International Journal of Control Vol. 80, No. 11, November 2007, 1814–1847
Hybrid modelling of homogeneous charge compression ignition (HCCI) engine dynamics—a survey J. BENGTSSON{, P. STRANDH{, R. JOHANSSON*z, P. TUNESTA˚Lx and B. JOHANSSONx {Volvo Powertrain, Inc., PD, SE 40508, Gothenburg, Sweden zDept. Automatic Control, Lund University, PO Box 118, SE 221 00, Lund, Sweden xDiv. Combustion Engines, Lund University, PO Box 118, SE-211 00, Lund, Sweden (Received 7 February 2007; in final form 31 May 2007) The Homogeneous charge compression ignition (HCCI) principle holds promise to increase efficiency and to reduce emissions from internal combustion engines. As HCCI combustion lacks direct ignition timing control and auto-ignition depends on the operating condition, control of auto-ignition is necessary. Since auto-ignition of a homogeneous mixture is very sensitive to operating conditions, a fast combustion phasing control is necessary for reliable operation. To this purpose, HCCI modelling and model-based control with experimental validation were studied. A six-cylinder heavy-duty HCCI engine was controlled on a cycle-to-cycle basis in real time using a variety of sensors, actuators and control structures for control of the HCCI combustion. Combustion phasing control based on ion current was compared to feedback control based on cylinder pressure. With several actuators for controlling HCCI engines suggested, two actuators were compared, dual fuel and variable valve actuation (VVA). Model-based control synthesis requiring dynamic models of low complexity and HCCI combustion models were estimated by system identification and by physical modelling, the physical models aiming at describing the major thermodynamic and chemical interactions in the course of an engine stroke and their influence on combustion phasing. The models identified by system identification were used to design modelpredictive control (MPC) with several desirable features and today applicable to relatively fast systems, the MPC control results being compared to PID control results. Both control of the combustion phasing and control of load-torque with simultaneous minimization of the fuel consumption and emissions, while satisfying the constraints on cylinder pressure, were included.
Nomenclature crank angle 50 crank angle of 50% burnt fuel ref 50 reference value for crank angle of 50% burnt fuel IVC crank angle at inlet valve closing n engine speed
*Corresponding author. Email:
[email protected]
Rf Tin Wf BDC CAD CAI EGR
International Journal of Control ISSN 0020–7179 print/ISSN 1366–5820 online ß 2007 Taylor & Francis http://www.tandf.co.uk/journals DOI: 10.1080/00207170701484869
dual-fuel ratio inlet temperature injected fuel energy the air/fuel ratio ( ¼ 1 represents stoichiometric air/fuel ratio) fuel/air equivalence ratio ( ¼ 1=) crank angle bottom dead centre crank angle degree controlled auto-ignition exhaust gas recirculation
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Modelling of HCCI engine dynamics—a survey
1. Introduction The motivation for studying the homogeneous charge compression ignition (HCCI) engine principle is the promise of low levels of exhaust emissions with regards to NOx, while still retaining an acceptable overall efficiency (Christensen et al. 1999). Pioneering efforts towards this new engine principle, also called controlled auto-ignition (CAI), were reported in Onishi et al. (1979), Stockinger et al. (1992), Christensen et al. (1997), Fieweger et al. (1997) and Hultqvist et al. (1997). Depending on the purpose, modelling of HCCI engine dynamics may exhibit different complexity and format such as multi-zone models including chemical kinetics to simulate engine operation in a large operating range (Aceves et al. 2000), . multidimensional CFD for optimization of fuel injection and combustion chamber design, . single-zone reduced-order dynamic models (for model-based control). .
A significant challenge with HCCI is the control of the combustion phasing, this is essential in order to control the load, to obtain low fuel consumption and emissions (Zhao 2003). For closed-loop control of the combustion phasing, feedback signals are necessary and in-cylinder pressure feedback is, perhaps, the most straightforward approach. In practice, the crank angle of 50% burnt fuel (CA50 or 50 ) has proved to be a reliable indicator of on-going combustion (Olsson et al. 2001, Bengtsson et al. 2004b). In closed-loop control of an HCCI engine, several means to actuate the combustion phasing have been tested, e.g., dual fuels (Olsson et al. 2001), variable valve actuation (VVA) (figure 1) (Agrell et al. 2003, Bengtsson et al. 2006c), variable compression ratio (Christensen et al. 1999, Haraldsson et al. 2003),
18 16 14 a50 [CAD]
EVC exhaust valve close EVO exhaust valve open FuelMEP mean effective pressure calculated from the quantity of fuel injected IMEPn the net indicated mean effective pressure IVC inlet valve close IVO inlet valve open LQG linear quadratic gaussian MPC model predictive control PRBS pseudo random binary sequence SMI system modelling and identification TDC top dead centre position VVA variable valve actuation VVT variable valve timing
12 10 8 6 4 2 0 500
520
540
560
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qIVC [CAD]
Figure 1. The effect of IVC changes on 50 at steady-state. The CAD was calculated from the combustion TDC.
and thermal management (Martinez-Frias et al. 2000, Haraldsson et al. 2004). For control design purposes appropriate models and system variables useful for feedback control are needed. Previously, it was shown that physical modelling and system identification can be used to obtain lowcomplexity models of the HCCI dynamics (Strandh et al. 2003, Bengtsson et al. 2004c, Shaver et al. 2004, Gatowski et al. 1984). For closed-loop HCCI engine operation, it was reported that the combustion phasing can be stabilized by means of a PID controller (Olsson et al. 2001); LQG control (Strandh et al. 2003); and MPC control (Bengtsson et al. 2006c). A fast and robust control of 50 appears to be necessary in order to stabilize HCCI engine control. It is also desirable that the load, peak cylinder pressure, peak rate of cylinder pressure and emissions are controlled simultaneously. This is a multi-input multi-output (MIMO) control problem where the controller has to be able to handle constraints on several variables. In a comparison among several control methods, it will be demonstrated that model predictive control (MPC) could be used with favourable properties (Bemporad et al. 2002, Maciejowski 2002). All of the actuators suggested have control constraints and MPC has the benefit of explicitly taking the constraints into account. Whereas monitoring of 50 or other methods to sense on-going combustion for feedback control of an HCCI engine all rely on pressure sensors, these sensors may be expensive. One candidate to replace pressure sensors is the use of electronic conductive properties for the reaction zone (Gillbrand et al. 1987). This phenomenon is called ion current for which no expensive sensor is needed. Ion current has been successfully used in closed-loop control of SI engines (Eriksson et al. 1997). The basic principle of ion current sensing is that
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a voltage is applied over an electrode gap inserted into the gas volume (combustion chamber) (Gillbrand et al. 1987). The common belief so far has been that ion current levels are not measurable for the highly diluted HCCI combustion. However, a recent study shows that it is not the dilution level in itself but the actual fuel/air equivalence ratio which is an important factor for the signal level (Franke 2002, Strandh et al. 2003). In this paper, we will report modelling and experimental results on HCCI control of a six-cylinder heavy-duty engine, evaluating a variety of control methods (MPC and PID) and actuators (VVA, dual fuel), and experimental results on HCCI control of a singlecylinder heavy-duty engine evaluating a variety of sensors (in-cylinder pressure, ion current). The purpose of this paper is to provide a survey of state-of-the-art HCCI engine modelling with particular attention to control-oriented modelling. The structure of the paper is the following. An overview of HCCI modelling approaches is given in x 2 with particular emphasis on modelling suitable for model-based control, followed by a model-based control description in x 3.1. The experimental set-ups are described in x 3. The result of the sensor, actuator and control evaluation is presented in x 4. The results are discussed in x 5. Finally, conclusions are stated in x 6.
