Stochastic Limit Control and Its Application to Knock Limit Control Using Ionization Feedback

Transcription

1 SAE TECHNICAL PAPER SERIES Stochastic Limit Control and Its Application to Knock Limit Control Using Ionization Feedback Guoming G. Zhu, Ibrahim Haskara and Jim Winkelman Visteon Corporation Reprinted From: Electronic Engine Controls 2005 (SP1975) 2005 SAE World Congress Detroit, Michigan April 1114, Commonwealth Drive, Warrendale, PA U.S.A. Tel: (724) Fax: (724) Web:

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3 Stochastic Limit Control and Its Application to Knock Limit Control Using Ionization Feedback Copyright 2005 SAE International Guoming G. Zhu, Ibrahim Haskara and Jim Winkelman Visteon Corporation ABRACT Spark timing of an Internal Combustion (IC) engine is often limited by engine knock in the advanced direction. The ability to operate the engine at its advanced (borderline knock) spark limit is the key for improving output power and fuel economy. Due to combustion cycletocycle variations, IC engine combustion behaves similar to a random process and so does the engine performance criteria, such as IMEP (Indicated Mean Effective Pressure), and knock intensity. The combustion stability measure COVariance of IMEP assumes the IMEP is a random process. Presently, the spark limit control of IC engines is deterministic in nature. The controller does not utilize any stochastic information associated with control parameters such as knock intensity for borderline spark limit control. This paper proposes a stochastic limit control strategy for borderline knock control. It also develops a simple stochastic model for evaluating the proposed stochastic controller. The stochastic limit control is applied to borderline knock limit control on a 3.0L V6 engine. INTRODUCTION Internal Combustion (IC) engines are designed to maximize power subject to meeting exhaust emission requirements with minimal fuel consumption. Spark timing is used as one of the optimization parameters for the best fuel economy within the given emission requirements. For normal operation, engine spark timing is often optimized to provide Maximum Brake Torque (MBT). Traditionally, it is determined by conducting a spark sweep, but it can also be determined through closed loop spark timing control (see references 1, 2, 3, 4, and 5). On the other hand, engine combustion stability and knock avoidance requirements also constrain engine spark timing within a certain region, called feasible spark timing region. For certain operational conditions, it is desirable to operate the engine at the borderline of the feasible region continuously. For instance, under certain operational conditions engine MBT timing is located outside of the feasible sparktiming region due to the requirement to avoid engine knock. In order to obtain the maximum brake torque, it is required to operate the engine at its knock limit or advanced limit of the feasible region. Due to the low signaltonoise ratio of existing (accelerometer based) knock sensors, traditionally, a dualrate countup/down scheme is often used for engine knock limit control. Conventional approaches are based upon the use of a single knock flag obtained by comparing the knock intensity signal of a knock sensor to a given threshold. The knock intensity signal is defined as the integrated value, over a given knock window, of the absolute value signal obtained by filtering the raw knock sensor signal using a bandpass filter. The disadvantage of this control scheme is that it continually takes the engine in and out of knock, rather than operating smoothly at the desired point. In addition at certain operating points it can be severely compromised by engine mechanical noises such as valve closures and piston slap which may be picked up by the accelerometer. Such issues result in conservative ignition timing that leads to reduced engine performance. The high quality incylinder ionization signal makes it possible to derive a linear knock intensity that is proportional the knock level due to the increased signal to noise ratio of ionization versus accelerometer based systems (see references 6, 7, and 8). Further, the cycletocycle variations in the combustion process result in an ionization knock intensity signal that is similar to a random process output when the engine is operated at knock conditions. This makes it almost impossible to use an existing (deterministic) limit control scheme to find true knock borderline ignition timing and operate the engine at this corresponding timing smoothly. This paper presents a stochastic ignition limit control strategy utilizing the stochastic properties of the knock intensity feedback signal, and demonstrates that the control system is able to operate the engine at its borderline knock limit smoothly despite the cycletocycle combustion variability and inherent ionization signal variations owing to that stochastic nature.

