Modeling and control of exhaust recompression HCCI using split injection

Transcription

1 American Control Conference Marriott Waterfront, Baltimore, MD, USA June -July, ThB9. Modeling and control of exhaust recompression HCCI using split injection Nikhil Ravi, Hsien-Hsin Liao, Adam F. Jungkunz and J. Christian Gerdes Dept. of Mechanical Engineering, Stanford University Abstract Homogeneous charge compression ignition (HCCI) is currently being pursued as a cleaner and more efficient alternative to conventional engine strategies. This paper presents an approach for modeling the effect of a small pilot injection during recompression on combustion in an HCCI engine with exhaust trapping, and a controller that uses the timing of this pilot injection to control the phasing of combustion. The model is incorporated into a nonlinear physical model presented in previous work that captures the effect of fuel quantity and intake and exhaust valve timings on work output and combustion phasing. It is seen that around the operating points considered, the effect of a pilot injection can be modeled as a change in the Arrhenius threshold, an analytical construct used to model the phasing of combustion as a function of the thermodynamic state of the reactant mixture. The relationship between injection timing and combustion phasing can be separated into a linear, analytical component and a nonlinear, empirical component. A feedback controller based on this model is seen to be effective in tracking a desired load-phasing trajectory and enables steady operation at low load conditions. I. INTRODUCTION Homogeneous charge compression ignition (HCCI) engines provide benefits over conventional engine technologies in terms of both efficiency and 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. Therefore closed-loop control is necessary in order to ensure reliable operation 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 [], [], [], []. Others control the relative proportion of two fuels in a dual-fuel mixture to affect the combustion characteristics [], []. Both these approaches, however, are challenging to implement in mass-produced engines. Fully flexible variable valve actuation (FFVVA) strategies suffer from 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 in practice. Fuel injection, however, offers a viable alternative to these when implemented on an HCCI engine with exhaust trapping/recompression. 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 [7]. Fuel injection quantity and timing, therefore, can be a powerful control knob in influencing HCCI combustion on a cycle-by-cycle basis. Direct fuel injection also provides the added opportunity to control every cylinder of a multi-cylinder engine independent of other cylinders at minimal cost. Near the low-load limit, emissions and stability have both been shown to improve by optimizing the timing of fuel injection [], [9]. The effects of early fuel injection, however, can be complex, and so interest in its use as a control knob has only risen recently. In this paper, an approach for control of HCCI using an early fuel injection around a set of operating conditions is presented. In this operating region, it is seen that the vaporization and pyrolysis of fuel dominate, and there is little fuel reforming or exothermic reaction. The modeling approach is based on a simple physical model of the process that integrates into a control model scheme presented in previous work [], []. A split injection strategy is used, with the injection timing of a small quantity of pilot fuel (mg) used to control combustion phasing, which is modeled with a global Arrhenius reaction rate equation. Combustion can be modeled to begin when the integral of this global reaction rate crosses a threshold value, designated as the Arrhenius threshold. The effect of the pilot injection on combustion is captured as a change in this threshold. A controller based on this model is then used to control the load and phasing of the engine over a range of conditions. Experimental results indicate that even this small of a pilot injection can be a very powerful control knob, and enable control of phasing over a wide load range. In particular, the pilot injection strategy enables steady operation at low loads that are otherwise unstable to operate at. II. MODELING THE EFFECT OF FUEL INJECTION TIMING A. Physical effects of early injection HCCI achieved with exhaust recompression involves closing the exhaust valve early, well before the piston reaches top-dead-center (TDC), thereby trapping a portion of the hot products of combustion within the engine cylinder. This mixture gets compressed and expanded during the recompression stroke. Any fuel injected into the moderately high pressure and temperature environment that exists during recompression can undergo reaction and thereby affect the characteristics of the main combustion event. Fuel injected early in the recompression stroke vaporizes and cools down the mixture. In addition, it can also undergo chemical reaction (especially in the presence of oxygen left over //$. AACC 797

