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1、International Congress and Exposition Detroit, Michigan February 26 March 2, 1990 The Engineering Society For Advancing Mobility Land Sea Air and Space I N T E R N A T I O N A L 400 COMMONWEALTH DRIVE, WARRENDALE, PA 15096-0001 U.S.A. SAE Technical Paper Series 900616 Mean Value Modelling of Spark I
2、gnition Engines Elbert Hendricks Inst. of Automatic Control Systems The Technical University of Denmark Spencer C. Sorenson Lab. for Energetics The Technical University of Denmark The appearance of the ISSN code at the bottom of this page indicates SAEs consent that copies of the paper may be made f
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9、nition Engines Elbert Hendricks Inst. of Automatic Control Systems The Technical University of Denmark Spencer C. Sorenson Lab. for Energetics The Technical University of Denmark ABSTRACT While a large number of dynamic simulation models have been presented for various four-cycle spark ignition engi
10、ne subsystems in the literature, very few have been presented for the entire engine which can claim an acceptable level of accuracy for engineering purposes. This paper presents a nonlinear three state (three differential equation) dynamic model of an SI engine which has the same steady state accura
11、cy as a typical dynamometer measurement of the engine over its entire speed/load operating range (2.0%). The models accuracy for fast transients is of the same order in the same operating region. Because the model is so mathematically compact, it has few adjustable parameters and is thus simple to f
12、it to a given engine either on the basis of measurements or given the steady state results of a larger cycle simulation package. The model can easily be run on a Personal Computer (PC) using a ordinary differential equation (ODE) integrating routine or package. The paper shows how the model can be f
13、itted using either experimental data or simulation results. Moreover it includes the results of simulations run on experimental data with large and fast throttle (tip-in/out) transients which show its excellent steady state and dynamic accuracy. The model is also useful for control system design and
14、 evaluation. 1.INTRODUCTION A type of simple mathematical engine model which is intermediate between large cyclic simulation models and simplistic phenomenological transfer function models is the mean value engine model. These engine models seek to predict the mean values of the gross external engin
15、e variables (f.ex. crank shaft speed and manifold pressure) and the gross internal engine variables f.ex. thermal and volumetric efficiency) dynamically in time. The time scale for this description is much longer than that required for a single engine cycle and much shorter than required for a cold
16、engine to warm up ( 1000 cycles or so). The time scale of the model is just adequate to describe accurately the change of the mean value of the most rapidly changing engine variable. Models of this nature are often useful for engine control system design, development and evaluation. Mean value spark
17、 ignition (S1) four-cycle engine models found in the literature often suffer from a number of deficiencies which limit their applicability to general engineering applications. Often they are too incompletely documented to judge their overall accuracy or they are specialized to study a particular phy
18、sical or control problem. Dobner (1) has presented a dynamic model for a carburated SI engine but the paper does not document in detail the equations or the overall accuracy of the model. Cho and Hedrick (2) present a multipoint injection engine model in their article on control system development.
19、For this reason they do not give an idea of its accuracy over the operating range of the engine. Neither do they treat the important fueling dynamics. An additional study (Aquino, (3) is focused on the fueling dynamics and thus is not applicable to varying engine speed. In contrast to these earlier
20、efforts the four-cycle mean value model to be reported here is designed to be applicable to the entire operating range of an engine. It should also to be applicable with very few changes to central fuel injection (CFI), simultaneous multipoint injection (EFI) and sequential fuel injection (SEFI) eng
21、ines. Another important consideration is how a model can be made of a given engine. Models can be built either using the results of a large cyclic simulation routine or from experimental engine mapping data. One of the authors of this paper has presented a mean value model of a large turbocharged di
22、esel engine based on the results of a very detailed (and hence large) cyclic simulation of the engine (Hendricks, (4). Cho and Hedrick (2) have presented a two state engine model based on a much more comprehensive time domain model due to Dobner (5). While it is possible to construct 2 900616 very a
23、ccurate mean value models on this basis, a large simulation package is not always available that has a sufficient accuracy. Thus the model to be presented here is based on experimentally obtained data and the modelling method is applicable by most engineers concerned professionally with engines. Giv
24、en the stated goal of constructing a simple model one is tempted to assume that such a model can only be qualitatively correct. It is generally assumed that high accuracy can be achieved only with complicated models. In fact this need not be the case and the target accuracy for the model here is of
25、the order as the experimental uncertainty for a typical dynamometer experiment, i.e. 2- 3%. The approach taken was that of selecting the correct physical variables as the backbone of the model. If they could be accurately represented then the accuracy of the overall model must necessarily follow 2.E
26、NGINE DIAGRAM A schematic block diagram of a four-cycle CFI SI engine is presented in figure 1. This is the most difficult injection engine to model due to the fuel flow dynamics in the intake manifold. The generalization to EFI and SEFI engines is suggested later. The figure shows the basic systems
27、 to be modelled: the fuel film dynamics in the intake manifold; the air mass flow past the throttle plate into the volume V, between the throttle plate and intake valves; the engine displacement volume, Vd; the crank shaft inertia and load dynamics. The placement of the fuel injector in front of the
28、 throttle plate shows that the figure is for a CH engine. 2.1NOMENCLATURE - The following symbols are used in this paper: ttime (sec) pambambient pressure (bar) Tambambient temperature (degrees Kelvin) throttle plate angle (degrees) a rate of change of mass in volume V (kg/see) at air mass flow rate