4 A OCHAIC KNOCK INTENSITY MODEL A typical ionization signal is shown in Figure 1. Following the ignition phase it usually consists of two peaks. The first peak of the ion signal represents the flame kernel growth and development, and the second peak is the reionization due to the incylinder temperature increase as a result of both pressure increase and flame development in the cylinder. An ionization signal shows detailed information about the combustion process through its waveform. It shows when a flame kernel is formed and propagates away from the gap, when the combustion is accelerating rapidly, when the combustion reaches its peak burning rate, and when the combustion ends RPM. The spark timing is at 18 DATDC (Degrees After Top Dead Center). Comparing the PDFs of a Gaussian process and Figure 3, the knock intensity PDF histogram is not symmetric and a Gaussian random process cannot approximate it directly. Figure 3: Knock intensity PDF In order to be able to use the Gaussian random process to model the knock intensity PDF, consider the nonlinear map described in Figure 4. This nonlinear map translates a symmetric Gaussian PDF into the knock intensity PDF shown in Figure 3 by compressing the left axis of the Gaussian PDF. Approximation of Knock PDF Figure 1: Typical Ionization signal and its knock detection window When an engine is operated at knock conditions, there exist high frequency oscillations superimposed on the ionization signal after the second peak (see Figure 1). A knock intensity signal can be obtained using incylinder ionization signals (see references 6, 7, and 8). Conventionally, knock intensity is defined as an integrated value, over a given knock window (defined in Figure 1) of the absolute value signal obtained by filtering the raw ionization sensor signal using a bandpass filter (see Figure 2). Ion Signal Bandpass Filter Amplifier Absolute Value Integration Over Knock Window Figure 2: Knock intensity calculation diagram Knock Intensity Figure 3 shows a PDF (Probability Density Function) of knock intensity signal obtained from an ionization signal. The engine is operated WOT (Wide Open Throttle) at Gaussian PDF Nonlinear Map Figure 4: Mapping from Gaussian to knock PDF With the help of the nonlinear mapping described in Figure 4, the knock intensity signal can be modeled using the following dynamic model. x x x y ET ( k + 1) ( k + 1) a( N ) x + [1 a( N)] u b( N ) x ET + [1 b( N )] u ET x + x ET P [ PM [ x ] + PS [ x ] w( k)] where u and u ET are engine spark timing and engine coolant temperature; a(n) and b(n) are first order (1)

5 dynamic coefficients as a function of engine speed N; states x and x ET are corrected spark timings corresponding to u and u ET, respectively; x is effective engine spark timing; PM and PS are nonlinear mapping defined by knock intensity mean and standard deviation shown in Figure 5; w is a Gaussian process with zero mean and unit variance; P is the nonlinear map defined in Figure 4; and finally, y is the modeled knock intensity output. Note that nonlinear mappings PM and PS shown in Figure 5 can be obtained through engine mapping process. As described in the Introduction section, a conventional knock controller uses countup/down logic, which is described in Equation (2) e u ( k + 1) y u u DESIRED y + gn + gn UP, DOWN, if e if e 0 < 0 where y DESIRED and y are desired knock intensity level and feedback knock intensity level, respectively; u is the control command (ignition timing); and gn UP and gn DOWN are countup/down gains. For this simulation, gn UP and gn DOWN are 0.1 and 3, respectively. That is, if the actual knock intensity is below the desired level, advance the ignition timing at 0.1 crank degree increment rate; and if the actual knock intensity is beyond desired level, retard the ignition timing at the 3 degrees decrement rate. (2) Figure 5: Mean and standard deviation of knock intensity Figure 6 shows the knock intensity signal and its PDF simulated by the model defined in Equation (1). The simulated operational condition is at 1500 RPM and WOT with ignition timing at 20 DATDC. Although the PDF shape shown in Figure 6 does not match with the one in Figure 3 exactly, we believe it is close enough for evaluating closed loop knock controllers. The nonlinear map defined in Figure 4 can be further improved to make the simulated PDF closer to the actual one shown in Figure 3, which is not the subject of this paper. Figure 6: Modeled knock intensity and its PDF OCHAIC KNOCK LIMIT CONTROL Figure 7: Countup/down control results Figure 7 shows the simulation results using countup/down controller specified in Equation (2). It is obvious that the countup/down control is not able to keep the actual knock intensity below the desired level and as a byproduct the engine ignition timing varies between 10 and 20 DATDC, leading to large variation of engine torque output. The large fluctuation of spark timing in Figure 7 is the nature of the countup/down control scheme. The fluctuation range may vary due to the different calibrations of the countup/down (advanced and retard) gains. The fluctuation range increases as gains increases, but the retard gain has to be large enough to eliminate engine knock at next combustion event for a given cylinder. The difference between countup/down and stochastic control scheme is that the stochastic control strategy utilizes full range knock intensity signal to control engine spark timing below audible level instead of using knock intensity signal only at audible level. This makes it possible to operate engine at its knock spark limit without large spark timing fluctuations.