2 Cylinder pressure (bar) Main injection Early injection Cylinder pressure (bar) mg fuel mg fuel Injection quantity(mg) Engine position Injection quantity (mg) 7 Engine position Fig.. In-cylinder pressure, main vs early injection ( engine cycles each) Fig.. In-cylinder pressure, mg vs mg fuel, early injection ( cycles) 7 from the prevoius combustion). Fuel vaporization removes energy from the system. Fuel molecules can then break down into smaller carbon chain molecules (pyrolysis). If there is sufficient oxygen, these smaller chain molecules can also undergo reforming to produce CO and H. Finally, in the presence of sufficient oxygen, there can be exothermic reaction with significant formation of end products. Due to the complex kinetics of the reactions involved, and their sensitivity to the in-cylinder thermal and composition state, different effects are seen to dominate at different operating points. Standing et al. [9] noted that early fuel injection (around exhaust valve closure, EVC) could result in exothermic reactions during negative valve overlap, which were thought to play an important role in affecting the lowload limit of operation. Koopmans et al. [] mentioned exothermic reaction with early injection, but stressed the generation of intermediate species via reforming reactions. Song and Edwards [7], through tests over a wide operating range, show the dominance of both fuel breakdown, and fuel reforming at different operating conditions. As different effects dominate at different operating points, the control of combustion phasing using early injection over a wide range of conditions is a challenging problem. Therefore the modeling effort is focused in an operating region where one of these effects dominates clearly over the others. B. Choice of operating condition The operating region chosen for control was a moderately lean condition where, as shown in [7], the fuel pyrolysis effect tends to dominate. Figure shows the in-cylinder pressure trace for two sets of conditions (at an engine speed of rpm) with constant fueling amount - one where all the fuel is injected at the end of recompression (called main injection), and one where all the fuel is injected early in the recompression stroke (called early/pilot injection). All other inputs (such as valve timings) are kept constant. Five engine cycles are plotted for each case. The early injection case is seen to have a combustion phasing that is about CAD earlier than the main injection case. As HCCI combustion is typically very fast, and occurs over about - CAD, this is a significant advancement of phasing. This causes a much higher peak pressure. However, the peak pressure during recompression is lower for the early injection case, which Fig.. CA Main injection timing: CAD Main injection quantity: 9mg Pilot injection quantity: mg 7 9 Pilot injection timing Variation of combustion phasing (CA ) with pilot injection timing indicates that the charge-cooling and fuel-breakdown effects (which are both endothermic) dominate. This is further confirmed by the results shown in Fig., where two cases are compared, both with early fuel injection, but with different quantities of fuel (mg vs mg). The top plot shows the in-cylinder pressure, while the bottom plot shows the injection timing and quantity for each case. The mg case has a much higher peak pressure (and expansion polytrope) due to more energy content, but has a lower (and earlier) recompression peak, which again indicates greater endothermicity than the mg case. Furthermore, it was seen that even a small quantity of fuel injected during the recompression stroke could have a significant effect on the phasing of combustion. Figure shows variation of combustion phasing with the timing of a mg pilot injection, with 9mg injected during the main injection, at the end of recompression ( CAD). All crank angles are referenced to deg at TDC, combustion. Such a strategy is referred to as a split injection strategy. A sweep of the pilot injection timing between and 9 CAD commands a combustion phasing range of about 7 CAD, which represents most of the desirable phasing range for HCCI. This testifies to the power of pilot injection as a cycleby-cycle control input. The shape of this curve is quite characteristic of the physical processes that govern recompression reactions. As the injection timing gets later and later, the conditions in the engine cylinder during injection become more like the conditions during a simple main injection. The residence time of the fuel, or the time available to it to react during recompression is very small. Therefore the effect on combustion phasing is minimal at very late pilot injections. At the other extreme, as the fuel is injected very early in the recompression stroke, the marginal effect on phasing is again 79

