Introduction to Modeling and Control of Internal Combustion Engine Systems P2 ppsx

The main engine sub models are then discussed, namely the air system that determines how much air is inducted into the cylinder; the fuel system that determines how much fuel is inducted

1.5 Structure of the Text 19

In heavy-duty applications, where fuel economy is a top priority, lean

de-N Ox systems using a selective catalytic reduction (SCR) approach are an interesting alternative Such systems can reduce engine-out N Ox by approxi-mately one order of magnitude This permits the engine to be calibrated at the high-efficiency/low-PM boundary of the trade-off curve (see Fig 1.11, early injection angle) The drawback of this approach is, of course, the need for an additional fluid distribution infrastructure (most likely urea)

While such systems are feasible in heavy-duty applications, for passenger cars it is generally felt that a solution with Diesel particulate filters (DPF) is more likely to be successful on a large scale These filters permit an engine cal-ibration on the high-PM/low-N Oxside of the trade-off Using this approach, engine-out N Oxemissions are kept within the legislation limits by using high EGR rates but without any further after-treatment systems

Radically new approaches, such as cold-flame combustion (see e.g., [190])

or homogeneous-charge compression ignition engines (HCCI, see [187], [188], [172] for control-oriented discussion) promise further reductions in engine-out emissions, especially at part-load conditions

In all of these approaches, feedforward and feedback control systems will play an important role as an enabling technology Moreover, with ever in-creasing system complexity, model-based approaches will become even more important

1.5 Structure of the Text

The main body of this text is organized as follows:

• Chapter 2 introduces mean-value10models of the most important phenom-ena in IC engines

• Chapter 3 derives discrete-event or crank-angle models for those subsys-tems that will need such descriptions to be properly controlled

• Chapter 4 discusses some important control problems by applying a model-based approach for the design of feedforward as well as feedback control systems

In addition to these three chapters, the three appendices contain the fol-lowing information:

• Appendix A summarizes, in a concise formulation, most of the control system analysis and synthesis ideas that are required to follow the main text

10The term mean-value is used to designate models that do not reflect the en-gine’s reciprocating and hence crank-angle sampled behavior, but which use a continuous-time lumped parameter description Discrete-event models, on the other hand, explicitly take these effects into account

• Appendix B illustrates the concepts introduced in the main text by show-ing the design of a simplified idle-speed controller This includes some remarks on parameter identification and on model validation using exper-imental data

• Appendix C summarizes some control oriented aspects of fuel properties, combustion, and thermodynamic cycle calculation

Mean-Value Models

In this chapter, mean-value models (MVM) of the most important subsystems

of SI and Diesel engines are introduced In this book, the notion of MVM1will

be used for a specific set of models as defined below First, a precise definition

of the term MVM is given This family of models is then compared to other models used in engine design and optimization The main engine sub models are then discussed, namely the air system that determines how much air is inducted into the cylinder; the fuel system that determines how much fuel is inducted into the cylinder; the torque generation system that determines how much torque is produced by the air and fuel in the cylinder as determined by the first two parts; the engine inertial system that determines the engine speed; the engine thermal system that determines the dynamic thermal behavior of the engine; the pollution formation system that models the engine-out emission; and the pollution abatement system that models the behavior of the catalysts, the sensors, and other relevant equipment in the exhaust pipe

All these models are control oriented models (COM), i.e., they model the input-output behavior of the systems with reasonable precision but low compu-tational complexity They include, explicitly, all relevant transient (dynamic) effects Typically, these COM are represented by systems of nonlinear differ-ential equations Only physics-based COM will be discussed, i.e., models that are based on physical principles and on a few experiments necessary to identify some key parameters

1 The terminology MVM was probably first introduced in [89] One of the earliest papers proposing MVM for engine systems is [195] A good overview of the first developments in the area of MVM of SI engine systems can be found in [167] A more recent source of information on this topic is [44]

2.1 Introduction

Reciprocating engines in passenger cars clearly differ in at least two aspects from continuously operating thermal engines such as gas turbines:

• the combustion process itself is highly transient (Otto or Diesel cycle, with large and rapid temperature and pressure variations); and

• the thermodynamic boundary conditions that govern the combustion pro-cess (intake pressure, composition of the air/fuel mixture, etc.) are not constant

The thermodynamic and kinetic processes in the first class of phenomena are very fast (a few milliseconds for a full Otto or Diesel cycle) and usually are not accessible for control purposes Moreover, the models necessary to describe these phenomena are rather complex and are not useful for the design

of real-time feedback control systems Exceptions are models used to predict pollutant formation or analogous tasks Appendix C describes the elementary ideas of engine thermodynamic cycle calculation (See Sec 2.5.3 for more details on engine test benches.)

yω

yλ

yα

y p

…

speed

uα

uϕ

uζ

uε

…

throttle

SI engine

load torque

("disturbance input") T l

injection

ignition

EGR-valve

etc

air/fuel-ratio air mass-flow manifold pressure etc

Fig 2.1.Main system’s input/output signals in a COM of an SI engine (similar for Diesel engines)

