For several years, the guide line relating to the fuel-injection control in a Diesel Rail engine has been the realization of a micro-controller able to find on-line, i.e., in real time while the engine is in use, through an optimization process aimed at cutting down the fuel consumption and the polluting emissions, the best injection strategy associated with the load demand of the injection-driving drivers.
Map control systems are known for associating a fuel-injection strategy with the load demand of a driver which represents the best compromise between the following contrasting aims: maximization of the torque, minimization of the fuel consumption, reduction of the noise, and cut down of the NOx and of the carbonaceous particulate.
The characteristic of this control is that of associating a set of parameters (param1, . . . , paramn) to the driver demand which describe the best fuel-injection strategy according to the rotational speed of the driving shaft and of other components.
The analytical expression of this function is:(param1, . . . , paramn)=f(speed, driver demand)  (1)
The domain of the function in (1) is the size space ∞2 since the rotational speed and the driver demand can each take an infinite number of values. The quantization of the speed and driverDemand variables (M possible values for speed and P for driverDemand) allows one to transform the function in (1) (param1, . . . , paramn) into a set of n matrixes, called control maps.
Each matrix chooses, according to the driver demand (driverDemandp) and to the current speed value (speedm), one of the parameters of the corresponding optimal injection strategy (parami):{tilde over (f)}(i)m,p={tilde over (f)}(i)(speedm, driverp)=parami  (2)where i=1, . . . , n, m=1, . . . , M e p=1, . . . , P
The procedure for constructing the control maps initially consists of establishing map sizes, i.e., the number of rows and columns of the matrixes.
Subsequently, for each load level and for each speed value, the optimal injection strategy is determined, on the basis of experimental tests.
The above-described heuristic procedure has been applied to a specific test case: control of the Common Rail supply system with two fuel-injection strategies in a diesel engine, the characteristics of which are reported in FIG. 1. FIG. 2 shows a simple map-injection control scheme relating to the engine at issue. In the above-described injection control scheme, the real-time choice of the injection strategy occurs through a linear interpolation among the parameter values (param1, . . . , paramn) contained in the maps.
The map-injection control is a static, open control system. The system is static since the control maps are determined off-line through a non sophisticated processing of the data gathered during the experimental tests; the control maps do not provide an on-line update of the contained values.
The system, moreover, is open since the injection law, obtained by the interpolation of the matrix values among which the driver demand shows up, is not monitored, i.e., it is not verified that the NOx and carbonaceous particulate emissions, corresponding to the current injection law, do not exceed the predetermined safety levels, and whether or not the corresponding torque is close to the driver demand. The explanatory example of FIG. 3 represents a typical static and open map injection control.
A dynamic, closed map control is obtained by adding to the static, open system: a model providing some operation parameters of the engine when the considered injection strategy varies, a threshold set relative to the operation parameters, and finally a set of rules (possibly fuzzy rules) for updating the current injection law and/or the values contained in the control maps of the system.
FIG. 4 describes the block scheme of a traditional dynamic, closed, map control.
It is to be noted that a model of the combustion process in a Diesel engine often requires a simulation meeting a series of complex processes: the air motion in the cylinder, the atomization and vaporization of the fuel, the mixture of the two fluids (air and fuel), and the reaction kinetics, which regulate the premixed and diffusive steps of the combustion.
There are two classes of models: multidimensional models and thermodynamic models. The multidimensional models try to provide all the fluid dynamic details of the phenomena intervening in the cylinder of a Diesel, such as: motion equations of the air inside the cylinder, the evolution of the fuel and the interaction thereof with the air, the evaporation of the liquid particles, and the development of the chemical reactions responsible for the pollutants formation.
These models are based on the solution of fundamental equations of preservation of the energy with finite different schemes. Even if the computational power demanded by these models can be provided by today's calculators, we are still far from being able to implement these models on a micro-controller for an on-line optimization of the injection strategy of engine.