3 small because beyond a point, there is little to be gained by allowing the fuel a longer residence time. Therefore the pilot injection has maximum control authority in the mid-region, where the relationship with phasing is approximately linear. Based on the above results, a split injection strategy was chosen as an effective control knob for HCCI. A physical model was developed assuming that the dominant effect was the breakdown of fuel into smaller C-chain molecules. C. Incorporation into existing model structure In previous work [], a nonlinear physical model that captures the basic dynamics of the HCCI process has been presented. This model was linearized about an operating point and shown to be useful for the development of controllers that could be used to control the work output and combustion phasing on a cycle-by-cycle basis on both a single and multi-cylinder engine. The primary control inputs used were the quantity of fuel and the intake and exhaust valve timings. The current effort focuses on expanding this model to include the effect of a split injection strategy. The existing model is a nonlinear dynamic model with four states. The states are given by x k+ = G(x k, u k ) y k = H(x k ) () ) Concentration of oxygen at a fixed location after IVC (θ s ), [O ] s,k ) Temperature of mixture at θ s, T s,k ) Concentration of fuel at θ s, [f] s,k ) Cylinder volume at intake valve closure, V IV Cs,k 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. Every engine cycle (indexed by k), therefore, is assumed to begin at this fixed crank angle location. The main outputs of this model are the phasing of combustion (measured in terms of the crank angle location where % of the energy from combustion is released, CA ) and the net work output (measured in terms of the net mean effective pressure, NMEP, which is a ratio of net work per cycle to cylinder volume displaced per cycle). The outputs are controlled using three inputs: ) Total moles of fuel injected in the current cycle, n f,k ) Cylinder volume at intake valve closure, V IV C,k and ) Cylinder volume at exhaust valve closure, V EV C,k This model assumes that the fuel is all injected at the end of the recompression stroke (during induction) and so does not consider the effect of a split injection strategy. A complete description of this model can be found in [], []. Combustion phasing is modeled with a global reaction rate equation is used as the basis for the development of the combustion phasing model. The reaction rate is a function of temperature and reactant concentrations. RR = A th e ( Ea RuT ) [fuel] a [O ] b () where E a is the activation energy and A th is a preexponential factor. Integrating this global Arrhenius rate equation from the point of state definition to the point of combustion gives an expression of the form θth,k A ( Ea the RuT ) [C7 H ] a [O ] b RRdt = dθ () ω θ s where θ th,k is the crank angle location at start of combustion. When the integral in Eqn. () crosses a threshold, K th, combustion is modeled to have begun. For a particular fuel, the values of A th, E a and K th are fixed. The integral can be condensed into a map that gives the phasing of combustion as a function of the reactant concentrations and temperature at the point of state definition. θ th,k = F([O ] s,k, T s,k, [f] s,k ) () The duration of combustion in HCCI is a strongly monotonic function of the phasing of combustion []. Here this duration, θ durn,k is approximated as a simple affine function of the start-of-combustion crank angle location, θ,k. This approximation is seen to be valid around an operating point. The CA, then, can be calculated as CA,k = θ th,k +.θ durn,k () When fuel is injected early in the recompression stroke, however, it breaks down into smaller C-chain molecules. These small molecules have a shorter ignition delay than heavier gasoline molecules. This leads to the advancing of phasing during the main combustion. A simple way of modeling the net effect within the existing model structure would be to lump all these changes into the Arrhenius threshold value, K th. 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. The relationship between pilot injection timing (or alternately, pilot fuel residence time during recompression) and combustion phasing can therefore be broken down into two separate relationships: ) A relationship between Arrhenius threshold (K th ) and the phasing of combustion (CA ) ) A relationship between fuel residence time (t res ) and the Arrhenius threshold D. The relationship between Arrhenius threshold and CA The relationship between CA and the Arrhenius threshold, K th already exists within the existing model structure. However, K th is treated as a constant in the model. With pilot injection, this now becomes variable on every cycle, based on the commanded injection timing. θ th,k = f ([O ] s,k, T s,k, [f] s,k, K th,k ) () Therefore, an additional state, K th is needed to capture the effect of pilot injection timing on the thermochemical state 799

4 CA Main injection quantity: 9mg Pilot injection quantity: mg Arrhenius threshold value Arrhenius threshold value Main injection quantity: 9mg Pilot injection quantity: mg. 7 9 Fuel residence time (ms) Fig.. Relationship between Arrhenius threshold and combustion phasing Fig.. Relationship between Arrhenius threshold and fuel residence time of the in-cylinder mixture before combustion. The full state, input and output vectors are now given by [O ] s T s n f x k = [f] s, u k = V EV C V IV Cs V IV C, y k = CA,k (7) u K th th k k As the oxygen and temperature states on cycle k + are a function of the combustion phasing on cycle k, Eqn. () implies that [O ] s,k+ and T s,k+ also depend on K th,k. The Arrhenius threshold state, however, is only affected by the pilot injection timing input on the previous cycle. This input can be abstracted to a threshold input, u th, based on the relationship between the Arrhenius threshold and the pilot injection timing (described in the next section). Therefore K th,k+ = u th,k. Incorporating this into the model, and then linearizing about an operating point gives a new set of linear system matrices. x k+ = Ax k + Bu k, y k = Cx k () The last three states have no dynamics of their own, but are purely dependent on the inputs on the previous cycle (respectively, n f, V IV C and u th. 