Mid-ranging control of a multi-cylinder HCCI engine using split fuel injection and valve timings*

6th IFAC Symposium Advances in Automotive Control Munich, Germany, July 12-14, 2010

Mid-ranging control of a multi-cylinder HCCI engine using split fuel injection and valve timings ! Nikhil Ravi ∗ Hsien-Hsin Liao ∗ Adam F. Jungkunz ∗ J. Christian Gerdes ∗ ∗

Dept. of Mechanical Engineering, Stanford University, Stanford, CA-94305, USA.

Abstract: Homogeneous charge compression ignition (HCCI), though a promising piston-engine strategy for the future, presents a significant control challenge due to the presence of cycle-tocycle dynamics and the absence of a direct combustion trigger. Several actuators can be used for controlling HCCI, but each of them presents unique hurdles to practical implementation. This paper presents an approach for controlling HCCI with exhaust recompression that addresses these challenges using the principle of mid-ranging control. The controller is based on a physical, discrete-time model of HCCI presented in previous work. A split injection strategy is used, with the timing of a small pilot injection of fuel during recompression being used to control the phasing of combustion on a cycle-by-cycle basis. A slower valve motion, easily achievable on an engine equipped with cam phasers, is then used to keep the injection timing in the middle of its range of influence, maintaining the control authority to handle fast transients while respecting actuator constraints. The controller is seen to be effective in tracking desired load and phasing trajectories in simulation, and on a multi-cylinder engine testbed. In particular, the controller enables steady operation at low load conditions on the engine. Keywords: HCCI, mid-ranging control, injection timing, recompression reactions

Homogeneous charge compression ignition (HCCI) engines provide two key benefits over conventional engine strategies - improved efficiency, and significantly lower NOx emissions. However implementing HCCI in practice is challenging due to the presence of cycle-to-cycle dynamics, and the lack of a direct combustion trigger. Closed-loop control is necessary in order to ensure reliable operation of HCCI over a wide operating region. Several methodologies have been proposed in the past to control HCCI. A significant number of these use variable valve actuation (VVA) to control the quantities of exhaust and fresh air in the engine cylinder (Agrell et al. (2003); Shaver et al. (2005b); Fischer et al. (2007); Ravi et al. (2009)). Olsson et al. (2001) and Strandh et al. (2004) control the relative proportion of two fuels in a dualfuel mixture to affect the combustion characteristics. Both these strategies, however, are impractical for cycle-by-cycle control on current production engines. Using fully flexible variable valve actuation implies steep costs and packaging issues, while dual-fuel strategies would require changes in gas pump infrastructure, as well as consumer refueling behavior. Therefore both these techniques would have, at best, limited applicability at present. Fuel injection, however, is a viable cycle-by-cycle control input when implemented in a recompression strat! The authors would like to acknowledge General Motors Company and Robert Bosch LLC for their support of this work.

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egy with direct injection. Fuel injected into the moderately high pressure-temperature environment created in the engine cylinder during recompression can undergo physical/chemical transformations that affect the combustion on the subsequent engine cycle (Song and Edwards (2008)). Fuel injection quantity and timing, therefore, can be powerful control knobs in influencing HCCI combustion on a cycle-by-cycle basis. Direct fuel injection also provides the added opportunity to individually control every cylinder of a multi-cylinder engine at minimal cost. Near the low-load limit, emissions and stability have both been shown to improve by optimizing the timing of fuel injection (Aroonsrisopon et al. (2004); Standing et al. (2005)).