2. HCCI modelling There are two often used methods to obtain models of HCCI engine dynamics suitable for control; physical modelling (Shaver et al. 2004, Egeland and Gravdahl 2002) and modelling by means of system identification (Bengtsson et al. 2004b, 2006b). Physical modelling based on conservation laws and chemical kinetics has attractive intuitive component-based features but suffers from complexity issues with adverse effects in application. Whereas system identification has proved to be a very effective modelling tool for prototyping, it may provide results hard to interpret from a physical point of of view. The purpose of modelling has an obvious influence on focus and the complexity of modelling (Bengtsson et al. 2004b, 2006b). As modelling and simulation may easily become too detailed and computationally expensive to serve purposes of model-based control, low-complexity models and reduced-order models become relevant. A minimum requirement of physical modelling is explanation of the nature of the in-cylinder pressure traces (cf. figures 2 and 3) where adiabatic compression combines with fuel-dependent auto-ignition (Gavillet et al. 1993, Oppenheim et al. 1996, 2004, Bitar et al. 2006). In previous work, modelling choices involve
aspects of chemical kinetics, cycle-to-cycle coupling, in-cylinder concentrations of reactants, wall temperature dynamics, pressure dynamics, and auto-ignition timing (Flowers et al. 2000). Modelling details fall into categories of single-zone model, multi-zone models, multidimensional computational fluid dynamics (CFD) models, sometimes combined with exosystem simulation on the form of stochastic disturbances, load modelling, sensor modelling. Both physical aspects and operational aspects require attention. Shaver et al. (2005) singled out six distinct stages in modelling of HCCI engine operation, i.e., induction, compression, combustion, expansion, exhaust and residence in the exhaust manifold. As for stable operation, combustion phasing control design requires appropriate models and system output variables usable for feedback control. Recently, mode-transition operation and control of Diesel–HCCI and SI–HCCI engines and other hybrid control aspects have received attention (Shaver 2006b). 2.1 Fuel modelling The necessity of developing a practical iso-octane mechanism for HCCI engines was presented after various different experiments and currently available mechanisms for iso-octane oxidation being reviewed and the performance of these mechanisms applied to experiments relevant to HCCI engines being analysed (Semenov 1934, Jia and Xie 2006). A skeletal mechanism including 38 species and 69 reactions was developed, which could predict satisfactorily ignition timing, burn rate and the emissions of HC, CO and NOx for HCCI multi-dimensional modelling (Jia and Xie 2006). Comparisons with various experiment data including shock tube, rapid compression machine, jet stirred reactor and HCCI engine indicate good performance of this mechanism over wide ranges of temperature, pressure and equivalence ratio, especially at high pressure and lean equivalence ratio conditions. By applying the skeletal mechanism to a single-zone model of an HCCI engine, it was found that the results were substantially identical with those from the detailed mechanism developed by Curran et al. (2002) but the computing time was reduced greatly (Jia and Xie 2006). A model for the auto-ignition of hydrocarbons applicable to 3D internal combustion engine calculations was proposed (Colin et al. 2005). The limits of classical methods using an auto-ignition delay are investigated when cool flame phenomena are present. A method based on tabulated reaction rates was presented to capture the early heat release induced by low temperature combustion. Cool flame ignition delay when present and cool flame fuel consumption are also
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Modelling of HCCI engine dynamics—a survey 7
× 106
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Figure 2. Pressure trace (left), temperature trace (middle), and heat release (right) from experiment at Tin ¼ 373 K, Qin ¼ 1400 J, n ¼ 1200 rpm (solid) and n ¼ 1500 rpm (dashed).
tabulated. The reaction rate, fuel consumption, and cool flame ignition delay tables were built a priori from complex chemistry calculations. The reaction rates, which directly depend on instantaneous changes of thermodynamic conditions, were then integrated during the 3D engine calculation. The model is first validated through comparisons with complex chemistry calculations in constant and variable volume configurations where good agreement was found. The model was applied both to a Diesel computation with spray injection and residual gases, and to a Diesel-HCCI configuration. Comparisons with experimental results showed that the auto-ignition essential features were well reproduced in these cases (Colin et al. 2005). The combination of CFD computations with detailed chemistry leads to excessive computation times, and is not achievable with current computer capabilities. A reduced chemical model for n-heptane is described,
in view of its implementation into a CFD simulation code (Maroteaux and Noel 2006). Firstly, the reduction process to get to the 61-step mechanism is detailed and then the 26-step mechanism is described; this further reduction is carried out under various conditions that include a range of interest in engine applications. Validation work in reference to the original detailed mechanism and two reduced mechanisms was published in the literature, focusing on the prediction of ignition delay times under constant as well as variable volume conditions (Maroteaux and Noel 2006). A good and accurate reproduction of both ignition delay times and heat release was reported to be reached with the 26-step model (Maroteaux and Noel 2006). Despite the rapid combustion typically experienced in HCCI, components in fuel mixtures do not ignite in unison or burn equally (Wasnatz et al. 2001).
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J. Bengtsson et al. × 106 1600 7 1400 6 1200 1000 4
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Figure 3. Pressure trace (left), temperature trace (middle), and heat release (right) of simulation at nominal conditions, Tin ¼ 373 K, Qin ¼ 1400 J, n ¼ 1200 rpm for PRF90 fuel.
In experiments and modelling of blends of diethyl ether (DEE) and ethanol, the DEE led combustion and proceeded further toward completion, as indicated by 14 C isotope tracing (Mack et al. 2005). A numerical model of HCCI combustion of DEE and ethanol mixtures supports the isotopic findings. Although both approaches lacked information on incompletely combusted intermediates plentiful in HCCI emissions, the numerical model and 14 C tracing data agreed within the limitations of the single-zone model. Despite the fact that DEE is more reactive than ethanol in HCCI engines, they were sufficiently similar and prevented incidence of a large elongation of energy release or significant reduction in inlet temperature required for light-off, both desired effects for the combustion event. This finding suggests that, in general, HCCI combustion of fuel blends
may have preferential combustion of the blend components (Mack et al. 2005).
some
of
2.2 Auto-ignition modelling Whereas HCCI engines have been shown to have higher thermal efficiencies and lower NOx and soot emissions than spark ignition engines, the HCCI engines experience very large heat release rates which can cause too rapid an increase in pressure. One method of reducing the maximum heat release rate is to introduce thermal inhomogeneities, thereby spreading the heat release over several crank angle degrees (Sjo¨berg and Dec 2004a). Direct numerical simulations (DNS) showed that both ignition fronts and deflagration-like fronts may be present in systems with such inhomogeneities (Cook et al. 2007). Here, an enthalpy-based flamelet
