EVC and EVO. An investigation on Model 3 has been done, using the values of the parameters c03, c13 c23 c33 and c43 in (5.3) given by estimation data when the offset is set to 0.4 mm. These parameters are then used with validation data with the offsets 0.4 mm, 1 mm and 0.2 mm. In Model 3, both Vd,IV C and pim,IV C will be affected. Table 7.1 shows validation results for offsets 0.4, 1 and 0.2 mm for Model 3. The results show that the model accuracy is dependent on the offset value.

43 44 7 Discussion and conclusions

Table 7.1: Validation results for Model 3 for the oﬀset values 0.4, 1 and 0.2 mm.

ﬁt NRMSE ﬁt NMSE Mean |RE| Max |RE| Model 3 [%] [%] [%] [%] 0.4 mm 94.41 99.69 6.38 35.28 1 mm 89.11 98.81 10.13 54.07 0.2 mm 92.37 99.42 6.75 27.09

7.2 Discussion

In this work, four diﬀerent models have been derived, each with the goal to accurately estimate the air mass that ﬂows through a diesel engine. Table 7.2 shows the validation for all four models.

Table 7.2: Model validation results for all four models.

Validation Ref model Model 1 Model 2 Model 3 Model 4 ﬁt NRMSE [%] 78.83 84.96 95.07 94.41 94.24 ﬁt NMSE [%] 95.52 97.74 99.76 99.69 99.67 Mean |RE| [%] 25.73 18.20 5.25 6.38 6.24 Max |RE| [%] 139 69.75 29.26 35.28 30.53 Max positive AE [kg/s] 0.0422 0.0304 0.0178 0.0184 0.0126 Max negative AE [kg/s] -0.0521 -0.0333 -0.0110 -0.0136 -0.0267

All models seem to have most difficulty in estimating the air mass flow for strategy (b) Symmetric phasing for very large inlet and exhaust cam phase angles. Model 1 also estimates strategy (c) Early exhaust very poorly and does not accurately model the dependency of the air mass flow on the cam phase angles. Hence, it is not enough to only know the volume of the engine cylinder at IVC. Model 2 and 3 are however able to estimate the air mass flow for strategy (c). Models 2 and 3 have a direct dependency on the inlet and exhaust cam phase angles, which improves the estimation accuracy. In theory, Model 3 should estimate the air mass flow more accurately than Model 2, since it includes the cylinder volume at IVC as well as the intake manifold pressure at IVC. In practice, however, Model 2 is slightly better. Model 4 should be able to estimate the air mass flow most accurately, given that each sub-model estimates its part well. But as can be seen in Table 7.2 this is not the case. Model 4 is based on more physical insight than the other models and it does not include a direct dependency on the inlet and exhaust cam phase angles resulting in that the volumetric efficiency contains fewer parameters in Model 4 than in Models 2 and 3. 7.2 Discussion 45

Models 1, 3 and 4, all include input signals that are dependent on a speciﬁc CAD. The CAD dependent signals are the manifold pressures and the cylinder volume since they are dependent on when the inlet and exhaust valves open and closes. If a signal value is taken at the wrong CAD the value of the signal will be wrong since it varies a lot over one four-stroke cycle. IVC and EVC for zero cam phasing are extracted from the valve proﬁles, i.e. the lift and duration. If these values are wrong, then all volumes and pressures dependent on IVC or EVC will be wrong. One reason for this is if the valve duration in the engine does not equal the valve duration assumed when extracting IVC and EVC. Figure 7.1 shows manifold and in-cylinder pressures. The circles show at which CAD that the intake manifold pressure value is taken. The diamonds show at which CAD that the exhaust manifold pressure value is taken.

2.5

1.5

0.5 -360 -270 -180 -90 0 90 180 270 360

Figure 7.1: Manifold and in-cylinder pressures. The circles show at which CAD that pim,IV C is taken and the diamonds show at which CAD that pem,EV C is taken.

Looking at this plot, the cylinder pressures at IVC and EVC are much higher than the manifold pressure, both for intake and exhaust. About 20 CAD before IVC and EVC, the intake manifold pressure and the exhaust manifold pressure are more close to the cylinder pressure. This can also be seen as the cylinder pressure increases before the circles and the diamonds, respectively, meaning that the valve closes and the in-cylinder pressure rapidly increases. 46 7 Discussion and conclusions

7.3 Future work

There are several ways to continue with this work in the future. One issue today is to know exactly when inlet valve opening and closing, as well as exhaust valve opening and closing, occurs. So in the future, more consideration should be put into making these input signals more accurate in order for the models to better estimate the air mass flow. In this work, only measurements from one cylinder have been collected since sensors have not been available for all cylinders. An assumption in this project was that the air mass flow was equally distributed over all cylinders. Since they are implemented on a straight line, with different distance to the fresh air, for example the intake manifold temperature will differ for each cylinder. One solu- tion is to have at least measurements from the cylinders closest to and furthest away from the fresh air and assume a linear behavior between them, in order to get a more true distribution of the air mass flow for each cylinder. When estimating the air mass that flows through the valves during the overlap period in Section 6.2.1, only data for the case where pim > pem were available. Measurements for pem > pim causing exhaust gas to be pushed out to the inlet manifold should also be studied. Throughout this project only models linear in the parameters have been derived. In the future, non-linear models such as neural networks could be investi- gated.