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1. INTRODUCTION

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The effect of a small pilot fuel injection (1mg) during recompression can be seen in Fig. 1, which shows the variation of combustion phasing (measured in terms of CA50 , the crank angle location at which 50% of the fuel has been burned) with the timing of a 1mg pilot injection. The rest of the fuel (9mg) is injected during the main injection, at the end of recompression (420 CAD). All crank angles are referenced to 0 deg at TDC, combustion. Such a strategy is referred to as a split injection strategy. As seen, with a sweep of the pilot injection timing between 310 and 395 CAD, a combustion phasing range of about 7 CAD can be achieved, which represents most of the desirable phasing range for HCCI. However, this control input is seen to have a limited range at a fixed valve timing - as seen in the figure, pilot injection has maximum control authority in the middle of the region depicted, with its influence on phasing saturating near the extremes. By contrast, the exhaust valve timing has a strong influence on combustion phasing over a wide range, but is impractical to vary on a cycle-by-cycle basis, for the reasons described earlier. Slower variations, though, would be easily achievable with existing cam phaser mechanisms on production engines. This paper, therefore, presents a control strategy that uses a combination of split injection and slowly changing valve timings to control the work output and phasing of combustion in a gasoline HCCI engine. The work output is controlled by varying the total fuel mass injected into the cylinder. A mid-ranging control scheme is used to control combustion phasing through the timings of the exhaust valve event and the pilot injection. The faster input, injection timing, is used to control the phasing on a cycle-by-cycle basis, while the exhaust valve timing is used to gradually bring the injection timing back to the middle of its range where it has the maximum control authority. This ensures fast, cycle-by-cycle control action, while at the same respecting constraints on the motion of the valves. The mid-ranging controller is developed on the basis of a physical model of HCCI presented in previous work (Ravi et al. (2009), Ravi et al. (2010)). The controller is seen to be effective over a range of conditions both in simulation and on a multi-cylinder HCCI engine testbed. The pilot injection strategy also enables steady operation at low loads that are otherwise unstable to operate at. 2. HCCI MODEL FOR CONTROL 2.1 Model overview A brief overview of the model used for controller development is presented here, details of which can be found in Ravi et al. (2009) and Ravi et al. (2010). This model is a discrete-time model that relates the state of the cylinder constituents on one engine cycle to the next. Induction of fresh air is assumed to occur at constant pressure, and the mixing process is modeled as an instantaneous event at intake valve closure (IVC). The compression, expansion and exhaust processes are assumed to be polytropic. Complete combustion over a finite duration to major products is assumed. A model for ignition is constructed from fundamental but simple chemical kinetics relationships, where the global Arrhenius rate shown in Eqn. (1) is assumed to capture the underlying physics of the combustion reaction. Ea RR = A e( Ru T ) [f uel]a[O ]b (1) th

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where Ea is the activation energy, Ath is a pre-exponential factor, Ru is the universal gas constant and a and b are constants. Integrating this global Arrhenius rate equation from IVC to the start of combustion gives an expression of the form !

RRdt =

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(2)

When the integral in Eqn. (2) crosses a pre-determined threshold, Kth , combustion is assumed to begin. The crank angle location where 50% of the fuel has been burnt, CA50 , can then be calculated from θsoc , and the combustion duration, which is assumed to be a linear function of the start of combustion location. Therefore we have CA50 = F ([O2 ], T, [f uel], Kth) (3) The effects of fuel injection during recompression can be complex and varied, depending on the operating region, as shown by Song and Edwards (2008). This model considers split injection in an operating regime where the breakdown of the fuel into smaller C-chain molecules dominates. Only 1mg of fuel is injected during the pilot injection, with the timing of this injection being controlled on every engine cycle. The rest of the fuel is injected at a fixed location after recompression. The small molecules obtained when the pilot fuel breaks down have a shorter ignition delay than heavier gasoline molecules. This leads to the advancement of phasing during the main combustion. Though the inherent chemical processes are complex, a simple way of modeling the net effect within the existing model structure is to lump all these changes into a change in the Arrhenius threshold value, Kth . The rationale behind this is that the smaller fuel molecules can be considered to have a lower threshold to combustion than the molecules of gasoline fuel, thereby lowering the overall threshold for the global reaction. 2.2 Model states, inputs and outputs The states of the model are chosen so as to capture the relevant thermodynamic aspects of the in-cylinder mixture. The states are defined at a fixed crank angle location after intake valve closure - this represents a point where both valves are closed, and all the reactants are present in the cylinder, ready for combustion. This point can be chosen as an arbitrary fixed point after intake valve closure, and is here chosen as θs =-60 CAD (60 CAD before TDC-combustion). Every engine cycle (indexed by k), therefore, is assumed to begin at this fixed crank angle location. The particular states are chosen as (1) (2) (3) (4) (5)