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Modelling of HCCI engine dynamics—a survey model was presented and applied to four cases of varying initial temperature variance. This model used a mean scalar dissipation rate to model mixing between regions of higher and lower enthalpies. The predicted heat release rates agree well with the heat release rates of the four DNS cases. The model was shown to be capable of capturing the combustion characteristics for the case in which combustion occurs primarily in the form of spontaneous ignition fronts, for the case dominated by deflagration-type burning, and for the mixed mode cases. The enthalpy-based flamelet model shows considerably improved agreement with the DNS results over the popular multi-zone model, particularly, where both deflagrative and spontaneous ignition are occurring, that is, where diffusive transport is important (Cook et al. 2007). Another fuel model is the Shell model used for auto-ignition below (Halstead et al. 1977). Further contributions on auto-ignition modelling can be found in (Sankarana et al. 2005). 2.3 Thermal modelling and auto-ignition HCCI combustion is often achieved without a completely homogeneous mixture. In order to derive a control-relevant model, however, we might firstly proceed by assuming that the mixture is homogeneous, thus allowing a single-zone cylinder model (Bengtsson et al. 2004a). Such assumptions may be justified by laser-diagnostic measurements in our experimental set-up (Richter et al. 2000). To reproduce the effects relevant for combustion phasing control it is required that the auto-ignition model captures the effects on ignition delay (induction time) of varying species concentrations, temperature trace, and fuel quality. Several alternative approaches are possible for modelling the instant of auto-ignition for fuels. High-complexity models, e.g., primary reference fuels (PRF), 857 species, 3,606 reactions, CHEMKIN/ LLNL (Sjo¨berg and Dec 2003)—have been used to model complete combustion. In addition to ignition prediction, such models are also aimed at describing intermediate species and end product composition. Reduced chemical kinetics models, e.g., PRF fuels, 32 species, 55 reactions, CHEMKIN (Tanaka et al. 2003), have also been proposed, where reactions with little influence on the combustion have been identified and removed. For simulation of multi-cycle scenarios it is necessary to keep the model complexity low in order to arrive at reasonable simulation times. An attractive and widespread alternative is to use the Shell model (Halstead et al. 1977), which is a lumped chemical kinetics model using only five representative species in eight generic reactions. This model is aimed at prediction of auto-ignition rather than describing the complete
combustion process. Compression ignition delay may also be described by empirical correlations, such as the knock integral condition Z ti dt ¼ 1, ð1Þ t¼0 where ti is the instant of ignition and is the estimated ignition time (ignition delay) at the instantaneous pressure and temperature conditions at time t, often described by Arrhenius type expressions (Heywood 1988). A drawback is that dependence on species concentrations is normally not regarded. An integral condition with concentration dependence was used in (Shaver et al. 2003, 2004) in a similar study for propane fuel, where also auto-ignition models based on very simple reaction mechanisms were evaluated. Alternatives to physical or physics-based models are to use system identification to obtain models or to use empirical look-up tables. The latter gives insufficient physical insight, and require substantial efforts to calibrate. In this work, the Shell model was chosen to describe the process of auto-ignition. A static model is then used to describe the major part of the actual combustion and corresponding heat release. The result from the Shell model was compared to results from an integrated Arrhenius rate threshold model and the planet mechanism model (Amne´us 2002, Ahmed 2003). To the purpose of detailed treatise, modelling of the cylinder, auto-ignition, integrated Arrhenius threshold, combustion, and heat transfer are now provided. 2.3.1 Cylinder gas model—first law of thermodynamics. The cylinder gas dynamics are described by conservation laws such as the the first law of thermodynamics cv cv QHR ¼ 1 þ p dV þ V dp þ QHT , R R
ð2Þ
where p is the cylinder pressure, V the volume, Ru the universal gas constant, cv ¼ cp Ru the specific heat capacity, and n the molar substance amount contained in the cylinder. The time derivatives of QHR and QHT denote rates of heat released by the combustion process and heat flowing from the wall, respectively. 2.3.2 Gas properties. The gas is described as a mixture of dry air and fuel, and the combustion products are nitrogen, carbondioxide and water. Specific heat for each species i is described by NASA polynomial approximations of JANAF data cp,i ðT Þ ¼
5 Ru X ai, j T j3 , Mi j¼1
ð3Þ
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where Mi is the molar mass of species i and T is the cylinder temperature. The mixture specific heat is then cp ðT Þ ¼
1X ni Mi cp,i ðT Þ, n i
k
p R ! R þ products and heat
f1 kp
R ! R þ B f k
ðinitiationÞ
ðpropagation forming BÞ
f k
3 p R ! out ðlinear terminationÞ
f k
4 p R ! R þ Q ðpropagation forming QÞ
kt
2R ! out ðquadratic terminationÞ kb B ! 2R
ðdegenerate branchingÞ:
ð7Þ ð8Þ ð9Þ ð10Þ ð11Þ ð12Þ
Auto-ignition is described by integrating the time variations of species concentrations from the beginning of the compression stroke d ½R 2 f3 kp ½R ¼ 2 kq ½RH½O2 þ kb ½B kt ½R dt
ð13Þ
d ½B þ f2 kp ½Q½R kb ½B ¼ f1 kp ½R dt
ð14Þ
d ½Q f2 kp ½Q½R ¼ f4 kp ½R dt d ½O2 ¼ gkp ½R: dt
kp ¼
1 1 1 1 þ þ : kp,1 ½O2 kp,2 kp,1 ½RH
ð18Þ
To capture dependence of induction periods on fuel and air concentrations the terms f1, f2, f3, and f4 are expressed as fi ¼ fi ½O2 xi ½RHyi :
ð5Þ
ðpropagation cycleÞ ð6Þ
ðpropagation forming BÞ
2 p R þ Q ! R þ B
ð17Þ
where q is the exothermicity per cycle for the regarded fuel. The propagation rate coefficient is described as
2.3.3 Shell auto-ignition model. The Shell auto-ignition model for hydrocarbon fuels (Halstead et al. 1977), CaHb, is based on a general eight-step chain-branching reaction scheme with lumped species: the hydrocarbon intermediate species Q, and the fuel RH, radicals R, chain branching agent B. kq
dQHR ¼ kp qV ½R, dt
ð4Þ
where ni is the mole of species i.
RH þ O2 ! 2R
with oxygen consumption g ¼ 2½að1 Þ þ b=4=b mole per cycle. The heat release from combustion is given by
ð19Þ
Rate coefficients and rate parameters ki and fi are then described by Arrhenius rate coefficients
Ei ki ¼ Ai exp , Ru T
fi
Ei ¼ Ai exp Ru T
ð20Þ
We use the acronym FuelMEP to denote the mean effective pressure calculated from the quantity of fuel injected. Calibrated parameters for a number of fuels, including a set of primary reference fuels (PRF), are found in the literature (Halstead et al. 1977). PRFx is a mixture of n-heptane and iso-octane, where the octane number x is defined as the volume percentage of iso-octane. Parameters for PRF90 were used in the simulations. Auto-ignition was defined as the crank angle where the explosive phase of combustion starts. 2.3.4 Integrated Arrhenius rate threshold. The Arrhenius form can be used to determine the rate coefficient describing a single-step reaction between two molecules Turns (1996). The single-step rate integral condition is based on the knock integral with Z
1= d=w
Kth ¼
ð21Þ
IVC
ð15Þ 1= ¼ A expðEa =ðRu T ÞÞ½Fuela ½O2 b , ð16Þ
Q, and B are not considered in thermoThe species R, dynamic computations for the gas mixture. The stoichiometry is approximated by assuming a constant CO=CO2 ratio, , for the complete combustion process,
ð22Þ
where is the crank angle and IVC is the crank angle of the inlet valve closure. The integral condition describes a generalized reaction of fuel and oxygen and this is an extreme simplification of the large number of reactions that take place during combustion. The empirical parameters A, Ea, a, b and Kth are determined
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Modelling of HCCI engine dynamics—a survey from experiments. Values for n-heptane and iso-octane from Turns (1996) were used in the comparison below with A ¼ 4:65 1011 , Ea ¼ 15:1, a ¼ 0.25, b ¼ 1.5, K ¼ 1:6 105 (figures 3 and 4). Auto-ignition was defined as the crank angle where the integral condition has reached the threshold Kth. 2.3.5 Combustion. When auto-ignition is detected by the Shell model or the integrated Arrhenius rate threshold, the completion of combustion is described by a Wiebe function (Wiebe 1970). "
# 0 mþ1 xb ðÞ ¼ 1 exp a ,
2.3.6 Heat transfer. Heat is transfered by convection and radiation between in-cylinder gases and cylinder head, valves, cylinder walls, and piston during the engine cycle. In this case the radiation is neglected. This problem is very complex, but a standard solution is to use the Newton law for external heat transfer dQW ¼ hc AW ðT TW Þ, dt
where QW is the heat transfer by conduction, AW the wall area, TW the wall temperature, and the heat-transfer coefficient hc given by the Nusselt–Reynold relation by Woschni (1967)
ð23Þ
where xb denotes the mass fraction burnt, is the crank angle, 0 start of combustion, is the total duration, and a and m adjustable parameters that fix the shape of the curve. The heat release is computed from the rate of xb and the higher heating value of the fuel.
ð24Þ
hc ¼ 3:26B0:2 p0:8 T0:55 ð2:28Sp Þ0:8 ;
ð25Þ
where Sp is the mean piston speed and B is the bore. 2.3.7 Experiments. In the experiments, the fuel ratio, Rf, of the dual fuels ethanol and n-heptane, fuel energy per cycle, Win, inlet air temperature, Tin, and the
100
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0 q [°]
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Figure 4. Concentrations of gas species from Shell model ignition dynamics for nominal conditions, Tin ¼ 373 K, Qin ¼ 1400 J, n ¼ 1200 rpm for PRF90 fuel.
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J. Bengtsson et al. Table 1.