7.4 Conclusions

The goal of this thesis has been to estimate the air mass flow through an engine with variable valve timing. This has been done with physical insights combined with grey-box models where unknown parameters have been estimated from measurements. Throughout the work, only measurements from steady-state conditions have been used. One purpose has been to only use sensors in commercial vehicles which has been true for all models except one sub-model including the temperature in the exhaust manifold. All models derived in this project have been based on the estimation approach in use today with fix cam phasing, which is based on the ideal gas law together with a volumetric efficiency factor. It has been seen that the best model fit occurs when only the inlet and exhaust cam phase angles are directly included in the model. Further development to reach better estimation results with lower relative error is needed. However, for the work in this thesis, the models are estimating the air mass flow well enough to use as a base for further control. The best model fit presented in this thesis has a mean absolute relative error of 5.25 % and a max absolute relative error of 29.26 %. Comparing to existing methods with a mean and max absolute relative error of 25.73 % and 139 %, respectively, this is a big improvement. It has been concluded which parameters the air mass flow is dependent on. A major conclu- sion is how important it is to use input signals measured at the right CAD, since they vary during one four-stroke cycle. A constant volume and mean values of 7.4 Conclusions 47 pressure signals give more accurate estimates than if the signals are taken at the wrong CAD. The models to develop further should therefore be Model 3, which includes signals taken at inlet valve closing, and Model 4, which includes signals at both inlet valve and exhaust valve closing.

Bibliography

A. Akimoto, H. Itoh, and H. Suzuki. Development of Delta P method to optimize transient A/F-behavior in MPI Engine. JSAE Review, 10(4), 1989. Cited on page 2. J. M. Desantes, J. Galindo, C. Guardiola, and V. Dolz. Air mass ﬂow estimation in turbocharged diesel engines from in-cylinder pressure measurement. Ex- perimental Thermal and Fluid Science, 34(1):37–47, 2010. ISSN 0894-1777. Cited on page 2. L. Eriksson and L. Nielsen. Modeling and Control of Engines and Drivelines. John Wiley & Sons, 2014. Cited on pages 6, 15, 17, and 34. S. García-Nieto, J. Salcedo, M. Martínez, and D. Laurí. Air management in a diesel engine using fuzzy control techniques. Information Sciences, (179): 3392–3409, 2009. Cited on page 1. C. Gray. A Review of Variable Engine Valve Timing. SAE Technical Paper, 1988. ISSN 0148-7191. Cited on pages 1 and 2. J. B. Heywood. Internal Combustion Engine Fundamentals. McGraw-Hill, Inc., 1988. Cited on page 5. T. Leroy, G. Alix, J. Chauvin, and A. et al. Duparchy. Modeling Fresh Air Charge and Residual Gas Fraction on a Dual Independent Variable Valve Timing SI Engine. SAE Int. J. Engines, 1(1):627–635, 2009. Cited on pages 2, 3, 33, and 36. S. Nikkar. Estimation of In-cylinder Trapped Gas Mass and Composition. Dis- sertation, Linköping University, 2017. Cited on page 10. A. G. Stefanopoulou, J. A. Cook, J. W. Grizzle, and J. S. Freudenberg. Control- Oriented Model of a Dual Equal Variable Cam Timing Spark Ignition En- gine. J. Dyn. Sys., Meas., Control, 120(2):257 – 266, 1998. Cited on page 3. A. Thomasson, S. Nikkar, and E. Höckerdal. Cylinder Pressure Based Cylin- der Charge Estimation in Diesel Engines With Dual Independent Vari- able Valve Timing. SAE Int. J. Engines, 04 2018. ISSN 0148-7191. Cited on pages 2, 3, and 33.

49 50 Bibliography

J. Wahlström and L. Eriksson. Modeling diesel engines with a variable- geometry turbocharger and exhaust gas recirculation by optimization of model parameters for capturing non-linear system dynamics. Proceedings of the Institution of Mechanical Engineers, Part D, Journal of Automobile En- gineering, 225(7):960–986, 2011. Cited on page 2.