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, u th - 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 that smaller fuel molecules have on it. 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. Figure shows the relationship between the analytically calculated combustion threshold and the measured combustion phasing on an engine testbed. As seen, this relationship is linear over the entire range of injection timings considered. The slope of this curve, then, represents the element of the C-matrix that relates CA,k to K th,k. This validates the assumption made in linearizing Eqn. () as part of the linear state-space model. This linear system can now be used to develop a linear controller, that would command a specific Arrhenius threshold, u th for a desired phasing of combustion, CA. The next step is to be able to determine the relationship between this threshold, and the physical input, the pilot fuel injection timing. E. The relationship between fuel residence time and Arrhenius threshold Pilot injection timing, or pilot fuel residence time can be abstracted into the Arrhenius threshold using steadystate engine data, and the Arrhenius map given in Eqn. (). The model is first parameterized at a particular operating condition with all the fuel injected during the main injection. Sweeping out a range of pilot injection timings, and inverting the Arrhenius map for each measured value of CA then gives the corresponding u th value for each value of injection timing/fuel residence time. This gives the functional relationship between the fuel residence time and the Arrhenius threshold input. u th,k = f (t res,fuel ) (9) The residence time here is calculated as the time between the end of the pilot injection, and CAD (which is the end-of-injection timing for the main injection). Hence a main injection would have a residence time of zero for recompression reactions, while an earlier injection would have more time. It is also assumed as before, that the threshold input does not affect the oxygen and temperature states. This allows an inversion of Eqn. () at fixed [O ] s and T s. The steady state relationship in Eqn. (9) can now be used to relate the control input from the linear model, u th on every engine cycle to the physical input, t res,fuel or injection timing. Figure shows the relationship between the threshold and the fuel residence time input calculated from experimental steady-state data as described above. This function can be approximated by a polynomial curve as shown.

5 F. Model summary The overall model relating pilot injection timing to the phasing of combustion is shown conceptually in Eqn. (). t res,fuel u th CA () The fuel residence time, therefore, is related to the phasing through the Arrhenius threshold which is an analytical construct. The model therefore has two distinct parts. ) CA,k = f ([O ] s,k, T s,k, [f] s,k, u th,k ), the relationship between the Arrhenius threshold and the phasing of combustion. This relationship is in the form of a linear, five state model. ) u th,k = f (t res,fuel ), the relationship between the Arrhenius threshold and the fuel residence time. This relationship is obtained through steady state experiments, and is described by a nonlinear function. The data presented suggests that the nonlinear relationship between fuel injection timing and combustion phasing is an input nonlinearity that can be separated from the state description. A simple linear controller can be used to generate a desired combustion threshold, which can then be related to a commanded fuel residence time through the nonlinear relation f. This separability also means that differing behavior in other operating regimes could all potentially be incorporated into the function f, while leaving the linear model intact. III. CONTROLLER DEVELOPMENT The linearized model is used as a platform for controller development. The model states (oxygen concentration and temperature) are not directly measurable in practice. Therefore a Luenberger observer is used to estimate the state values based on a measurement of combustion phasing. In previous work, it has been shown that the two outputs, NMEP and CA can be controlled separately with the fuel quantity and valve timings respectively []. This is because the NMEP is a strong function of the total fuel injected into the cylinder within a range of combustion phasing. CA, on the other hand, has a negligible dependence on the fuel quantity injected on the same cycle. This observation can be extended to the case of pilot injection, where the timing of the injection can be used to control CA, and total fuel quantity used to control NMEP. A simple feedforward-feedback controller is used to control the NMEP. A map relating fuel quantity to NMEP derived empirically is the feedforward portion of this controller. In general, NMEP also depends on combustion phasing - however, for the range of CA considered here, it is fuel quantity that has the dominant effect on NMEP. A closed-loop integral controller is then added to correct this map in feedback to get the exact NMEP desired. This