Controlling Cyclic Combustion Variations in Lean-Fueled Spark-Ignition Engines

Transcription

1 Controlling Cyclic Combustion Variations in Lean-Fueled Spark-Ignition Engines C. S. Daw*, J. B. Green, Jr.*, R. M. Wagner*, C. E. A. Finney*, L. I. Davis**, Jr., L. A. Feldkamp**, J. W. Hoard**, F. Yuan**, and F. T. Connolly** *Oak Ridge National Laboratory, National Transportation Research Center, 236 Cherahala Boulevard, Knoxville, Tennessee **Ford Research Laboratory, Dearborn, Michigan Abstract. Under conditions of lean fueling or high exhaust gas recirculation, interactions between residual cylinder gas and freshly injected fuel and air produce undesirable combustion instabilities in spark-ignition engines. The resulting dynamics can be described as noisy bifurcations of a nonlinear map and are complicated by cylinder-to-cylinder coupling. We discuss the key dynamic features relevant to control and demonstrate simple feedback control of a multi-cylinder test vehicle. INTRODUCTION Cycle-by-cycle combustion variations (CV) can be particularly severe in sparkignited, internal combustion engines for lean air-fuel mixtures (i.e., when the ratio of air to fuel is greater than required by chemical stoichiometry) or for high levels of exhaust gas recirculation (EGR). CV is a problem because it increases engine roughness, decreases fuel efficiency, and produces excessive emissions of unburned hydrocarbons. Up to now, the approach for minimizing CV has been to simply avoid operating conditions where it occurs. In the current regulatory climate, however, lean fueling and high EGR are needed to reduce nitrogen oxide emissions. Thus there is strong interest in understanding and controlling the CV phenomenon. Grunefeld et al. [1] discuss deterministic fluid dynamic effects during engine intake and exhaust strokes and conclude that they are dominant contributors to CV. The importance of the residual cylinder gas (both composition and amount) has also been recognized and is generally regarded as the cause of the frequently observed alternating pattern of high and low work output cycles, although other mechanisms have been proposed [2]. Stevens, Shayler, and Ma [3] considered CV from the standpoint of understanding the mechanism well enough to effect a reduction in the variation by imposing control. They found that significant correlation exists between consecutive firings of a particular cylinder, and that various measurable quantities of combustion intensity, such as indicated mean effective pressure, are subject to reasonable prediction one cycle in advance. These authors also considered various means of imposing control, such as through changes of spark timing and fuel delivery.

2 In previous publications (see for example, [4-6]), we presented evidence for a dominant (but noisy) period-doubling bifurcation that develops during lean fueling. The visibility of low-dimensional period doubling is remarkable when one considers the complexity of internal combustion engines and the high-dimensional inputs (e.g., turbulent mixing in the cylinder). In this paper we focus on improved characterization of the low-dimensional dynamics and linking those dynamics to engine control. EXPERIMENTAL EQUIPMENT AND PROCEDURES The experiments reported here were done with three different types of engines: 1) a single-cylinder Cooperative Fuel Research (CFR) engine; 2) a four-cylinder 2.3-liter General Motors (GM) Quad-4 engine; and 3) a 4.6-liter V8 Ford engine used on both the Expedition and Grand Marquis vehicles. Common features of all of these engines include throttled intake, spark ignition, and individual port fuel injection. For the first two engines, lean-fueling combustion dynamics were studied with the engines mounted on test stands and connected to dynamometers. Fuel-to-air ratio was adjusted only with injected fuel pulse width, and throttle position was held constant to minimize changes to the air intake dynamics. Spark timing was set at stoichiometric fueling to achieve minimum ignition advance for maximum brake torque and minimum variance and was then held fixed at all fueling conditions investigated. The CFR dynamometer had both absorbing and motoring capability, allowing us to maintain a constant speed. The Quad-4 dynamometer had absorbing capability only, so that speed could only be maintained by reducing frictional load as the amount of fuel relative to inlet air was reduced. Nominal operating conditions for the CFR engine were 1 rpm and a spark advance of 27? before top dead center (BTDC). Nominal operating conditions for the GM engine were 12 rpm and a spark advance of 23? BTDC. The CFR residual cylinder gas fraction was varied by throttling the exhaust (i.e., more exhaust back pressure decreases the pressure ratio of intake to exhaust and increases the residual gas fraction). This allowed us to directly observe the effects of residual gas on the bifurcation dynamics. Two different V8 engine configurations were used, one test-stand-mounted and one vehicle-mounted. Each of these engines was of the same basic type but not completely identical. Specifically, the test-stand engine was configured for a recent edition Ford Expedition (a sport utility vehicle), while the vehicle engine was installed in a 1994 Grand Marquis (a large sedan). The test-stand configuration included an absorbing/motoring dynamometer to maintain constant speed, and fueling adjustments were made by manipulating both throttle position and fuel injection to maintain constant torque. Nominal test-stand conditions for all fueling levels were 12 rpm, 25 N-m torque, and 2? BDTC spark timing. The vehicle experiments were conducted with the engine idling 4-7 rpm (automatic transmission set in park position) at constant throttle and a constant nominal fuel-to-air equivalence ratio of.7 (with no EGR). While the objective of the test-stand experiments was to study the dynamic behavior of eight cylinders in detail, the vehicle experiment focused on demonstrating simultaneous feedback control implementation in eight cylinders using existing sensors and reprogramming of the electronic engine control (EEC) computer.