Concentration of oxygen at θs , [O2 ]s,k Temperature of mixture at θs , Ts,k Concentration of fuel at θs , [f ]s,k Cylinder volume at intake valve closure, VIV Cs ,k Arrhenius threshold, Kth,k

Of these states, the first two - oxygen concentration and mixture temperature - capture the essential dynamics of the HCCI process, as shown in Ravi et al. (2006). The next two states complete the description of the thermodynamic state of the cylinder, by providing a measure of the quantity of fuel in the cylinder, and a proxy for the

AAC 2010 Munich, Germany, July 12-14, 2010

total amount of reactants. The final state, the Arrhenius threshold, captures the effect of the pilot injection input during recompression on the previous engine cycle.

the application of these inputs, the model then updates the states on the next cycle.

The inputs available for control in the model are

2.3 Linearization

(1) (2) (3) (4)

Total moles of fuel injected, nf,k Cylinder volume at intake valve closure, VIV C,k Cylinder volume at exhaust valve closure, VEV C,k and Arrhenius threshold, uth,k

The valve timings can be used to vary the relative amounts of air and trapped residual. A fixed valve duration is assumed - therefore intake and exhaust valve opening timings are functions of the closing timings. Direct injection gives independent control of the amount of fuel in the cylinder. The fourth input, uth , is a proxy for the timing of the pilot injection, and directly affects the state Kth on the next engine cycle. Therefore Kth,k+1 = uth,k (4) The main output of this model is the phasing of combustion (measured in terms of the crank angle location where 50% of the energy from combustion is released, CA50 ). The other quantity of interest that needs to be controlled accurately is the work output of the engine (measured in terms of N M EP , the net mean effective pressure in the engine cylinder). The relationship between the states and N M EP can be derived from the model based on the in-cylinder pressure at different points during the cycle. However, the work output is strongly dependent on the quantity of fuel injected into the cylinder when the engine is operating as desired. Therefore control of N M EP can be handled based on an empirically derived relationship between fuel quantity and work output, and the physical model is used purely to control CA50 .

Output 1. CA − k 50

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Fig. 2. Control model summary A graphical representation of the model is shown in Fig. 2, which shows the locations of the states, output and inputs within one cycle with respect to each other along an incylinder pressure trace. The states, as seen, are defined at a fixed location after the intake valve has closed, which is where the k’th cycle is assumed to begin. After combustion the output, CA50 , is determined. The measurement of this output can then be used by a controller to subsequently determine the appropriate inputs on that cycle - valve timings, total fuel quantity and the pilot injection timing (represented by the Arrhenius threshold input, uth ). With 799

In order to enable the synthesis of simple linear controllers, the nonlinear model described above is linearized around an operating point. The analytical Jacobian of the system equations with respect to the states and inputs is computed, giving linear system equations around the particular operating condition. x˜k+1 = A˜ xk + B u ˜k y˜k = C x ˜k

(5)

Here A, B and C are matrices that are functions of the operating point at which the system is linearized. The conceptual structure of these matrices is shown in Eqn. (6), where X represents a non-zero value (determined by the particular operating condition).   [O2 ]s X X X X   Ts    0 0   [f ]s    0 0 VIV Cs  Kth k 0 0   X X 0  nf X X 0  V 0 0 0   EV C  VIV C  0 1 0 uth k 0 0 1   [O2 ]s  Ts    CA50,k = [ X X X 0 X ]  [f ]s  V  IV Cs Kth k

[O2 ]s  Ts   [f ]s V IV Cs Kth 

X  X   = 0   0 0 k+1  X X  + 1 0 0 

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(6)