controller is used to vary the quantity of fuel injected during the main injection (at a fixed timing of CAD) while keeping the pilot injection quantity fixed at mg (but at a varying timing controlled by a model-based feedback controller described below). To control the phasing with injection timing, the fuel and injection timing inputs need to be separated out in the linear model. x k+ = Ax k + B u k + B u k () where u k = n f,k, which is commanded by the NMEP - fuel map controller, and u k = V IV C,k V EV C,k, which is used u th,k to control the combustion phasing. A reference input is used as described in []. The matrices N x and N u are defined such that in steady state, the output follows the reference, with a corresponding reference state value. N x r = x ss, N u r = u ss The control input, then, is of the form u k = K x (x k x ss ) + u ss = K x x k + (N u + K x N x )r k () where r is the reference input (representing the desired output trajectory) and K x is the controller gain matrix. Control gains are selected such that only the Arrhenius threshold input, u th is used, while the valves are kept fixed. IV. EXPERIMENTAL RESULTS The controller is implemented on a multi-cylinder HCCI engine. The test conditions for the results presented here are given in Table I. TABLE I TEST CONDITIONS Parameter Value Units Engine speed rpm IVO CAD IVC 7 CAD EVO CAD EVC CAD Main injection quantity Controlled mg Main injection timing CAD Pilot injection quantity mg Pilot injection timing Controlled CAD Figure shows a step change of bar in desired NMEP at constant phasing. The particular choice of the desired combustion phasing for these tests was a moderate-phasing point (as HCCI exhibits undesirable behavior at either very early or very late phasing). The results are plotted for all four cylinders. All the cylinders maintain their timing over the step change, and track the desired work output trajectory exactly. The controller delays the pilot injection timing to compensate for the advanced phasing that a greater amount of fuel injection would cause. As seen, all the cylinders converge to the same steady-state outputs. The fuel quantity input for one of the cylinders is seen to be less than the others, which is an anomaly that disappeared after later calibration. The controller works effectively over a wide range of load conditions at this engine speed - from as low as about. bar to as high as.7 bar. Figure 7 shows the controller

6 CA Injection timing NMEP (bar) Total fuel (mg) Cyl Cyl 7 Desired 7 7 Cyl Cyl 7 Time (s) Fig.. Experimental control results - feedback + feedforward + integral controller (dotted line - desired trajectory, solid line - actual trajectory) NMEP (bar) CA Injection timing Total fuel (mg) Time (s) Fig. 7. Experimental control results - controller range (dotted line - desired trajectory, solid line - actual trajectory) response to a series of step changes. The results are plotted for one of the four cylinders (response on other cylinders is similar). The controller is seen to be very effective at low load conditions, and shows promise in terms of expanding the operating range of HCCI on the low load end. The combustion is seen to be more variable at lower loads, but the controller still ensures stable operation. In practice the range of the injection timing input is limited at fixed valve timing due to the saturation seen in Fig.. Therefore operation over a wider range of conditions would require coordinated control of both valve timings and the pilot injection timing. Such a coordinated control strategy is the subject of current work. V. CONCLUSION HCCI as a combustion technology hold great promise and yet presents several control challenges that need to be surmounted before implementation on mass-produced automobiles. As demonstrated in this paper, the use of fuel injection as a control knob represents a simple way of controlling HCCI combustion on a cycle-by-cycle basis over a range of load conditions. Fuel quantity can be used to control load, while the timing of a small pilot injection can be used to control the phasing of combustion. The effects of fuel injection during recompression as a whole are complex, and so around a set of operating conditions, it was assumed that the effect of a small pilot injection was dominated by pyrolysis. This pyrolysis effect was modeled as a change in the Arrhenius threshold, a construct used to model the phasing of combustion using a global reaction rate. This model fits into the existing model structure presented in earlier work, and allows a separability of the injection timing effect into a linear and nonlinear component. This separability could be advantageous for the application of this model to other operating regimes of HCCI. A tracking controller developed on the basis of this model is seen to be highly effective in tracking desired load-phasing trajectories. The controller is also able to sustain HCCI at low loads. As each engine cylinder has its own direct injector, the injection of pilot fuel can be a powerful control knob for balancing cylinder differences. Its high speed of response also implies the possibility of cycle-by-cycle control of HCCI at minimal cost. REFERENCES [] Agrell F., H-E. Angstrom, B. Eriksson, J. Wikander, and J. Linderyd. 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