3 In all test-stand experiments, pressures in each cylinder were recorded at the rate of once per crank angle degree. Pressure data were later converted to integrated combustion parameters including net heat release (HR) and indicated mean effective pressure (IMEP) [7]. Whenever engine settings were changed (e.g., fuel adjustments made), data recording was delayed until the engine stabilized (i.e., reached steady state ). All engine feedback controllers were shut off to minimize non-combustion artifacts, and operation was entirely open loop except for the dynamometer speed controllers. Data set sizes for one operating condition on the CFR and Quad-4 engines typically included 1, and 3, engine cycles, respectively. Data sets for the teststand V8 were typically limited to 35 engine cycles (all eight cylinders recorded simultaneously) by the memory of the data acquisition system. Because of this limitation, multiple 35-cycle blocks were collected at each operating condition. Measurements of the vehicle-mounted engine were made using standard sensors available on the car. Specifically, we used existing measurements from the crankshaft position encoder that produces a timing interval (the so-called PIP interval) to estimate changes in crankshaft acceleration. With the proper care, it is possible to correlate crankshaft acceleration to the corresponding energy release from each combustion event. This correlation allowed us to use estimated crankshaft speed fluctuations as a surrogate for direct combustion measurements. Based on the surrogate combustion measurements, cycle-by-cycle adjustments were then made to the fuel injection pulse to offset combustion instabilities. As described later, the successful implementation of control (by means of reprogramming the EEC computer) required overcoming complex interactions among the cylinders as well as constraining the net effect of all the control actions to leave the total mean fueling level unchanged. The only nonstandard equipment in the vehicle experiments was a second interfacing computer, which was used to program and record output from the on-board EEC computer. As with the test stand, computer memory only allowed recording of approximately 35 contiguous cycles from all cylinders. Thus, repeated blocks of 35 cycles were recorded to improve statistics and gain information about long-term behavior. EXPERIMENTAL RESULTS AND DISCUSSION The primary experimental data for all test-stand experiments consisted of heat release time series for each cylinder at each operating condition. For the vehicle experiments, the primary data were estimated crankshaft acceleration time series. In the following discussion we describe the test-stand experimental results and then describe how feedback control was implemented in the vehicle. CFR and Quad-4 Test Stand Experiments Typical return maps for combustion heat release in the single-cylinder CFR engine are shown at four different fuel-to-air ratios in the top row of panels in Fig.1. As has been reported previously, the heat release pattern near stoichiometric fueling appears as a noisy fixed point on the diagonal, and a characteristic bowed pattern of scattered points develops as the fuel-to-air ratio decreases. This transformation progresses