The thermodynamic models make use of the first principle of thermodynamics and of correlations of the empirical type for a physical but synthetic description of different processes implied in the combustion; for this reason these models are also called phenomenological. In a simpler approach, the fluid can be considered of spatially uniform composition, temperature and pressure, i.e. variable only with time (i.e. functions only of the crank angle). In this case, the model is referred to as “single area” model, whereas the “multi-area” ones take into account the space uneveness typical of the combustion of a Diesel engine.
In the case of a Diesel engine, as in general for internal combustion engines, the simplest way to simulate the combustion process is determining the law with which the burnt fuel fraction (Xb) varies.
The starting base for modelling the combustion process in an engine is the first principle of the thermodynamics applied to the gaseous system contained in the combustion chamber. In a first approximation, even if the combustion process is going on, the operation fluid can be considered homogeneous in composition, temperature and pressure, suitably choosing the relevant mean values of these values.
Neglecting the combustible mass that Q flows through the border surface of the chamber, the heat flow dissipated by the chemical combustion reactions
  (            ⅆ      Qb              ⅆ      θ        )is equal to the sum of the variation of internal energy of the system (dE/dθ), of the mechanical power exchanged with the outside by means of the piston (dL/dθ) and of the amount of heat which is lost in contact with the cooled walls of the chamber
      (                  ⅆ        Qr                    ⅆ        θ              )    ⁢      :  
                                          ⅆ            Qb                                ⅆ            θ                          =                                            ⅆ              E                                      ⅆ              θ                                +                                    ⅆ              L                                      ⅆ              θ                                +                                    ⅆ              Qr                                      ⅆ              θ                                                          (        3        )            
By approximating the fluid to a perfect gas of medium temperature equal to T, E=mcvT, wherefrom, in the absence of mass fluids, it results that:
                                          ⅆ            E                                ⅆ            θ                          =                  m          ⁢                                          ⁢                      c            v                    ⁢                                    ⅆ              T                                      ⅆ              θ                                                          (        4        )            
The power transferred to the piston is given by
                                          ⅆ            L                                ⅆ            θ                          =                  p          ⁢                                    ⅆ              V                                      ⅆ              θ                                                          (        5        )            
By finally exploiting the status equation, the temperature can be expressed as a function of p and V:
                    T        =                  pV          mR                                    (        6        )            
By differentiating this latter:
                                          ⅆ            T                                ⅆ            θ                          =                                            p              mR                        ⁢                                          ⅆ                V                                            ⅆ                θ                                              +                                    V              mR                        ⁢                                          ⅆ                p                                            ⅆ                θ                                                                        (        7        )            
By suitably mixing the previous expressions, the following expression is reached for the dissipation law of the heat:
                                          ⅆ            Qb                                ⅆ            θ                          =                                            [                                                                    c                    v                                    /                  R                                +                1                            ]                        ⁢            p            ⁢                                          ⅆ                V                                            ⅆ                θ                                              +                                    [                                                c                  v                                /                R                            ]                        ⁢            V            ⁢                                          ⅆ                p                                            ⅆ                θ                                              +                                    ⅆ              Qr                                      ⅆ              θ                                                          (        8        )            
By measuring the pressure cycle, being known the variation of the volume according to the crank angle and by using the status equation, it is possible to determine the trend of the medium temperature of the homogeneous fluid in the cylinder.
This is particularly useful in the models used for evaluating the losses of heat through the cooled walls
            ⅆ      Qr              ⅆ      θ        .
By finally substituting V(θ), p(θ) and
      ⅆ    Qr        ⅆ    θ  in the previous equation the dissipation law of the heat is obtained according to the crank angle
                    ⅆ        Q            ⁢                          ⁢      b              ⅆ      θ        .
The integral of
            ⅆ      Q        ⁢                  ⁢    b        ⅆ    θ  between θi and θf, combustion start and end angles, provides the amount of freed heat, almost equal to the product of the combustible mass mc multiplied by the lower calorific power Hi thereof.