Tin ð8CÞ n (rpm) Win (J) Rf (vol%)
100–115 1200 1400 0.93
Experimental conditions. 100 1000–1500 1400 0.93
100 1200 1000–1500 0.93
100 1200 1400 0.892–1.0
engine speed, n, were changed according to table 1. By changing the injected fuel energy per cycle the load is changed and Win ¼ 1000 J/cycle corresponds to a FuelMEP of 5 bar and Win ¼ 1500 J/cycle corresponds to a FuelMEP of 7.5 bar, i.e., with a rate of 200 J/bar. As the engine was naturally aspirated this corresponds to a variation of , the air/fuel ratio, in the range 6.2 to 4.1. Only low load experiments in open loop were performed, when the engine temperature was at steady state. At each operating point, data of 500 cycles were collected. The mean value of these 500 cycles was thereafter used in comparison with the result from the model. 2.3.8 System identification. Whereas several system identification methods for estimating linear models and model representations exist (Johansson 1993), only results from subspace-based methods are presented here. The subspace-based method used was the MOESP of the SMI Toolbox for Matlab (Haverkamp and Verhaegen 1997). The estimated models were on discrete-time state-space form. The subspace-based methods also calculate Kalman filters for the estimated models. As two different actuators for controlling the combustion phasing are compared in this paper, dynamic HCCI models are required where either of these two different control signals was used as input. An HCCI engine is a MIMO system. To the purpose of combustion-phasing control, the system can be reduced to a SISO system where the input was either Rf or IVC and the output was 50 . For multivariable control, MIMO models where the inputs were Rf or IVC , and Tin, Win, n and the outputs 50 , IMEPn and dp=d were estimated. The experiments were performed in open-loop control and at low load. System identification models were used for the MPC control design. In order to have persistent excitation, the two different inputs Rf and IVC were excited by a PRBS signal. The variable geometry turbo was tuned to a low boost pressure. Offsets were removed from all of the data. 2.4 EGR modelling Karagiorgis et al. (2006a) studied exhaust gas recirculation (EGR) modelling relevant for HCCI
engine dynamics. Experiments were performed for the oxidation of mixtures of n-heptane and iso-octane and of n-heptane and toluene in a jet-stirred reactor (JSR) under dilute conditions, at 10 atm. The effect of the addition of variable initial NO concentration was also studied. A detailed kinetic model was performed to rationalize the results. Experiments were also performed using an HCCI engine to characterize the effect of EGR rates (from 0 to 500 ppmv) on ignition delays at low and high temperatures for an equivalence ratio of ¼ 0.3 ( ¼ 3.33) and a constant intake temperature of 350 K. Two surrogate automotive fuels (n-heptane/iso-octane, n-heptane/toluene) were used and compared to the pure n-heptane case. Zero-dimensional single zone modelling was also performed using the detailed kinetic scheme and compared to the experimental results in terms of cool and principal flames ignition delays, phasing time and also the importance of the cool flame combustion heat release in comparison to the main one (Dubreuil et al. 2007). Based on thermodynamics, gas exchange and heat transfer modelling, Karagiorgis provided a simple control-oriented model to predict pressures and temperatures in the HCCI engine cycle (Karagiorgis et al. 2006a, b). A common belief is that EGR permits late combustion with favourable properties such as lower pressure, pressure gradients, noise, and NOx emissions. Whereas this may be a true property without feedback control, the conclusion may need a significant revision for closed-loop operation. Olsson et al. (2003) showed that for accurate and feedback-stabilized CA50-control, there is no significant improvement of high EGR as compared to lean operation. 2.5 Lean combustion ion sensing Whereas in-cylinder ion sensing and techniques for measuring ion currents in flames has been known for a long time (Clements and Smy 1976, Gillbrand et al. 1987), ion sensing of HCCI combustion was long overlooked, the common belief being that ion current levels are not measurable for the highly diluted HCCI combustion. A recent study showed, however, that it is not the dilution level per se but the actual fuel/air equivalence ratio which is an important factor for the signal level (Strandh et al. 2003). The basic principle of ion current sensing is that a small voltage is applied over an electrode gap inserted to the actual gas volume (combustion chamber). In a non reacting charge, no ion current through the gap will be present. As the ion current signal may provide information on the HCCI combustion, the phenomenon may be considered for monitoring of auto-ignition. The aim of this research is to show that a measurable ion current exists even in the very lean
Modelling of HCCI engine dynamics—a survey combustion (equivalence ratio ¼ 0:35, ¼ 2.85) in an HCCI engine. Numerical models using detailed chemical kinetics for propane combustion, including kinetics for ion formation, support the experimental findings. The effects of the equivalence ratio, the intake mixture temperature, and the applied bias voltage on the ion signal are studied through a series of experiments. The findings are compared to the numerical model results. The research shows that an inexpensive ion sensor may replace the expensive pressure transducers currently used in HCCI engines. The ion current signal is very sensitive to the equivalence ratio of the intake fuel-air mixture. 2.6 Temperature modelling To characterize the ignition process in HCCI engines, high fidelity simulations were performed to study the effects of different initial temperature distributions on the auto-ignition of a turbulent homogeneous mixture at high pressure in a close volume vessel using a twodimensional direct numerical simulation (DNS) method (Sankarana et al. 2005). The effects of the initial temperature distribution on the ignition and subsequent heat release were studied by comparison of simulations with three initial random temperature fields having different skewness. It was found that the scalar mixing and turbulence have a significant influence on the initial location and further evolution of the ignition kernels. A comparison of the integrated heat release rates shows that the presence of a hot core leads to early ignition, while a cold core leads to a dormant end gas, which is consumed by slow combustion. The extent of flame fronts is quantified by a temperature gradient cut-off, revealing distinct behaviour in the appearance of flame fronts for the three cases. Finally, two distinct ignition regimes, namely the spontaneous propagation and the deflagration regimes, were identified, and a predictive criterion was defined based on the spontaneous propagation speed and deflagration speed at the local mixture conditions. It should be pointed out that DNS in the near future would not be applicable to three dimensional real engine simulations due to the extremely high demand on the grid resolution. A more feasible approach that can capture the temperature inhomogeneity and ignition kernel structure in 3-D real engines is the large eddy simulation (LES) approach (Richard et al. 2007, Yu et al. 2007). In a recent LES study of ethanol/air HCCI combustion in an optical engine (Yu et al. 2007), it was found that the temperature distribution prior to the onset of auto-ignition could be adequately simulated and the high sensitivity of in-cylinder pressure to the initial temperature distribution and piston geometry could be predicted successfully by the LES approach. The predictions
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were found to be consistent with the observed results, suggesting a potential strategy in the modelling of HCCI combustion process (Sankarana et al. 2005, Richard et al. 2007, Yu et al. 2007). 2.7 Emissions modelling Homogeneous-charge compression ignition (HCCI) engines have been shown to have higher thermal efficiencies and lower NOx and soot emissions than spark ignition engines. However, HCCI engines experience very large heat release rates which can cause too rapid an increase in pressure. One method of reducing the maximum heat release rate is to introduce thermal inhomogeneities, thereby spreading the heat release over several crank angle degrees. Cook et al. (2007) showed that both ignition fronts and deflagration-like fronts may be present in systems with such inhomogeneities. An enthalpy-based flamelet model was applied to the four cases of varying initial temperature variance. This model uses a mean scalar dissipation rate to model mixing between regions of higher and lower enthalpies. The predicted heat release rates agree well with the heat release rates of the four DNS cases. The model is shown to be capable of capturing the combustion characteristics for the case in which combustion occurs primarily in the form of spontaneous ignition fronts, for the case dominated by deflagrationtype burning, and for the mixed mode cases. The enthalpy-based flamelet model shows considerably improved agreement with the DNS results over the popular multi-zone model, particularly, where both deflagrative and spontaneous ignition are occurring, that is, where diffusive transport is important (Cook et al. 2007). Bhave et al. (2006) and Su et al. (2006) provided a multi-zone model with particular attention to CO modelling, using down-sampling techniques to reduce computational time. In the limit of homogeneous reactants and adiabatic combustion, ignition timing and pollutant emissions in HCCI engines would be solely governed by chemical kinetics. As one moves away from this idealization, turbulence and turbulence/chemistry interactions (TCI) play increasingly important roles. Here, the influence of TCI on auto-ignition and emissions of CO and unburned hydrocarbon (HC) is examined using a three-dimensional time-dependent computational fluid dynamics (CFD) model that includes detailed chemical kinetics. TCI is accounted for using a transported probability density function (PDF) method: the joint PDF of 40 chemical species and mixture enthalpy is considered. The modelled joint PDF equation is solved using a consistent hybrid particle/finite-volume method. Variations in global equivalence ratio,
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wall temperature, swirl level, degree of mixture inhomogeneity (premixed versus direct injection, and start-of-injection timing for direct-injection cases), and a top-ring-land crevice (TRLC) are investigated. For low-swirl nearly homogeneous conditions and no TRLC, TCI has little effect on ignition timing; however, even in that case the influence of TCI on emissions is not negligible. With increasing swirl, higher degrees of mixture inhomogeneity, and for cases that include a TRLC, TCI effects become increasingly important and result in significant changes in ignition timing and emissions. Unburned fuel is a non-negligible contribution to UHC for high swirl and in cases where a TRLC is considered. In addition to providing new insight into HCCI combustion processes, this work also demonstrates the feasibility of bringing transported PDF methods to support modelling of geometrically complex three-dimensional time-dependent turbulent combustion system (Zhang et al. 2005). Through numerical modelling, the N2O mechanism is shown to be the significant source of nitrogen oxides (NOx) generation in HCCI combustion (Strandh et al. 2003, Mehresh et al. 2005). Further contributions on emissions can be found in (Sjo¨berg and Dec 2003, 2004a, b).