As seen, the last three states have no dynamics of their own, but are purely dependent on the inputs on the previous cycle (respectively, nf , VIV C and uth , shown by the 1s in the last three rows of the B matrix). The oxygen and temperature states, however, depend on all the states on the previous cycle, as well as the first three inputs. It is assumed here that they do not depend on the final input, uth - or in other words, that the injection of a small quantity of pilot fuel during recompression has a much more significant effect on the Arrhenius threshold than on the oxygen concentration or temperature of the final reactant mixture after IVC. Therefore, though there is some endothermicity brought about by fuel-breakdown, it is assumed that the effect this decreased temperature has on combustion phasing is overpowered by the effect of the smaller fuel molecules. This assumption is justified by experimental results that show consistent advancing of the phasing of combustion with pilot fuel, which suggests that the shorter ignition delay for smaller C-chain molecules dominates over the lower mixture temperature. This linear system can now be used to develop a linear controller that would command a specific set of valve timings and an Arrhenius threshold, uth for a desired phasing of combustion, CA50 . The threshold can then be

AAC 2010 Munich, Germany, July 12-14, 2010

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Fig. 3. Mid-ranging controller - block diagram For the scenario of HCCI control, the timing of pilot injection is considered the fast input u1 , while the exhaust valve closure timing (EVC) is considered the slow input u2 . The intake valve is kept fixed in all the tests described in this paper, and is not used as an active input. The controller K1 that controls the injection timing is a reference-input tracking controller developed from the linear model as described in Franklin et al. (1994), with a feedforward and feedback component. The matrices Nx and Nu are defined such that in steady state, an input uss makes the output follow the reference, with a corresponding reference state value xss .

The controller is seen to perform well when tested on a continuous time simulation model. The model, described in Shaver et al. (2005a), is a ten-state model that includes much of the complex thermodynamics of the HCCI process. This continuous time simulation model is parameterized with experimental data, and can therefore serve as a virtual testbed, both to parameterize simpler models as well as test control strategies before implementation on the engine. Figure 4 shows results for a series of step changes in desired combustion phasing with a fixed total fuel quantity. The system initially reaches steady state in open-loop starting at a set of initial conditions, and the controller is switched on after 10 engine cycles. The integral gain K2 on EVC is set to zero, and so there is no mid-ranging action. As seen, the controller tracks the desired trajectory accurately by changing the pilot injection timing alone, while EVC is kept fixed. 8

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The phasing of combustion, CA50 is controlled using a mid-ranging control scheme. As stated in Allison and Ogawa (2003), mid-ranging refers to a class of control problems where there are more manipulated inputs than outputs to be controlled. The most common situation is when there are two inputs and one output. Often the inputs differ in their dynamic effect on the output, and the faster input has a more limited range than the slow one. The mid-ranging idea is to have the fast input u1 controlling the process output, and to use the effect of the slower input u2 to gradually reset or mid-range u1 to its desired value u1,ref . A conceptual block diagram representing a mid-ranging controller is shown in Fig. 3.

The controller is combined with a Kalman filter to estimate the oxygen concentration and temperature states, which are not measurable on an engine testbed. The Kalman filter uses the measurement of CA50 to estimate the states, which are then used by the controller to determine the desired control inputs. This controller-observer system can then be used to track a desired N M EP −CA50 trajectory.

CA

Of the two outputs to be controlled, N M EP and CA50 , it is seen that N M EP is almost wholly a function of the total fuel quantity injected (Ravi et al. (2009). Therefore a simple feedforward-feedback controller is used to control N M EP . An empirically derived map relating fuel quantity to N M EP is the feedforward portion of this controller. A closed-loop integral controller is then added to correct this map in feedback.

The controller K2 that controls EVC to mid-range the injection timing is a pure integral controller. The value of the integral gain is determined by the desired maximum slew rate of the valves, and can be set depending on the limitations of the physical system. An anti-windup scheme, as described in Haugwitz et al. (2005), is also added to maintain good performance in the event of saturation.

Pilot injection timing (CAD)

3. CONTROLLER DEVELOPMENT

where r is the reference input (representing the desired output trajectory) and Kx is the feedback controller. For the tests described in this paper, the controller gains are set such that the closed loop poles of the system are placed at 0.15 and 0.2. An integral component is added to compensate for steady state errors.

