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 associatedlevelvariable 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].
Since such a diagram shows the driving and the driven variables, the cause and effect relations become clearly visible.
time reservoir
levels
b) a)
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 relevantreservoirs (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 typicalport-injectedSI 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.6How- 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 torqueTe, the exhaust gas temperatureϑe, and the air/fuel ratioλe.
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.
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-injectionSI 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.
Thestatic propertiesof 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 signaluξ in Fig. 2.5) and the missing wall- wetting block [4] (see [197]). The signaluξ controls the injection process in its timing and distribution (multiple pulses are often used in GDI engines) while the signaluϕindicates 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 followingnew 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].
Fig. 2.6. Cause and effect diagram of a Diesel engine (EGR and intercooler not included).
Tc torque absorbed by the compressor.
Compared to an SI engine, there are several additional reservoirs to be modeled in a Diesel engine system. In the intake and exhaust manifolds, for instance, not only masses, but thermal (internal) energy is important. Accord- ingly, two level variables (pressure and temperature) form the output of these blocks. The turbocharger’s rotor, which stores kinetic energy, is an additional reservoir.
If EGR and intercooling are modeled as well, the cause and effect diagram has a similar, but even more complex structure. The most important addi-
tional variable is the intake gas composition, i.e., the ratio between fresh air and burnt gases in the intake. If perfect mixing can be assumed, this leads to only one additional reservoir, see Sect. 2.3.4.