2.8 Modelling for control An important goal of control-oriented modelling is to accurately predict the phasing of HCCI combustion for a single cylinder research engine using variable valve actuation (VVA). To this purpose, three simple single-zone models were developed and compared with experiments Shaver et al. (2003). The difference between the three modelling approaches centered around the combustion chemistry mechanism used in each. The first modelling approach, which utilized a temperature threshold to model the onset of the combustion reaction, did not work well. However, an integrated reaction rate threshold accounting for both the temperature and concentration did correlate well with experiment. Additionally, another model utilizing a simple two-step kinetic mechanism also showed good correlation with experimental combustion phasing Shaver et al. (2003). Shaver et al. (2006) considered a framework for developing control models to partition the engine cycle into four stages (1) mixing of reactant and re-inducted product gases during a constant pressure, adiabatic induction process (2) isentropic compression (3) constant volume combustion to major products (4) isentropic expansion
The re-inducted product temperature is directly related to the exhaust temperature from the previous cycle. The first model input is the inducted gas composition. The inducted gas composition is formulated as the ratio of the moles of re-inducted product Np to the moles of inducted reactant charge Nr, ¼ Np =Nr . The second model input is the IVC valve timing, which dictates the volume, V1 ¼ VðÞ, between the induction and compression stages, determining start of compression and therefore the effective compression ratio. Model outputs are the peak pressure, P, and the volume at the constant volume combustion event, V23 ¼ Vð23 Þ, which acts as a proxy for combustion timing. By linking the thermodynamic states of the system together, a dynamic model of peak pressure, P, and combustion timing, 23 , for residual-affected HCCI is formulated. Note that at points between stages, the cylinder volume is either known or is a model output as is the case for V23 ¼ Vð23 Þ. The modelling techniques are applied to propane-fueled HCCI. Other fuels also apply by making appropriate changes to the fuel-specific model constants. In their first model, the simplest of the three, a temperature threshold is used to model the onset of combustion Shaver et al. (2003). This approach shows poor correlation with experiment, failing to capture the dependence of combustion timing on concentration. In the second model, a two step mechanism implementing a series of Arrhenius reaction rates is used. Good correlation with experiment with respect to phasing is found, with slight discrepancy in pressure at the initiation of combustion. The third model implemented elements from the other two models through the use of an integrated Arrhenius rate as a threshold value. This approach showed good correlation with experiment with a slight discrepancy as combustion completes Shaver et al. (2003). Control-oriented reduced-order modelling was made by Millet et. al. (2006). Mismatch among model and experimental data was suggested to depend on heterogenous mix and imperfections in heat transfer modelling. Whereas the calibrated model reproduces the IMEP trace, no closed-loop control verification test was reported (Miller et al. 2006). Stability analysis in HCCI engines with high dilution was studied by Chiang and Stefanopoulou (2006) with demonstration both of stable and unstable equilibria. Some of the control-oriented modelling approaches aiming towards accurate auto-ignition assume constant wall temperature of 400 K (Shaver 2006b) and 500 K (Miller et al. 2006), respectively. 2.9 Hybrid multi-mode modelling In order to avoid difficult conditions of HCCI operation at high loads, mode transition control is relevant
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Modelling of HCCI engine dynamics—a survey and, thus, hybrid modelling for switching between SI and HCCI (or diesel-HCCI) combustion mode (Shaver et al. 2006a, b). Shaver et al. (2006a) outlined a two-input, two-state control-oriented system model of the residual-affected homogeneous charge compression ignition (HCCI) process. The combustion timing and peak pressure were selected as the model states, the inducted gas composition and effective compression ratio being the model inputs. In previous work, the authors utilized the self-stabilizing characteristic of residual-affected HCCI to neglect the combustion timing dynamics to arrive at a single-input, single-output dynamic model. The combustion timing dynamics were explicitly included for two reasons, the resulting model being more accurate and allowing the simultaneous, coordinated control of both in-cylinder pressure and combustion timing. Modelling approaches to multi-mode HCCI engines with VVA was made by Shaver et al. (2006b). For each of the three approaches investigated, the modelling was based on an open system first law analysis, with steady state compressible flow relations used to model the mass flow through the intake and exhaust valves. The model included nine states: the temperature, T; the concentrations of propane, [C3H8]; oxygen, [O2]; nitrogen, [N2]; carbon dioxide, [CO2], water, [H2O]; the mass in the exhaust manifold, me; the internal energy of the product gases in the exhaust, ue and carbon monoxide, [CO]; the crank angle, ; the cylinder volume, V; and for HCCI, an integrated Arrhenius rate to capture ignition timing. .
Volume rate equation: cos V_ ¼ B2 a_ sin 1 þ a pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 4 L2 a2 sin2
! ð26Þ
with crank-angle position , a half stroke length, connecting rod length L, and bore diameter B. . Valve flow equations: CD AR po m_ ¼ pffiffiffiffiffiffiffiffiffi RTo .
pT po
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi " 1= u ð 1Þ= # u 2 p T t 1 : ð27Þ 1 po
.
Energy and temperature rate equations: The first law of thermodynamics gives dðmc uc Þ _ c þ m_ ic hi þ m_ ci hc þ m_ ec he þ m_ ce hc ¼ Q_ c W dt ð29Þ where mc is the in-cylinder mass of species, uc is the in-cylinder internal energy, Q_ c ¼ hc As ðT Twall Þ _ c ¼ pV_ the is the in-cylinder heat transfer rate, W in-cylinder work, hi is the enthalpy of species in the exhaust manifold, hc is the in-cylinder enthalpy. The in-cylinder pressure and mass flow are modelled as P p ½X_ i pT_ þ p_ ¼ P T ½Xi i X X m_ c ¼ V_ ½Xi MWi þ V ½X_ i MWi p¼
X ½Xi RT,
ð30Þ ð31Þ
from which the temperature dynamics can be calculated (Shaver et al. 2006b, equation (25)). . Combustion chemistry modelling: Denoting the lean equivalence ratio , the combustion reaction is modelled as C3 H8 þ 5O2 þ 18:8N2 ! 3CO2 þ 4H2 O þ 5ð1 ÞO2 þ 18:8N2 with auto-ignition modelled Arrhenius threshold
by the integrated
Ea AT exp Kth ¼ ½C3 H8 a ½O2 b d, RT VC Z
i
n
ð32Þ
where i is the crank angle of auto-ignition and VC is the crank angle of valve closure, the values A, Ea /R, ak, bk and n being empirical fuel parameters independent of the particular engine. Using this model for studies of SI-HCCI mode transition, it is predicted that the combustion events occur first earlier and, then, progressively later as a transient effect of the cycle-to-cycle exhaust gas coupling (Shaver et al. 2006b). In our simulations, we used A ¼ 8:6 1011 , Ea ¼ 50, a ¼ 0.1, b ¼ 0.5, n ¼ 1, K ¼ 1 109 (figure 5).
Concentration rate equations: _ i _ i N_ i VN VN d Ni 2 ¼ wi 2 , ½X_ i ¼ ¼ dt V V V V
2.10 Model validation ð28Þ
where Ni is the in-cylinder number of moles of species i and wi, the rate of change of mole of species i per unit volume wi ¼ N_ i =V.
Model validation may be approached by qualitative comparison in model reproduction of observations, mathematical approximation accuracy, predictive accuracy, statistical error analysis, and capacity to serve as a basis for high-precision model-based control. In the following experimental evaluation, model
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Figure 5. Effects on combustion phasing of variations from nominal conditions, Tin ¼ 373 K, Qin ¼ 1400 J, n ¼ 1200 rpm. The experimental results are marked as ‘*’, the Shell model results with ‘o’, the Arrhenius rate integral results with ‘þ’, and the Planet mechanism with ‘’.
validation is approached in these various ways with detailed attention to predictive accuracy (which also serves as a basis for model-based control), statistical model validation, and model-based control.
3. Experimental set-up Two different experimental set-ups were used, both set-ups using the same control and data acquisition system. The control performance comparison between the two actuating methods, i.e., dual fuel and VVA, were performed on a six-cylinder heavy-duty Volvo D12C engine converted to HCCI operation. By changing the inlet valve close (IVC) crank angle IVC , the effective compression ratio was changed, resulting in a temperature change and change in 50 (figure 1). The other valve variables such as exhaust valve open (EVO), exhaust valve close (EVC) and intake valve open (IVO) were operated according to the standard valve strategy. Therefore, it was not possible to have neither positive
nor negative overlap, which would have resulted in trapment of residual gas. The control performance comparison between ion current and cylinder pressure measurements were performed on a modified single cylinder version of a Volvo heavy-duty engine TD100 converted to HCCI operation. The engine was fitted with a spacer that had six evenly mounted modified spark plugs. The only modification of the spark plugs was the removal of the side electrode. A cylinder pressure transducer was fitted to the engine for control and monitoring. Dual-fuel operation was used to control the combustion phasing. By changing the fuel ratio Rf between the two fuels used, n-heptane and ethanol, the auto-ignition properties were changed, resulting in a change of the combustion phasing. The fuel ratio when using the IVC approach was 0.9, this resulting in an octane number range similar to that of gasoline. To be able to change the fuel ratio, each cylinder had two injectors, one for each fuel. For both engines, the same control software and hardware were used.