4 through a series of modified bow shapes with increasingly lean fueling until finally, another noisy fixed point is reached and combustion is shut down. For purposes of predictive control, we assume there is an underlying nonlinear map dominating the observed cycle-to-cycle heat release variations similar to our previously proposed physical model [5]. We are inspired by numerical experiments with this model, which demonstrate that the noise-free dynamics can be reconstructed by appropriately averaging noisy realizations of the return map. We want to increase the generality of our method, however, by not assuming a priori that our experimental data will be completely consistent with this specific model. Instead we want to use empirically derived maps that minimize model assumptions. Based on the success of our model studies, we attempted to reconstruct approximations of the experimental maps by two methods: 1) least-square fitting of the observed heat release pairs to simple polynomial functions (i.e., HR(i+1) = f[hr(i)] = a + b*hr(i) + c*hr(i) 2 m*hr(i) n ) and 2) dividing the values of HR(i) into discrete bins and determining the average corresponding value of HR(i+1). In the first method, the appropriate polynomial order is determined by fitting the data with increasingly higher-order polynomials until the goodness of fit reaches a plateau. Typically, we find that the best polynomial order is 4-7, which is consistent with our numerical model studies. From the second method, we also obtain an estimate of map uncertainty based on the dispersion of the HR(i+1) values around the mean value. Example fitting results are illustrated in the bottom two rows of panels in Fig. 1. The second row depicts results from polynomial fitting of the data in the top row, while the third row illustrates results from bin averaging. Both methods appear to give consistent results. Even though there is considerable noise in the original data, the general features of these estimated maps are similar to the noise-free version of our physical model [5]. Two interesting characteristics are shown in the two lower rows. First, stable fixed points for the noise-free maps are plotted as dark circles in the second row, illustrating a transition from period-1 to period-2 and then back toward period-1 at the leanest condition. Second, the estimated maps show a peak in HR(i+1) at low values of HR(i) and a sharp decline in HR(i+1) at lower HR(i). This latter feature is more prominent for experimental data than for our physical model. Similar plots are shown in Fig. 2 for conditions where the residual in-cylinder gas fraction is increased. Comparing Fig. 2 with Fig.1, we observe, as expected, that higher residual fraction increases the degree of bifurcation at a given fuel-to-air ratio. Likewise, it is apparent that noise-free dynamics with higher-order periodicities and possibly chaos are possible. The latter can be seen more clearly in Fig. 3(b), which is an estimate of the low-dimensional component of the experimental bifurcation sequence shown in Fig. 3(a). The noise-free version of the bifurcation sequence was produced by estimating the noise-free map at each fueling level from 5 pairs of observed heat release values. Compared with Fig. 3(c), which is the noise-free bifurcation sequence predicted by the physical model, we note that the relative fueling range over which higher-order periodicities and chaos occur experimentally is larger than predicted by the model. This difference suggests that control strategies should be able to handle more complex behavior than simple periodic oscillations.

5 9 9 9? =.66? =.68 9? =.7? = FIGURE 1. Heat release return maps for the single-cylinder CFR engine operating with a residual gas fraction of.9. Top row is raw data. Middle row is polynomial fit with stable fixed points indicated as solid circles. Bottom row is binned fit with 95% confidence limits ? =.68? =.7? =.72? =.74 9 FIGURE 2. Heat release return maps for the CFR engine operating with a residual gas fraction of.16. Top row is raw data. Solid circles indicate fixed points of fitted map.