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The control input, then, is of the form u ˜th,k = −Kx (˜ xk − xss ) + uss = −Kx x˜k + (Nu + Kx Nx )rk

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related to the pilot injection timing through an empirical map obtained from steady-state engine data, where the Arrhenius relation in Eqn. 3 is inverted for a measured value of CA50 to give the corresponding uth . Therefore the Arrhenius threshold input commanded by the linear controller translates directly to the physical input, the timing of the pilot injection.

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Fig. 4. Phasing controller without mid-ranging action simulation results When the gain K2 is set to a non-zero value, however, the EVC value is changed gradually so as to enable the pilot injection timing to track a reference value, as shown in Fig.

5. The CA50 tracking remains practically unchanged, and the phasing reaches a new steady-state within a few cycles, due to the fast action of the injection timing. Therefore accurate tracking is maintained, while ensuring that the fast control input always stays away from saturation.

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AAC 2010 Munich, Germany, July 12-14, 2010

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Fig. 5. Phasing controller with mid-ranging action - simulation results

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Fig. 6. Mid-ranging control - experimental results

The test conditions for the results presented here are given in Table 1. The three main control inputs are the main fuel injection quantity, the pilot injection timing, and the EVC timing. A fixed valve open duration of 140 CAD is assumed, and so the EVO timing is determined from the EVC input. Value 1800 430 570 EVC-140 Controlled Controlled 420 1 Controlled

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Fig. 7. Low load operation - Cylinder 3

Table 1. Test conditions Parameter Engine speed IVO IVC EVO EVC Main injection quantity Main injection timing Pilot injection quantity Pilot injection timing

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The multi-cylinder engine testbed used to test the controller is a four cylinder GM gasoline engine modified to run HCCI. The engine runs on a compression ratio of 12:1. A common rail direct injection system is used to inject fuel directly into each cylinder. A fully flexible electrohydraulic VVA system is used to actuate the intake and exhaust valves on each cylinder independently. Cylinder pressure is measured with a Kistler 6125 piezoelectric transducer in each cylinder. The controller is run independently on each cylinder of the four cylinder engine.

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5. EXPERIMENTAL RESULTS

in Fig. 7, where the controller tracks NMEP down to about 1.2bar (results shown for only one of the four cylinders). This shows the ability of this control knob in expanding the operating range of HCCI on the low load end.

Units rpm CAD CAD CAD CAD mg CAD mg CAD

Figure 6 shows the output and input trajectories from a test where a series of step changes in N M EP are commanded at constant combustion phasing. As seen, the controller tracks a step change in NMEP of 1 bar while maintaining a constant phasing due to the cycle-by-cycle action of the injection timing. The slower EVC motion eventually brings the injection timing back towards its reference value. All the cylinders are seen to converge to the same steady-state work output and phasing. Using a pilot injection also makes the controller very effective in stabilizing HCCI at low load conditions as seen 801

Figure 8 shows a step change in load at constant phasing for one of the four cylinders, with the plots zoomed in around the step change. As seen, the new steady-state is reached within 3-4 cycles, and there is no discernible change in the combustion phasing due to the increase in fuel quantity. Over the space of a few cycles the EVC value is practically constant as the mid-ranging action occurs over a much longer time scale. 6. CONCLUSION The results presented in this paper suggest that a control strategy that combines fuel injection and variable valve actuation can be an effective and practical way of controlling HCCI on a cycle-by-cycle basis. The controller presented here is based on the principle of mid-ranging control, and

Pilot timing (CAD) CA50 (CAD) EVC (CAD) NMEP (bar) Total fuel(mg)