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Modelling of HCCI engine dynamics—a survey The control was performed on a cycle-to-cycle basis and the controllers were designed in Simulink and converted to C-code using the automatic code generation tool of Real-time Workshop in Matlab. As HCCI engine operation is generically unstable (Olsson et al. 2002), it is necessary to include preliminary stabilizing control already in the experimental set-up. To that purpose, we used manually tuned PID control (which also served for benchmark purposes). 3.1 HCCI combustion control Previously, it was reported that PID and LQG can be used for control of the HCCI combustion phasing (Strandh et al. 2003). This paper presents a comparison between cycle-to-cycle control of HCCI combustion using MPC or PID control. The identified models obtained by identification methods described in x 2 were used for control design of the MPC and PID controllers. As there were differences among the cylinders, the controllers were designed to have cylinder-individual control. A major reason for using MPC is that it explicitly takes the constraints into account. Another reason is that it is well suited for controlling MIMO as well as SISO plants, and can be used to control a great variety of processes (Bemporad et al. 2002, Maciejowski 2002). The tuning parameters of the MPC controllers used for controlling HCCI were as follows. Constraints: The control constraints were 0 Rf 1 or 550 IVC 620 and Win 0, and the output constraint was dp=d dplimit . The input constraints were hard and the output constraint soft, and a tolerance band was specified to each constraint. . Weights: Input variables, input variables rate and output variables. The weights also included a slack variable, " , used for relaxing the constraints. . Horizons: The control horizons used were 1 Hu 15 and the prediction horizons used were 1 Hp 25. . State estimation: Input noise, output noise and measurement noise were defined and used in the calculation of the Kalman filter. Another approach was to use the estimated Kalman filter obtained by the identification methods used in x 2. .
angle was calculated from the combustion TDC. Note that there were two possibilities to obtain the same 50 , either by closing the inlet valve during the expansion before BDC or during the compression after BDC. In this paper, only IVC at or after BDC was used. A non-linear calibration map based on cubic spline was made. 4.2 HCCI modelling 4.2.1 Physical modelling Simulations: The described models were implemented and simulated in MatlabTM for single engine cycles with given initial gas mixtures and states. Simulation conditions were set according to table 2 and cylinder specifications according to table 3. Experiments: Experiments were carried out to investigate the influence on combustion phasing from inlet temperature, engine speed, fuel energy, and fuel ratio. There are several alternatives of how to calculate the combustion phasing and in this work the combustion phasing was calculated as the crank angle where 50% of the fuel has burned, 50 , (Bengtsson et al. 2004b). The phasing effects on 50 were studied by varying the corresponding variables from a nominal operating condition of Tin ¼ 373 K, Qin ¼ 1400 J, n ¼ 1200 rpm, and Rf ¼ 0:93 vol% as described in table 1. The pressure acquired, reconstructed temperature traces, and reconstructed heat release (Gatowski et al. 1984) for the nominal condition are shown in figure 2. Figure 3 shows pressure trace, temperature trace, and heat release for a simulation of a nominal operating point of Tin ¼ 373 K, Qin ¼ 1400 J, n ¼ 1200 rpm for PRF90 fuel, the dynamics of the ignition model being illustrated by the species concentrations in figure 4. Q, and B Note that the concentrations of R, are frozen as the Shell model is switched for the Wiebe combustion model. As described earlier the Table 2. Tin ð8CÞ n (rpm) Qin (J)
4. Results 4.1 IVC calibration Due to the nature of the piston motion, a change of IVC has a non-linear effect on the effective compression ratio, and thereby non-linear effect on 50 (figure 1). The crank
Table 3. HCCI Tin Pin n
100–115 1200 1400
Simulation conditions. 100 1000–1500 1400
100 1200 1000–1500
100 1200 1400
Experimental conditions for Cases 1 and 2. Case 1
Case 2
80 C 1.45 1000 rpm
93 C 1.33 bar 1000 rpm
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auto-ignition was defined as the crank angle where the explosive phase of the combustion phase begins and it can be observed that approximately 10% of the fuel has been burned at this crank angle. This is slightly higher than that measured of burned fuel in the experiment at the point where the ignition started. Phasing effects on 50 from variations of inlet temperature, fuel energy and engine speed according to tables 1 and 2 are summarized in figure 5. It can be noted that the Shell model gave quite an accurate estimation of the phasing for the temperature and the engine speed sweep. The model was slightly less accurate when changing the load, but still giving the correct trend. Results from simulations using the integrated Arrhenius model are also shown in figure 5. This method gave good results for load variations. The results for speed variations were less accurate at higher speeds. In order to compare the ignition prediction accuracy of these low-complexity models with more refined ones, results from homogeneous calculations using detailed chemical kinetics are included in figure 5. Here, detailed chemistry for an ethanol/ n-heptane mixture was obtained through the planet mechanism for PRF fuels. From figure 5 it can be observed that the Shell model gave similar results of prediction of 50 as the planet mechanism for inlet temperature variations. Whereas this observation was also true for the speed variations, the planet mechanism gave significantly better results in the case of load variation.
The residual distribution was similar to normal distribution with zero-mean value (figure 10). It can also be noted that the residual magnitude increased with later combustion phasing, i.e., higher 50 -value. The singular values of the Hankel matrix indicated that a second-order model was the appropriate model order choice (figure 11). The second-order model had a pole and a zero close to one (figure 11). The zero was to the left of the poles and of magnitude less than one (jzj 1) for all of the models of the six cylinders. Dual-fuel actuation: In the experiment, only the fuel ratio was excited. In this case, a second-order model gave a good fit (figure 12). The residual distribution was similar to a normal distribution with zero-mean value (figure 12). The singular values of the Hankel matrix indicated that a second-order model was the appropriate model order choice (figure 13). As in the case when IVC was the input, the second-order model has a pole and a zero close to
HCCI engine u¯ ′
u¯
u
a50
Dynamics
Figure 6. Compensating for the non-linear characteristics of IVC control, where u is IVC . 10
4.2.2 System identification
9
(
xkþ1 ¼ Axk þ B½uk u2k u3k u4k T yk ¼ Cxk þ Duk :
8 7 6 u¯′
Actuator—VVA: The static non-linearity between ivc and 50 can be estimated as a polynomial of fourth order (figure 1). A method to linearize the system was to estimate the inverse of the non-linearity and add this to the system (figure 6). The system was then 0 approximately linear from u to u. As the compensation of the static non-linearity was 0 successful u can be approximated by u (figure 7). The inverse was obtained using a look-up table. As the non-linearity could be described by a polynomial of power four, a method to identify the dynamics was to use inputs up to power four (figure 8). The identified models were provided in state-space representation.
5 4 3 2 1 0 0
1
Figure 7. Result non-linearity.
2
3
of
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the
5 u¯
6
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compensation
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9
of
the
10
static
ð33Þ
A second-order model was able to catch most of the 50 dynamics (figures 9 and 10).
[qIVC q 2IVC q 3IVC q 4IVC]
Figure 8.
Engine
a50
Inputs and output used in the identification.
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Modelling of HCCI engine dynamics—a survey one (figure 13). The zero was to the left of the poles and less than one for all of the models of the six cylinders. As it was also desirable to control the load and avoiding too high cylinder pressure gradient per crank angle, dp=d, MIMO models were needed. The MIMO model had fuel ratio (Rf), injected fuel energy (Win), inlet temperature (Tin) and engine speed (n) as inputs and 50 , IMEPn and dp=d as outputs (figure 27). Note that whereas Rf and Win could be changed to any given combination, it was the combination of Rf and Win that determined the amounts of the two fuels to be injected. A sixth-order MIMO model succeeded in capturing the significant dynamics (figure 14). The residual distribution was similar to the normal distribution with zero-mean value (figure 15).