6 (a) (b) (c) FIGURE 3. Bifurcation diagrams for the single-cylinder CFR engine operating with a residual gas fraction of.16. Part (a) is original experimental data; part (b) is reconstruction from polynomial map approximations; part (c) is physical model prediction without parametric noise. Further analysis of the model and map differences has confirmed that the model assumptions are inadequate to account for the effect of reduced in-cylinder temperature on subsequent combustion events. Interestingly, this effect is only apparent in the map shape in the lower 1-15% of the heat release range, and yet this small difference in shape seems to be the major cause of more rapid experimental bifurcation. While an improved physical model can provide additional fundamental insight, it is also clear that empirically derived maps should be suitable for control. Figure 4 illustrates experimental return maps and fitted functions for multi-cylinder data from the Quad-4 engine. Here we observe that, although the same nominal amount of fuel is fed to each cylinder, there is clearly a varying degree of bifurcation. This cylinder-to-cylinder difference reflects the intake air imbalance problem common to all multi-cylinder engines. Due to inevitable differences in the path between each cylinder and the air intake manifold, there is always some air imbalance at any given operating condition. As engine speed and load change, complex flow dynamics and acoustic interactions shift air distribution in unpredictable ways. Because fuel injection occurs in the intake port to each cylinder, air-fuel mixing is also uneven. Thus it may not generally be possible to predict a priori how individual cylinders will differ. For the condition in Fig. 4, it appears that the cylinders farthest from air intake (cylinders 3 and 4) receive the least amount of air. There also appear to be differences in the level of parametric noise experienced by each cylinder. V8 Test-Stand Experiments Typical return maps for lean fueling in the test-stand-mounted V8 engine are illustrated in Fig. 5. Note again the considerable variation from cylinder to cylinder. Simultaneous measurements of all cylinders also permitted investigation of possible cylinder-to-cylinder interactions (i.e., synchronization). One approach we used for synchronization detection was cross correlations between cylinder pairs as illustrated in Fig. 6(a). For one pair (cylinders 1 and 5), a positive correlation developed when the as-injected fuel-to-air equivalence ratio was decreased to.66. Likewise, a strong anti-correlation developed for the cylinder pair 1-3. There was little or no correlation for the pairs 1-6 and 2-6. When all cylinders are bifurcated to some degree, one expects occasional apparent correlations or anti-correlations due to chance.

7 7 Cylinder 1 Cylinder 2 Cylinder 3 Cylinder FIGURE 4. Heat release return maps for the GM Quad-4 engine with a fuel-to-air ratio of.586. Top is raw data. Bottom is polynomial approximation. Solid circles indicate fixed points of fitted map , J 4 4, J FIGURE 5. Heat release return maps for the test-stand-mounted V8 engine at a fuel-to-air ratio of? =.66. Numbers in panels refer to physical location of cylinder. Firing order was In this case, the cross-correlation plot was averaged for three discontinuous segments of 35 cycles, making the likelihood of a chance artifact remote. Additional analyses of many similar simultaneous data sets compared to truly independent heat release series provide convincing evidence for persistent positive and negative correlations between cylinders. We find that symbolic methods are also useful for discerning synchronization. In one version of this approach, heat release values from each cylinder are converted into 1-bit symbols (i.e., or 1) based on whether each value falls above or below the median for that cylinder. Symbol "words" (i.e., short symbol sequences loosely analogous to time-delay embedding vectors) are then constructed according to:

8 S2(j) = [X(j-1), Y(j-1), X(j), Y(j), X(j+1), Y(j+1)] (1) where S2(j) is the symbolic "state" of the cylinder pair at engine cycle j, and X(j) and Y(j) are the symbolic heat release values at cycle j for the first and second cylinder pair members, respectively. For convenience, we refer to each particular symbol sequence according to a unique index number between and 63 and defined by: Index(S2) = X(j-1)*32 + Y(j-1)*16 + X(j)*8 + Y(j)*4 + X(j+1)*2 + Y(j+1) (2) Figure 6(b) illustrates a "synchrogram" from above scheme for two selected cylinder pairs. Engine cycle number is on the horizontal axis, while the current sequence index number is on the vertical axis. When combustion oscillations develop in both cylinders, peaks typically appear at sequence indices 12, 25, 38, and 51, respectively corresponding to symbol sequences [,,1,1,,], [,1,1,,,1], [1,,,1,1,], and [1,1,,,1,1]. When the cylinders remain unsynchronized, the heights of these target peaks occur with equal probability and there is no persistent relationship between the cylinders. However, when the cylinders become synchronized (Fig. 6(b)), peaks 12 and 51 (for correlated behavior) or peaks 25 and 38 (for uncorrelated behavior) become persistently dominant. As seen in Fig. 6(b), patterns of correlation or anti-correlation can persist for long periods. Cross Correlation (F-,F-1) (F-,F-4) (F-,F-5) (F-3,F-4) Sequence Index (a) Equivalence Ratio Cycle Number FIGURE 6. Cross correlation (a) between selected pairs of cylinders in the stand-mounted V8 engine as fuel-to-air ratio is changed. Symbol synchrogram (b) illustrating a predominantly anti-correlated cylinder pair in the test-stand-mounted V8 engine at?=.66. Persistent dark bands indicate synchronization. From observations over many experiments, we have observed that synchronization occurs simultaneously with the onset of bifurcations in two or more cylinders. When one cylinder becomes strongly bifurcated, it can act as a "driver", stimulating other cylinders to bifurcate. The most easily recognizable form of synchronization is when pairs of cylinders develop persistent correlation or anti-correlation with each other. Synchronization appears to occur episodically, so that a certain patterns can persist for long periods and then suddenly shift to a different pattern. The mechanisms for 1 (b)