AAC 2010 Munich, Germany, July 12-14, 2010

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Fig. 8. Cycle-by-cycle action of controller - Cylinder 2 is developed from a physical model presented in previous work. The mid-ranging framework is an effective way of satisfying two key objectives - achieving cycle-by-cycle control to track fast transients, and respecting constraints on the available actuators (saturation limits on the pilot injection timing, and slew rate limits on the valve motion). The controller is seen to be effective in controlling the work output and phasing of combustion both in simulation and on a multi-cylinder HCCI engine testbed, and enables stable operation at low load conditions. These results demonstrate the potential of mid-ranging control as a viable control strategy for HCCI engines, enabling the coordination of multiple actuators with different performance characteristics to achieve tracking of the desired outputs in a wide operating range. ACKNOWLEDGEMENTS The authors would like to thank the General Motors Company and the Robert Bosch LLC Research and Technology Center, Palo Alto, for their technical and financial support of this work, and in particular, Dr. Man-Feng Chang, Dr. Jason Chen, Mr. Paul Najt, Dr. Jun-Mo Kang, Dr. Nicole Wermuth, Dr. Han-Ho Song, Dr. Sungbae Park, Dr. Nalin Chaturvedi, and Dr. Aleksandar Kojic. REFERENCES Agrell, F., Angstrom, H.E., Eriksson, B., Wikander, J., and Linderyd, J. (2003). Integrated simulation and engine test of closed loop HCCI control by aid of variable valve timings. SAE 2003-01-0748. Allison, B.J. and Ogawa, S. (2003). Design and tuning of valve position controllers with industrial applications. Transactions of the Institute of Measurement and Control, 25, No. 1, 3–16. Aroonsrisopon, T., Werner, P., Waldman, J., Sohm, V., Foster, D., Morikawa, T., and Iida, M. (2004). Expanding the HCCI operation with the charge stratification. SAE paper 2004-01-1756. Fischer, W., Karrelmeyer, R., Loffler, A., Kulzer, A., and Hathout, J.P. (2007). Closed-loop control of a multi802

mode engine with CAI. In Proceedings of the 2007 IFAC Symposium on Advances in Automotive Control, 495– 502. Franklin, G., Powell, J., and Emami-Naeini, A. (1994). Feedback Control of Dynamic Systems. Addison Wesley Publishing Company, 3rd edition edition. Haugwitz, S., Karlsson, M., Velut, S., and Hagander, P. (2005). Anti-windup in mid-ranging control. In Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference 2005. Olsson, J., Tunestal, P., and Johansson, B. (2001). Closedloop control of an HCCI engine. SAE paper 2001-011031. Ravi, N., Liao, H.H., Jungkunz, A.F., and Gerdes, J.C. (2010). Modeling and control of exhaust recompression hcci using split injection. In American Controls Conference, 2010 (accepted paper). Ravi, N., Roelle, M., Jungkunz, A.F., and Gerdes, J.C. (2006). A physically based two state model for controlling exhaust recompression HCCI in gasoline engines. In Proceedings of the 2006 ASME International Mechanical Engineering Congress and Exposition, 15331. Ravi, N., Roelle, M., Liao, H.H., Jungkunz, A.F., Chang, C.F., and Gerdes, J.C. (2009). Physical modeling and control of a multi-cylinder hcci engine. In Proceedings of the 2009 Dynamic Systems and Controls Conference. Shaver, G., Gerdes, J., Roelle, M., Caton, P., and Edwards, C. (2005a). Dynamic modeling of HCCI engines utilizing variable valve actuation. ASME Journal of Dynamic Systems, Measurement and Control, 127(3), 374–381. Shaver, G., Roelle, M., Caton, P., Kaahaaina, N., Ravi, N., Hathout, J.P., Ahmed, J., Kojic, A., Park, S., Edwards, C., and Gerdes, J. (2005b). A physics-based approach to the control of homogeneous charge compression ignition engines with variable valve actuation. International Journal of Engine Research, 6(4), 361–375. Song, H. and Edwards, C.F. (2008). Optimization of recompression reaction for low-load operation of residualeffected HCCI. SAE World Congress, SP-2182, 79–97. Standing, R., Kalian, N., Ma, T., Zhao, H., Wirth, M., and Schamel, A. (2005). Effects of injection timing and valve timings on CAI operation in a multi-cylinder DI gasoline engine. SAE paper 2005-01-0132. Strandh, P., Bengtsson, J., Johansson, R., Tunestal, P., and Johansson, B. (2004). Cycle-to-cycle control of a dual-fuel HCCI engine. SAE transactions, (2004-010941), 589–598.