4.3 Control and actuator comparison 4.3.1 Actuator—VVA. In the comparison between performance of PID and MPC, experiments were performed at similar operating conditions. Results at two different operating conditions are presented in table 3. The two cases will be denoted by Cases 1 and 2. PID control: The PID controller was capable to follow the reference value and to compensate for the load disturbance for Case 1 (figures 16 and 17). Note the differences among the cylinders. Notice that the amplitude on the control signal was decreased when the combustion phasing was retarded. This effect was due to the non-linearity between IVC and 50 . Due to the dynamics of the cylinder wall temperature, the step response was not symmetric. Results from the Case 2 experiment, are shown in figures 18 and 19. The PID control was capable of reference value tracking and to compensate for the load disturbances, but the closed-loop bandwidth was decreased. The PID controller parameter used for Case 1 could not be used for Case 2, as it resulted in large oscillations. Note that the amplitude on the control signal increased in comparison to the amplitude used in Case 1. The cycle-to-cycle variations were increased as the combustion phasing was retarded.
6 5 4 a50
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MPC control: The MPC controller was able to follow the reference value and to compensate for the load disturbance (figures 20 and 21). The step response was achieved in 5–6 cycles. Results from an experiment with later combustion phasing and where the load increased, when using an MPC controller are shown in figure 22. The MPC controller was able to follow the reference value and to compensate for the load disturbance.
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Figure 9. Upper figure shows measured output (gray) and model output from a second-order model (black). Lower figure shows the input PRBS signal.
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Figure 10. The left figures shows a closer view of the measured output (thin line) and the model output from a second-order model (thick line) presented in figure 9. The right figures show the residual and the residual distribution for the second-order model.
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In order to better illustrate the step-response performance in figure 22, results from one of the cylinders are shown in figure 23.
by Win as 50 has little effect on the IMEPn (Christensen et al. 2002). The dynamics between Win and IMEPn can be observed in figure 24. Neither IMEPn nor Rf were changed instantaneously. Apparently, the dynamics are due to the effect of wall wetting, fuel vaporization and wall temperature. It can be noticed that the step change resulted in a saturating control signal at fuel ratio equal to one (figure 25). Fuel ratio equal to one was not sufficient in order to change 50 from 1 CAD to 4 CAD in one sample, but in the next cycle ref 50 was reached. At cycle 168, a negative step was applied and also in this case the control signal was saturated. Around 4 cycles
4.3.2 Dual-fuel actuation. Figure 24 shows experimental step response results from an MPC controller, where the objective was to control 50 . During the sequence, ref 50 and Win were changed. Still, the MPC controller kept 50 at the reference value. It can be observed that the step response in the Win had no noticeable effect on 50 , and the new IMEPn was reached in few samples. To a great extent, the IMEPn was determined
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were needed before the desired ref 50 was reached in this case. The time constants for a positive and negative step were not equal and the time constants depended on the operating conditions.
As the cycle-to-cycle variations on a HCCI engine are significant, it was desirable that the controller avoid increasing these variations. In figure 26, the histogram of the control error when the reference value of 50
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was 5 CAD and for a open-loop experiment where the 50 was close to 5 CAD. The distributions were similar to the normal distribution. 4.3.3 The MIMO control problem. In figures 28 and 29, the results of step changes in IMEPn are shown. In this example, the constraint on dp=d was 20 bar/CAD. It can be observed that the controllers were able to control IMEPn. In figure 29, the results from one cylinder are shown. In the experiment, the reference value of IMEPn was changed from 2 bar to 4 bar in increments of 0.5 bar, and the constraint on dp=d was 15 bar/CAD. It can be observed that the IMEPn reference was quickly reached. A closer examination of the IMEPn reference step, showed that a step response was often reached in 1–2 cycles. When the constraint on dp=d was set too soft and the cycle-to-cycle variations were significant, the constraint on dp=d might be exceeded. In this case, there was no guarantee that the dp=d constraint
was not exceeded. However, dp=d was kept around the limit of 15 bar/CAD, and this was mainly achieved by retarding of 50 . When satisfaction of the dp=d constraint was impossible, then the IMEPn reference of 4.5 bar was not achieved. The MPC controller showed practical robustness to disturbances in IVC (figure 30). Recall that IVC was not included in the model, still the IMEPn was kept at the reference value of 3 bar. 4.4 Emissions As previously stated, the main purpose for HCCI is the promise of low NOx emissions. To the purpose of verification, figure 31 shows the resulting NOx emissions when the engine was operated at high load. It can be observed that the concentrations of NOx emissions are kept below 2 ppm (parts per million) and that the NOx emissions increased when the load increased. These values can be considered to be very low. In experiments where NOx was measured, the concentrations of NOx
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PID control of 50 using IVC for Case 1. Result from Cylinder 3.
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MPC control of 50 using IVC for Case 2. Result from Cylinder 3.
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never exceeded 3 ppm. These concentrations could be compared with the concentration of NOx in SI engines where they often are few thousands ppm before aftertreatment of the emissions, and the concentration of NOx in CI engines where the concentrations are few hundreds of ppm before aftertreatment of the emissions. For the experiment shown in figure 31, the HC emissions were around 2500 ppm and the CO emissions were around 1200 ppm. Whereas these levels are not low, these emissions may be reduced to acceptable levels by an oxidation catalyst. 4.5 Control comparison of cylinder pressure vs. ion current The ion current rise flank coincided with the heat release and pressure rise flanks (figure 32).
Another characteristic was that there was heat release before the appearance of any ion current, indicating that ion current measurement is local (Vressner et al. 2004). The combustion phasing was estimated by using the ion current rise flank, the midpoint of this flank being designated ion 50 . Combustion phasing 50 based on pressure measurements was estimated by finding the crank angle degree (CAD) value where the heat release had reached half of it’s maximum (Bengtsson et al. 2004b). The correlation between ion 50 and 50 was almost centered along the line representing identity figure 33. The cases noted ‘þ’ and ‘‘x’’ both had a correlation coefficient of 0.87 for experiments carried out in open-loop operation. The coherence spectrum between ion 50 and 50 was fairly close to one for several frequencies, suggesting that a linear relationship between ion 50 and 50 might exist. The PID controller was manually tuned and the parameters were the same for the two different feedback cases and no feedforward was present. The control system response when using feedback from ion current measurements (ion 50 ) to step changes together with the corresponding 50 are shown in figure 34. Both cylinder pressure and ion current were measured simultaneously. Figure 34 shows the step response where feedback from pressure sensors (50 ) was used and the corresponding ion 50 . The step responses were performed at the same operation point of 3 bar IMEPn, inlet temperature of 150 C, an engine speed of 1000 rpm and no EGR. The closed-loop control
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based on ion current gave good results with similar performance as the closed-loop control based on cylinder pressure. In this experiment, the standard deviation of the control error was 0.65 CAD for ion 50 and 0.56 CAD for 50 . This corresponds to previous studies in which ion 50 and 50 gave very similar results (Strandh et al. 2003). In figure 35, the distribution of the residuals is shown when controlling using ion 50 or 50 . Note that the residual distribution, when ion 50 was used as feedback variable, was similar to the normal distribution with zero-mean value. The corresponding residuals for 50 had an offset. As expected the residual distribution was similar to normal distribution with zero-mean value, when 50 was used as feedback. The corresponding residuals for ion 50 had an offset. The two offsets were similar. The resulting autocorrelation of the control error, when using ion 50 , had residuals of low magnitude and approximately uncorrelated, thus providing sufficient model validation. As this was also the case in feedback control using 50 , sufficient model validation was provided.
5. Discussion Among components relevant and necessary for controloriented physical models in x 2.3, we single out a fuel model (the Shell model), a cylinder gas model, a gas property model, a combustion model and a heat transfer model. Beyond the necessities of stable operation, performance-oriented control may require extensions with physical model components such as EGR models and emission models (Ishyama et al. 2007). Based on comparison to the identification-based MPC control, the results indicate that the proposed physical model of x 2.3 may be used as a base for successful feedback strategies for ignition control. Whereas model-based HCCI control entirely based on physical modelling has not been achieved, some progress has been made.