29、 past throttle plate (kg/see) ap air mass flow rate into cylinder (kg/sec) fi injected fuel mass flow (kg per see) f cylinder port fuel mass flow (kg per sec) ff fuel film mass flow (kg per sec) fv fuel vapor mass flow (kg per sec) Xfraction of the injected fuel which is deposited on manifold as fue
30、l film Lthstoichiometric air/fuel mass ratio for gasoline (14.67) air/fuel equivalence ratio = a/ (fLth) pmammanifold air pressure (bar) Tmanmanifold air temperature (degrees Kelvin) pexhexhaust pressure (bar) spark advance angle (degrees) iindicated efficiency volvolumetric efficiency (based on int
31、ake conditions) vambvolumetric efficiency (based on ambient conditions) ncrank shaft speed (rpm) Itotal moment of inertia loading engine (kg m2) crank shaft angular speed (rad/sec) pmeppumping mean effective pressure, pmep (bar) fmepfrictional mean effective pressure, fmep (bar) Piindicated power (W
32、atts) Pffrictional power (Watts) Pppumping power (Watts) Pbload power (Watts) Hufuel heating value (kJ/kg) Vdengine displacement (m3 or liters) Vmanifold + port passage volume (m3) Rgas constant ratio of the specific heats = 1.4 for air Ctflow coefficient of throttle body throat Ddiameter of throttl
33、e body throat (m) 2.2 TERMONOLOGY - In order to discuss an engine dynamically in a logical way it is necessary to establish a convention for which variables control others and for what is meant by a parameter. This is a necessary preliminary for a physical discussion of the engine alone without its
34、control m m m m m m m m m 3910177 system.7 The engine input variables are those which can be adjusted external to the engine to control it. These are the throttle angle, , the injected fuel flow, fi, and the ignition timing angle, (degrees BTDC). State variables are those which are determined by int
35、egrating the differential equations which are used to describe the engine. The choices for these variables determine in large measure how complicated the differential equations are and how many subsidiary algebraic equations are required to give a coherent physical picture of an engine. The variable
36、s which will be selected are those which give a picture of engine operation which is as close as possible to that which is conventionally used by engine specialists. In the engine model to be presented the state variables are the fuel film mass flow, ff, the crank shaft speed, n, and the absolute ma
37、nifold pressure, pman. The measurable state variables are also output variables of the engine. The gross internal engine variables such as the thermal and volumetric efficiencies are determined as functions of the state variables. The engine load (power or torque) in this work is considered as a dis
38、turbance of the engine. That is, it is an input which disturbs the engine away from its unloaded operating condition. It will be assumed that sufficient controls are being applied that the engine will function in the normal operating range. This can be achieved experimentally by using a spark look-u
39、p table and independent control of the throttle angle and the fuel flow. Such a control system will be referred to as open loop control. When the engine state variables are measured in some way and fed back to control other engine variables (f. ex. control of stoichiometry) then this will be referre
40、d to as closed loop control. The concept time constant can refer only to a linear system described by a simultaneous set of linear differential equations with constant coefficients. In fact the time constants of a system are exactly determined from the constant coefficients of the differential equat
41、ions. If a system is nonlinear then the “time constants” vary with operating point or with time. A small signal time constant or response time for such a system is nevertheless a valid concept if it is considered only as a local (approximate) phenomenon. It will be used in this sense here. A time de
42、lay is distinct from a time constant and is the operation where a time varying signal is shifted backwards in time. It corresponds to a transport time. 3. MODELLING PHILOSOPHY: TIME SCALING In a mean value engine model there are two basic kinds of relationships between engine variables: instantaneou
43、s and time developing. The difference between the two types of relationships is the relative time scales on which the relevant subsystems respond physically. Instantaneous relationships are those in which equilibrium is established in the course of one or a few engine cycles. On the time scale in wh
44、ich the mean value model is to operate such relationships are instantaneous and can be expressed as algebraic equations. An example of such a process in an SI engine would be the control of the air mass flow past the throttle plate by the throttle angle and manifold pressure. This process reaches eq
45、uilibrium very rapidly, in the course of only one or two engine cycles: this can be written as an algebraic equation. A time developing relationship between engine variables is one which takes between about 10 and 1000 engine cycles to reach equilibrium. Such relationships are expressed by different
46、ial equations in a mean value engine model. One can point to the acceleration of the crank shaft against its inertial and frictional loads by the energy in the air and fuel mixture as an example of such a process. A mean value engine model can be constructed either by finding its instantaneous engin
47、e relationships first or its time developing (differential) equations first. In the case of four-cycle spark ignition engines it is the second approach which is easiest due to the large amount of literature which is already available on various engine subsystems. Some examples of such work were revi
48、ewed in the introduction of this paper. Given the differential equations, the algebraic equations for the fast engine processes must be derived. These relate the state variables (time developing variables) to the gross internal engine Figure 1. Schematic block diagram of a CFI engine. The different
49、physical components of the engine are indicated by the abbreviations. These are Tb (throttle body), Fi (fuel injector), Tp (throttle plate), Im (intake manifold), E (engine) Em (exhaust manifold), F (engine internal frictional losses) and L (load). The physical variables to be used to describe the dynamics of the engine are also placed on the diagram in their proper locations and are summarized in the section Nomenclature. The important dynamic engine subsystems are also indicated: 1. the fuel mass flow in the vapor, fv, and liquid phases, ff, 2. the cran