                              Q          ⁢                                          ⁢          b                =                                            ∫                              θ                ⁢                                                                  ⁢                i                                            θ                ⁢                                                                  ⁢                f                                      ⁢                                                                                ⅆ                    Q                                    ⁢                                                                          ⁢                  b                                                  ⅆ                  θ                                            ⁢                                                          ⁢                              ⅆ                θ                                              ≅          mcHi                                    (        9        )            
This approximation contained within a few % depends on the degree of completeness of the oxidation reactions and on the accuracy of the energetic analysis of the process. Deriving with respect to θ the logarithm of both members of the previous equation, one obtains the law relating how the burnt combustible mass fraction xb (θ) varies.
                                          1                                                           Q                            ⁢                                                          ⁢              b                                ⁢                                          ⁢                                                    ⅆ                Q                            ⁢                                                          ⁢              b                                      ⅆ              θ                                      =                                            1                              m                c                                      ⁢                                                  ⁢                                          ⅆ                                  m                  c                                                            ⅆ                θ                                              =                                                                      ⅆ                                      x                    b                                                                    ⅆ                  θ                                            ⇒                                                                    ⅆ                    Q                                    ⁢                                                                          ⁢                  b                                                  ⅆ                  θ                                                      =                                          m                c                            ⁢              Hi              ⁢                                                          ⁢                                                ⅆ                                      x                    b                                                                    ⅆ                  θ                                                                                        (        10        )            
The combustible mass fraction xb (θ) has an S-like form being approximable with sufficient precision by an exponential function (Wiebe function) of the type:
                              x          ⁢                                          ⁢          b                =                  1          -                      exp            [                          -                                                a                  ⁡                                      (                                                                  θ                        -                        θⅈ                                                                                              θ                          ⁢                                                                                                          ⁢                          f                                                -                        θⅈ                                                              )                                                                    m                  +                  1                                                      ]                                              (        11        )            with a suitable choice of the parameters a and m. The parameter a, called efficiency parameter, measures the completeness of the combustion process. Also m, called form factor of the chamber, conditions the combustion speed. Typical values of a are chosen in the range [4.605; 6.908] and they correspond to a completeness of the combustion process for (θ=θf) comprised between 99% and 99.9% (i.e. xb ε[0.99; 0.999]). From FIGS. 8 and 9 it emerges that for low values of m the result is a high dissipation of heat in the starting step of the combustion (θ−θi<<θf−θi) to which a slow completion follows, whereas for high values of m the result is a high dissipation of heat in the final step of the combustion.
In synthesis, the simplest way to simulate the combustion process in a Diesel engine is to suppose that the law with which the burnt-fuel fraction xb varies is known. The xb can be determined either with points, on the basis of the processing of experimental surveys, or by the analytical via a Wiebe function. The analytical approach has several limits. First of all, it is necessary to determine the parameters describing the Wiebe function for different operation conditions of the engine. To this purpose, the efficiency parameter a is normally supposed to be constant (for example, by considering the combustion almost completed, it is supposed a=6.9) and the variations of the form factor m and of the combustion duration (θf−θi) are calculated by means of empirical correlations of the type:m=mr(τa,r/τa)0.5(p1/p1,r)(T1,r/T1)(nr/n)0.3θf−θi=(θf−θi)r(Φ/Φr)0.6(nr/n)0.5  (12)where the index r indicates the data relating to the reference conditions, p1 and T1 indicate the pressure and the temperature in the cylinder at the beginning of the compression and τa is the hangfire. An approach of this type covers however only a limited operation field of the engine and it often requires in any case a wide recourse to experimental data for the set-up of the Wiebe parameters. A second limit is that it is often impossible for a single Wiebe function to simultaneously take into account the premixed, diffusive step of the combustion. The dissipation curve of the heat of a Diesel engine is in fact the overlapping of two curves: one relating to the premixed step and the second relating to the diffusive step of the combustion. This limit of the analytic model with single Wiebe has been overcome with a “single area” model proposed by N. Watson:xb(θ)=βf1(θ, k1, k2)+(1−β)f2(θ, a2, m2)  (13)