9 cylinder-to-cylinder coupling are not well understood, but it appears that acoustic and flow effects in the intake and exhaust air manifolds and fuel spillover (described later) are all involved. V8 Vehicle Experiments Figure 7 illustrates typical uncontrolled crankshaft acceleration return maps for all cylinders in the Grand Marquis when the engine was idling at a fuel-to-air equivalence ratio of.77. The labels Sync, Sync 1, etc. refer to the temporal firing order of the cylinders. The average acceleration due to all cylinders is depicted in the center return map and the time series at the bottom. Even though crankshaft acceleration measurements are less accurate than direct combustion measurements, they appear to be quite adequate for detecting combustion bifurcations. As with previous multicylinder observations, there is considerable variation from cylinder to cylinder. It appears that some of the cylinders (e.g., 5, 6, and 7) are fully bifurcated into a noisy period-2 condition. One or two of the cylinders (e.g., 1 and 4) appear to be even further bifurcated, possibly into higher-order periodicities or chaos. A simple (but naïve) approach for controlling combustion oscillations is to perturb the fueling for each cylinder to be out of phase with dominant high-low combustion fluctuations. Thus if the current acceleration is low, one anticipates that the next acceleration will be high and reduces the fueling by an appropriate amount. If one targets the period-1 fixed point as the control objective, the simplest strategy would be to make the fueling adjustments proportional to the current deviation. The only major constraint needed would be to make sure that the overall fueling perturbations sum to zero so that the average fuel-to-air ratio remains unchanged. Our experience shows that, unfortunately, such a simple approach is not effective because of cylinder-tocylinder interactions. Typical experimental results are illustrated in Fig.8 where the variation in rms crankshaft speed for the Grand Marquis is plotted against the magnitude of the applied (anti-correlated) feedback gain. As the gain is increased from zero, the rms magnitude continues to increase, indicating that this control increases combustion instability. We now understand that a more sophisticated approach is needed for multi-cylinder control. It is well known that fuel injection to one cylinder can influence other cylinders through the so-called spillover effect. Spillover is due to the considerable fraction of injected fuel that wets the walls of the intake port and does not become completely vaporized and inducted into the intended cylinder. This residual fuel then becomes available for induction into successively fired cylinders and creates an unintended fuel spike in those cylinders. Also, because the cylinders tend to synchronize, one must be careful that the control actions themselves don t become globally correlated. For an improved control strategy, we developed a modified prediction for the next acceleration event for each cylinder based on consideration of the current acceleration, the previous fueling perturbation, and the previous fueling perturbations made to all the other cylinders. The form of this prediction is: A i (k+1) = a*a i (k) + b i *? f i (k+1) + b i-1 *? f i-1 (k) + b i-2 *? f i-2 (k) b i-7 *? f i-7 (k) (3)