Qualitative phasing behaviour is correctly reproduced at variations in inlet temperature, engine speed, and load. To this purpose, model calibration remains a key issue. The fuel model used was only crudely calibrated and the quantitative results are expected to improve with calibration. The Shell-model parameters of Halstead et al. (1977) were obtained from experiments on a rapid compression machine. Preliminary attempts with manual tuning of the parameters have shown to yield better agreement with the ignition process in a heavy-duty engine. The proposed physical model performed better than the integrated Arrhenius model in the comparisons. It should be noted that the results were obtained with nominal PRF90 parameters from the literature. The latter model has an advantage of having few parameters and engine specific calibration is likely to be easier. As stated in (Turns 1996), the integral expression can also include explicit temperature dependence, which also was included in (Shaver et al. 2004). It may then be possible to improve the results for temperature variations. In the prediction of 50 , the Shell model gave almost similar behavior as the detailed chemistry Planet mechanism, indicating that low-complexity models can be used on feedback strategies for ignition control. Feedback control of HCCI engines was successfully accomplished using MPC control based on estimated linear models for various operating points. Whereas interpolation among linear models obtained for different operating points was successful in control design, an HCCI engine has non-linear characteristics and nonlinear models may improve the result. In this paper, we have used gain scheduling organized as linear interpolation among control outputs based on the models identified on a coarse grid of IMEP operation points. In future work, elaboration on gain scheduling will be relevant (Ishyama et al. 2007). In the early tests presented here, the step sizes were purposely chosen small in
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order to secure the integrity of the experimental set-up. In order to have a fast and robust control of the HCCI combustion phasing in the whole operation range, it would appear necessary to apply gain-scheduled controllers, if piecewise linear control design methods are to be used (Rugh and Shamma 2000). In principle, the cancellation of the non-linearity could give rise to singularities and add sensitivity to the noise. In practice, no such problem was experienced.
The models used by the MPC controller were all of low order, the MIMO model being of sixth order per cylinder. There were only four constraints, three on the control variables and one on the output variable dp=d. Therefore, the quadratic programming problem had low complexity when the control horizon was short. As the engine had fast dynamics, there was no significant improvement when the prediction horizon was chosen larger than ten cycles (samples), and when
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the control horizon was larger than five cycles (samples). As the computational effort of solving the optimization problem was small, however, longer horizons may be applied to increase the robustness. There are several commercial and research VVA systems available and they provide various degrees of freedom. The VVA system used was a research system aiming for production and only the inlet port could be varied. If the exhaust port could be controlled, the residual gas in the cylinder could be controlled using negative overlap. This would result in successful cycleto-cycle control of the temperature of the gas mixture to be controlled. An additional benefit is that there
was no need for a heater (though with the drawbacks of a more complex and expensive system). The benefit of using control by IVC only is that it requires a less expensive and complex system. In this comparison, a heater has low complexity and cost. The drawback with only using IVC is that at high load, when the combustion phasing must be retarded in order not to damage the engine, late IVC closing may be needed. This results in decreased volumetric efficiency, which is the opposite to what is desired when aiming towards high loads. The dual-fuel approach does not have this drawback. A benefit with VVA is that there is less dynamics between IVC and 50 than between Rf and 50 , as wall wetting and heat of vaporization do not change with IVC . A drawback with the dual-fuel approach, however, is that two fuels need to be refueled. But even this could be a commercial solution. Ideally, the amount of secondary fuel consumed would be minimal, and the secondary tank needed only to be refueled at maintenance intervals. This is the case for the SCR catalyst using an active substance such as Urea. The cylinder pressure measurements provided a more robust estimation of the combustion phasing than ion current measurements as the ion current measurements were only detectable in a part of the HCCI operation range. In this experimental set-up, the upper limit of -value (relative air/fuel ratio) seemed to be 2.7 for a reliable ion current signal. At higher -values, the noise level corrupted the measurements. As this range is only a small part of the HCCI operation range, more studies on how to extend the operation range for ion current measurements in HCCI are required. The HC and CO emissions were kept low by aiming at complete combustion. This was achieved by having an early combustion phasing. The NOx emissions were no problem as the combustion temperature was kept low in the experiments, which can be achieved by not allowing high cylinder pressure. Before dangerous levels due to peak pressure were reached, the pressure gradient per crank angle often reached dangerous levels for the engine and the sensors. Therefore, the magnitude of cylinder pressure gradient per crank angle was used as a safety limit instead of cylinder peak pressure. Then, the MIMO control problem could be formulated as controlling the load, without exceeding limits on the cylinder pressure gradient per crank angle. The load should be reached by using the minimum amount of fuel and the combustion should be complete, IMEPn being used as a measurement of the load. In order to avoid too high dp=d, a maximum constraint was specified. Other constraints were the maximum and minimum constraints of Rf. Control of the load was achieved by
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using a weight factor for the load. The objectives to minimize fuel consumption and to have complete combustion for the desired load were achieved by weight-factors for 50 and Win, and by setting the reference value for 50 to zero. This results in the earliest possible combustion phasing, while still satisfying the constraint on dp=d. The combustion was more complete in early combustion phasing than in late combustion phasing, where the cylinder volume has increased. As the increased cylinder volume would decrease the cylinder temperature, the combustion might stop before all fuel was burned out. The manipulated variables were Rf, Win, the measured disturbances were Tin and n, and the manipulated outputs were 50 and IMEPn. Note that the cylinder pressure gradient per crank angle was not manipulated by feedback, only monitored. Attempts to increase the load range to high-load operation require attention to modification of high-pressure transients and fuel reactivity:
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Attention to the reactivity and sensitivity may also be prompt revision of calculation. Recently, efforts towards higher prediction accuracy of auto-ignition timing based on a knock-integral method were reported (Shakbakhti
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et al. 2007). A team from Robert Bosch GmbH recently reported a predictive feedforward control strategy for improved load control and controlled auto-ignition (Kulzer et al. 2007). Whereas several control-oriented modelling approaches aiming towards accurate auto-ignition assume constant wall temperature of 400 K (Shaver 2006b) and 500 K (Millet et al. 2006), respectively, there are significant transients in the control signals related to dynamic effects as manifested in the response to setpoint changes (figure 29). As obvious from figure 29, there is room for improved modelling of wall temperature dynamics and resultant effects in cycle-to-cycle and auto-ignition dynamics. In Chang et al. (2007), a finite element model of the heat transfer to the combustion chamber walls was used to design a compensation for thermal transients. It was found that more hot residuals were needed to maintain correct combustion phasing when the combustion chamber walls are colder that the steady state temperature (and vice versa). Finally, system identification and model predictive control provide effective and pragmatic means to control system design fulfilling both design objectives and control constraints.
6. Conclusion A survey of HCCI modelling with special emphasis to modelling instrumental for model-based control has
been presented. Dynamic models of HCCI were estimated, both SISO and MIMO models. It was found that low-order models gave satisfactory results. Two different actuator approaches were used and models for both approaches were estimated. Whereas dynamics were different between the models, it was found that satisfactory results were obtained for both approaches. The VVA approach was found to give a more direct control of 50 than dual fuels. The VVA approach has the benefit that it could be used in a larger region without need for changing the inlet temperature. In order to use the dual-fuel approach in the whole HCCI operating range, the inlet temperature must be changed significantly. A new sensor candidate, i.e., ion current measurement, was evaluated for HCCI engine control. Successful closed-loop experiments were performed and it was found to work well for a range of of ½2, 2:7. At these operating points, the performance was similar to the case where pressure sensors were used. Successful cycle-to-cycle control of the combustion phasing results in a six-cylinder heavy-duty engine using PID and MPC control was presented. It was found that an MPC controller gave best results as it was found to combine practical robustness and acceptable bandwith. The PID controllers’ bandwidth had to be decreased when the load increased in order to not result in significant oscillations, this resulted in slow response. An MPC controller was proposed and validated by experiments as a solution to the problem of load-torque control with simultaneous minimization of the fuel consumption end emissions, while satisfying the constraints on cylinder pressure. The results presented indicate that a fairly low complexity auto-ignition model may be used to predict phasing behavior of HCCI engines at low load. The Shell model used for detecting auto-ignition of HCCI combustion gives qualitatively correctly reproduced phasing behavior at variations in inlet temperature, engine speed and load. The model suggested has an appropriate ratio between complexity and accurate prediction of the combustion phasing in HCCI. Modelling of sufficient dynamic accuracy to allow model-based closed-loop HCCI engine control constitute challenges in issues of model complexity, model reduction, model calibration, state estimation. As yet, modelling efforts have only accomplished component models and with insufficient test of the predictive accuracy. Model-based control including model calibration and state estimation remain challenging research issues.
Modelling of HCCI engine dynamics—a survey Acknowledgments This research was supported by Vinnova, Volvo Corp., Volvo Car and Scania Corp. under the contract GIHR of the Vehicle Research Program. This research was partially done in the framework of the HYCON Network of Excellence, contract number FP6-IST-511368 and the Swedish Research Council grant 2006-5243.
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