In this model β represents the fuel fraction which burns in the premixed step in relation with the burnt total whereas f2(θ, a2, m2) and f1(θ, k1, k2) are functions corresponding to the diffusive and premixed step of the combustion. While f2(θ, a2, m2) is the typical Wiebe function characterized by the form parameters a2 and m2, the form Watson has find to be more reasonable for f1(θ, k1, k2) is the following:
                              f1          ⁡                      (                          θ              ,              k1              ,              k2                        )                          =                  1          -                                    [                              1                -                                                      (                                                                  θ                        -                                                  θ                          ⁢                                                                                                          ⁢                          i                                                                                                                      θ                          ⁢                                                                                                          ⁢                          f                                                -                                                  θ                          ⁢                                                                                                          ⁢                          i                                                                                      )                                    k1                                            ]                        k2                                              (        14        )            
Also in this approach, a large amount of experimental data is required for the set-up of the parameters (k1; k2; a2; m2) which characterize the xb (θ) in the various operating points of the engine.
Both the model with single Wiebe and that of Watson are often inadequate to describe the trend of xb in Diesel engines supplied with a multiple fuel injection. FIG. 10 reports the typical profile of an HRR relating to our test case: Diesel Common Rail engine supplied with a double fuel injection.
This HRR, acquired in a test room for a speed=2200 rpm and a double injection strategy (SOI; ON1; DW1; ON2)=(−22; 0.18; 0.8; 0.42), is in reality a medium HRR, since it is mediated on 100 cycles of pressure. Both in the figures and in the preceding relations, while the SOI parameters (Start of Injection) is measured in degrees of the crank angle, the parameters ON1 (duration of the first injection, i.e. duration of the “Pilot”), DW1 (dead time between the two injections, i.e. “Dwell time”) and ON2 (duration of the second injection, i.e. duration of the “Main”) are measured in milliseconds as schematized in FIG. 11.
From a first comparison between FIGS. 7 and 10, the absence or at least the non clear distinguishability is noted, in the case of the HRR relating to a double fuel injection, of a pre-mixed and diffusive step of the combustion. A more careful analysis suggests the presence, however, of two main steps in the described combustion process. These two steps are called “Pilot” and “Main” of the HRR. The first step develops between about −10 and −5 crank angle and it relates to the combustion primed by the “Pilot”.
The second one develops between about −5 and 60 crank angle and it relates to the combustion part primed by the “Main”. In each one of these two steps it is possible to single out different under-steps difficult to be traced to the classic scheme of the pre-mixed and diffusive step of the combustion process associated with a single fuel injection.
Moreover the presence of the “Pilot” step itself is not always ensured, and if it is present, it is not sure that it is clearly distinguished from the “Main” step. FIGS. 12 and 13 summarize what has been now exposed. From the figures it emerges that for small values of SOI, i.e. for a pronounced advance of the injection, it is not sure that the “Pilot” step of the combustion is primed.
In conclusion, the models used for establishing xb in a single injection Diesel engine are often inadequate to describe the combustion process in engines supplied with a multiple fuel injection.
When the number of injections increases, the profile of the HRR becomes more complicated. The characterizing parts of the combustion process increase, and the factors affecting the form and the presence itself thereof increase. Under these circumstances, a mode, which effectively establishes the xb trend, should first be flexible and general.
That is, it adapts itself to any multiple fuel-injection strategy, and thus to any form of the HRR. In second place, the model reconstructs the mean HRR, relating to a given engine point and to a given multiple injection strategy, with a low margin of error. In so doing, the model could be used for making the map injection control system closed and dynamic.
Therefore, a need has arisen for a virtual combustion sensor for a real-time feedback in an injection management system of a closed-loop type for an engine (closed loop EMS).
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