This text focuses on the second class of phenomena using control-oriented models, and it simplifies the fast combustion characteristics as static effects The underlying assumption is that, once all important thermodynamic bound-ary conditions at the start of an Otto or Diesel cycle are fixed, the combustion itself will evolve in an identical way each time the same initial starting condi-tions are imposed Clearly, such models are not able to reflect all phenomena (the random combustion pressure variations in SI engines, for example)

As shown in Fig 2.1, in the COM paradigm, the engine is a “gray box” that has several input (command) signals, one main disturbance signal (the

2.1 Introduction 23 load torque) and several output signals The inputs are signals, i.e., quantities that can be arbitrarily chosen.2 Rather than physical quantities, the outputs also are signals that can be used by the controller without the system behavior being affected The only physical link of the engine to the rest of the power train is the load torque, which in this text is assumed to be known

The reciprocating behavior of the engine induces another dichotomy in the COM used to describe the engine dynamics:

• Mean value models (MVM), i.e., continuous COM, which neglect the dis-crete cycles of the engine and assume that all processes and effects are spread out over the engine cycle;3and

• Discrete event models (DEM), i.e., COM that explicitly take into account the reciprocating behavior of the engine

In MVM, the time t is the independent variable, while in DEM, the crankshaft angle φ is the independent variable Often, DEM are formulated assuming a constant engine speed In this case, they coincide with classical sampled data systems, for which a rich and (at least for linear systems) com-plete theoretical background exists These aspects are treated in detail in Chapter 3

In MVM, the reciprocating behavior is captured by introducing delays between cylinder-in and cylinder-out effects (see Fig 2.2) For example, the torque produced by the engine does not respond immediately to an increase

in the manifold pressure The new engine torque will be active Only after the induction-to-power-stroke (IPS) delay [166]

τIP S≈ 2πω

e

(2.1)

has elapsed.4

Similarly, any changes of the cylinder-in gas composition, such as air/fuel ratio, EGR ratio, etc will be perceived at the cylinder exhaust only after the induction-to-exhaust-gas (IEG) delay

τIEG≈ 3πω

e

(2.2)

The proper choice of model class depends upon the problem to be solved For example, MVM are well suited to relatively slow processes in the engine periphery, constant engine speed DEM are useful for air/fuel ratio feedforward

2 In order to allow full control of the engine, usually these will be electric signals, e.g., the throttle plate will be assumed to be “drive-by-wire.”

3 In MVM, the finite swept volume of the engine can be viewed as being one that

is distributed over an infinite number of infinitely small cylinders

4 The expression (2.1) is valid for four-stroke engines Two-stroke engines have half

of that IPS delay As shown in Chapter 3, additional delays are introduced by the electronic control hardware

aspiration

center

torque center

τIPS

TDC BDC

p

τIEG

exhaust center

BDC

Fig 2.2.Definition of IPS and IEG delays for MVM using a pressure/crank angle diagram

control, and crank-angle DEM are needed for misfire detection algorithms based on measurement data of crankshaft speed

Most MVM are lumped parameter models, i.e., system descriptions that have no spatially varying variables and that are represented by ordinary differ-ential equations (ODE) If not only time but location also must be used as an independent variable, distributed parameter models result that are described

by partial differential equations (PDE) Such models usually are computa-tionally too demanding to be useful for real-time applications5 such that a spacial discretization is necessary (see e.g., Sect 2.8)

2.2 Cause and Effect Diagrams

In this section, the internal structure of MVM for SI and CI engines will be analyzed in detail When modeling any physical system there are two main classes of objects that must be taken into account:

• reservoirs, e.g., of thermal or kinetic energy, of mass, or of information (there is an associated level variable to each reservoir that depends directly

on the reservoir’s content); and

• flows, e.g., energy, mass, etc flowing between the reservoirs (typically driven by differences in reservoir levels)

A diagram containing all relevant reservoirs and flows between these reser-voirs will be called a cause and effect diagram (see, for instance, Fig 2.5)

5 There are publications which propose PDE-based models for control applications, see for instance [43]

2.2 Cause and Effect Diagrams 25 Since such a diagram shows the driving and the driven variables, the cause and effect relations become clearly visible

time

reservoir

levels

c)

input event

Fig 2.3 Relevant reservoirs: a) variable of primary interest, b) very fast and c) very slow variables

A good MVM contains only the relevant reservoirs (otherwise “stiff” sys-tems will be obtained) To define more precisely what is relevant, the three signals shown in Fig 2.3 can be useful Signal a) is the variable of primary interest (say, the manifold pressure) Signal b) is very fast compared to a) (say, the throttle plate angle dynamics) and must be modeled as a purely static variable which can depend in an algebraic way on the main variable a) and the input signals Signal c) is very slow compared to a) (say, the tem-perature of the manifold walls) and must be modeled as a constant (which may be adapted after a longer period) Only in this way a useful COM can

be obtained

Unfortunately, there are no simple and systematic rules of how to decide a priori which reservoirs can be modeled in what way Here, experience and/or iteration will be necessary, making system modeling partially an “engineering art.” Readers not familiar with the basic notions of systems modeling and controller design find some basic information in Appendix A

2.2.1 Spark-Ignited Engines

Port-Injection SI Engines

A typical port-injected SI engine system has the structure shown in Fig 2.4 In

a mean value approach, the reciprocating behavior of the cylinders is replaced

by a continuously working volumetric pump that produces exhaust gases and torque The resulting main engine components are shown in Fig 2.4 The different phenomena will be explained in detail in the following sections However, the main reservoir effects can be identified at the outset:

• gas mass in the intake and exhaust manifold;

Fig 2.4 Abstract mean-value SI-engine structure.