10 FIGURE 7. Return maps for crankshaft acceleration in uncontrolled vehicle-mounted V8 engine.

11 FIGURE 8. Effect of simple proportional feedback on overall engine speed variations in the test vehicle. Minimum fluctuations occur for zero feedback gain (i.e., no control). where A i (k) is the acceleration in cylinder i for cycle k,? f i (k) is the fueling perturbation made to cylinder i during cycle k, and the a and b i b i-7 are empirically determined coefficients reflecting the single-cylinder map and spillover response, respectively. When we wish to determine? f i (k+1) for any given cylinder, we have the previous acceleration in that cylinder (A i (k)), all the previous fuel perturbations made up to that moment (? f i-x (k)), and the target acceleration for the unstable period-1 fixed point (A i (k+1)). The above equation can then be solved directly to obtain? f i (k+1). To guard against control synchronization, we monitor the net acceleration phase (determined from the difference between the current acceleration and a running average of accelerations) averaged over the past eight events. An additional negative feedback correction is then applied to the initial fueling perturbation determined from Eqn. (3) (i.e., a further adjustment is made to offset global system oscillations). This correction also helps keep the average fueling level constant. We have confirmed that, without this negative feedback, large global oscillations inevitably result. The effectiveness of the improved feedback scheme is illustrated in Fig. 9. Now we observe a marked decrease in the combustion oscillations and engine speed fluctuations. We believe this degree of improvement is impressive considering that a single feedback gain has been used for all cylinders and no attempt has been made to explicitly account for the cylinder-to-cylinder differences. Figure 1 further illustrates the effect of the feedback gain on engine speed. Unlike the previous strategy (Fig. 8), there is now a clear minimum rms achieved for a finite feedback. (Note that a global rms minimum occurs for Gp =1., but this is not a desirable condition because some of the cylinders are completely shutdown). We expect that greater improvements are possible with adjustable gains for each cylinder and/or additional control actions that remove time-average cylinder imbalance. These results demonstrate that active control is clearly possible for the combustion instabilities in lean-fueled spark-ignition engines. Additional issues need to be addressed for commercial implementation including the large cylinder-to-cylinder differences that occur in multi-cylinder engines, the highly transient conditions under which most engines actually operate, and the use of other sensor measurements as control inputs (e.g., measurements of cylinder coupling and parametric noise).

12 FIGURE 9. Return maps for crankshaft acceleration in vehicle-mounted V8 engine using more sophisticated feedback control strategy.

13 Max Min Average FIGURE 1. Effect of more sophisticated feedback strategy on engine speed variations in the test vehicle. The bottom and top lines correspond to the best and worst cylinders, respectively. Minimum variations occur at a feedback gain of ACKNOWLEDGMENTS This work was funded by the U.S. Department of Energy and Ford Motor Company under Cooperative Research and Development Agreement ORNL DISCLAIMER This manuscript has been authored by a contractor of the U.S. Government under contract No. DE-AC5-OR Accordingly, the U.S. Government retains a nonexclusive, royalty-free license to publish or reproduce the published form of this contribution, or allow others to do so, for the U.S. Government. REFERENCES 1. Grunefeld, G., Beushausen, V., Andresen, P., and Hentschel, W., A major origin of cyclic energy conversion variations in SI engines, Society of Automotive Engineers (SAE) Technical Paper No (1994). 2. Hancock, M.S., Buckingham, D.J., and Belmont, M.R., The influence of arc parameters on combustion in a spark-ignition engine, SAE Technical Paper No (1986). 3. Stevens, S.P., Shayler, J., and Ma T.H., The impact of combustion phasing on cycle-to-cycle performance of a spark ignition engine, SAE Technical Paper No (1995). 4. Daw C.S., Finney, C.E.A., Kennel, and Connolly, F.T., Cycle-by-Cycle Combustion Variations in Spark-Ignited Engines, in Proceedings of the 4 th Experimental Chaos Conference, edited by M. Ding, W. Ditto, L. Pecora, M. Spano, and S. Vohra, World Scientific, Singapore, 1998, pp Daw, C.S., Kennel, M.B., Finney, C.E.A., and Connolly, F.T., Phys. Rev. E, 57:3, pp (1998). 6. Wagner, R.M., Drallmeier, J.A., and Daw, C.S., Int J Engine Research, 1:4, pp (2). 7. Heywood, J.B., Internal Combustion Engine Fundamentals, McGraw-Hill, New York (1988).