• internal energy in the intake and exhaust manifolds;

• fuel mass on the intake manifold walls (wall-wetting effect);

• kinetic energy in the engine’s crankshaft and flywheel;

• induction-to-power-stroke delay in the combustion process (essentially an information delay); and

• various delays in the exhaust manifold (including transport phenomena) Figure 2.5 shows the resulting simplified cause and effect diagram of an SI engine (assuming isothermal conditions in the intake manifold and modeling the exhaust manifold as a pure delay system) In the cause and effect diagram, the reservoirs mentioned appear as blocks with black shading Between these reservoir blocks, flows are defined by static blocks (gray shading) The levels

of the reservoirs define the size of these flows

Each of these blocks is subdivided into several other parts which will be discussed in the sections indicated in the corresponding square brackets.6 How-ever, the most important connections are already visible in this representation Both air and fuel paths affect the combustion through some delaying blocks while the ignition affects the combustion (almost) directly The main output variables of the combustion process are the engine torque Te, the exhaust gas temperature ϑe, and the air/fuel ratio λe

The following signal definitions have been used in Figs 2.4 and 2.5:

˙

mα air mass flow entering the intake manifold through the throttle;

˙

mβ air mass flow entering the cylinder;

pm pressure in the intake manifold;

˙

mψ fuel mass flow injected by the injectors;

˙

mϕ fuel mass flow entering the cylinder;

˙

m mixture mass flow entering the cylinder, with ˙m = ˙mβ+ ˙mϕ;

Te engine torque;

ωe engine speed;

6 The block [x] will be discussed in Sect 2.x

2.2 Cause and Effect Diagrams 27

Fig 2.5 Cause and effect diagram of an SI engine system (numbers in brackets indicate corresponding sections, gray input channel only for GDI engines, see text)

ϑe engine exhaust gas temperature; and

λe normalized air/fuel ratio

Direct-Injection SI Engines

Direct-injection SI engines (often abbreviated as GDI engines — for gasoline direct injection) are very similar to port-injected SI engines The distinctive feature of GDI engines is their ability to operate in two different modes:

• Homogeneous charge mode (typically at high loads or speeds), with injec-tion starting during air intake, and with stoichiometric air/fuel mixtures being burnt

• Stratified charge mode (at low to medium loads and low to medium speeds), with late injection and lean air/fuel mixtures

The static properties of the GDI engine (gas exchange, torque generation, pollution formation, etc.) deviate substantially from those of a port injected engine as long as the GDI engine is in stratified charge mode These aspects will be discussed in the corresponding sections below

The main differences from a control engineering point of view are the additional control channel (input signal uξ in Fig 2.5) and the missing wall-wetting block [4] (see [197]) The signal uξ controls the injection process in its timing and distribution (multiple pulses are often used in GDI engines) while the signal uϕindicates the fuel quantity to be injected

2.2.2 Diesel Engines

As with SI engines, in a mean value approach, CI engines are assumed to work continuously The resulting schematic engine structure has a form similar to the one shown in Fig 2.4 The cause and effect diagram of a supercharged direct-injection Diesel engine (no EGR) is shown in Fig 2.6 Even without considering EGR and cooling of the compressed intake air, its cause and effect diagram is considerably more complex than that of an SI engine

The main reason for this complexity is the turbocharger, which introduces

a substantial coupling between the engine exhaust and the engine intake sides Moreover, both in the compressor and in the turbine, thermal effects play an important role However, there are also some parts that are simpler than in

SI engines: fuel injection determines both the quantity of fuel injected and the ignition timing, and, since the fuel is injected directly into the cylinder,

no additional dynamic effects are to be modeled in the fuel path.7

The following new signal definitions have been used in Fig 2.6:

˙

mc air mass flow through the compressor;

˙

mt exhaust mass flow through the turbine;

pc pressure immediately after the compressor;

p2 pressure in the intake manifold;

p3 pressure in the exhaust manifold;

ϑc air temperature after the compressor;

ϑ2 air temperature in the intake manifold;

ϑ3 exhaust gas temperature in front of the turbine;

ωtc turbocharger rotational speed;

Tt torque produced by the turbine; and

7 For fluid dynamic and aerodynamic simulations, usually a high-bandwidth model

of the rail dynamics is necessary, see [127] or [143]