6 Figure 8 shows the simulation results using a PI controller with dual integration gains described below, e u ( k + 1) y DESIRED KPe KPe y + K + K IP IN e e,, if e 0 if e < 0 where y DESIRED, y, and u are defined the same as Equation (2); K P is the proportional gain; and K IP and K IN and are integration gains for positive and negative error e, respectively. For this simulation, K IP and K IN are selected to be 0.05 and 5, respectively, and K P is zero. Comparing Figure 7 and Figure 8, it is clear that a linear PI controller improves the performance of the countup/down controller, but is not able to keep the actual knock intensity level below the desired level, and the ignition timing varies in a much smaller range of around 4 crank degrees. (3) Figure 9 shows the architecture of the proposed closedloop stochastic limit controller. It's a part of an overall spark controller, which manages the spark timing for best fuel economy, power and emissions by employing a closed loop MBT timing strategy (see reference 8). For the ionization feedback system, the ionization signal from each cylinder is sampled and saved in a buffer at each combustion event. The overall spark control is triggered at every firing event and stochastic limit control processes the ionization signal from the most recent cycle to generate the feedback parameter (such as knock intensity) for the stochastic limit control. The objective of stochastic limit controller is to provide an ignitiontiming limit for the overall spark controller to avoid engine knock. The key part of the proposed limit controller is the stochastic analyzer block. The derived ionization feedback parameters from each firing cycle are gathered in a buffer of a userselected size for stochastic analysis of the data. Basically, the mean, standard deviation and PDF of data are constantly updated at the end of each firing event. Using the PDF, an achieved userspecified percentage confidence level number is also computed. For the knock intensity feedback signal, this number is defined as follows: saying 90% confidence number for knock intensity is 0.6 volt means that for the 90% of the combustion events in the buffer, the measured knock intensity are below 0.6 volt. A confidence level definition for combustion stability measure is provided in reference 9. Four main feedback actions are proposed in the stochastic limit controller. Their functionalities are listed below. Figure 8: PI control results After studying the simulation results for both countup/down and PI controllers, it is concluded that any deterministic controller, without utilizing the stochastic information of knock intensity, is not able to operate the engine smoothly at the borderline of its feasible ignition region. This leads to the proposed stochastic limit control strategy. Confidence level target Instantaneous feedback + Nominal Mean Target Computation Adaptive Seeking Algorithm + Stochastic analyzer Adaptation error Confidence level (achieved) Engine Speed/Load Mean (achieved) + Instant Correction Map Mean target value Adaptive seeking loop + + Stochastic control loop Feedforward PI Controller P Control I Control Instant correction loop Baseline Ignition Timing Saturation management Final Ignition Timing Regulation controller Figure 9: Stochastic closedloop limit controller REGULATION CONTROLLER FOR OCHAIC FEEDBACK The regulation loop is used to regulate the mean value of the stochastic limit feedback parameter to a mean target value. A nominal mean target value is determined from the confidence level target based on offline data as represented in Figure 9. Ideally, the mean target should be selected such that when operating at the corresponding spark timing the confidence level number for the gathered knock intensity distribution matches with the desired confidence level target. The regulation controller is structured as a PI controller with a feedforward term based on engine operating conditions. Despite the variability of the stochastic limit feedback, its mean value is a wellbehaved signal for regulation purposes. The regulation controller is tuned to provide the desired settling time and steadystate accuracy for the response. ADAPTIVE SEENG FEEDBACK The purpose of this loop is twofold: reducing the calibration conservativeness by providing the engine

7 with its true ignition timing limit target and improving robustness of stochastic limit controller when the engine operates under different conditions. This is accomplished by using an error signal between the desired confidence level target and the achieved one. Note that the confidence level is a secondorder property of PDF like variance. The adaptive seeking algorithm reduces the nominal mean target for the regulation controller if the confidence number is greater than the specified one; otherwise, increase the nominal mean target value. INANT CORRECTION FEEDBACK This block calculates an instant correction signal to be fed into the integration portion of PI controller. When the error between confidence level target and stochastic limit feedback parameter is greater than zero, the output is zero. That is, no correction is required, and when the error is less than zero, the error is fed into a one dimensional lookup table that outputs an instant correction for the integration portion of the PI controller. SATURATION MANAGEMENT This block represents the interaction of the stochastic knock limit controller with the overall spark controller. If the baseline spark is more retarded than the current knock (advanced) limit, then the baseline spark is used as it is. In that case, the knock limit controller pushes the limit in the maximum advanced direction by itself. This is due to the fact that the integration of the mean regulation loop keeps integrating until the maximum advanced allowed is reached (an antiwindup scheme is used) as it was designed. If the baseline spark controller pushes the ignition timing to a level at which the feedback signals generate corrections, then the advanced limit moves from its maximum limit to a new level as a variable saturation limit on the baseline spark. On the other hand, if the baseline controller still tends to push the spark in the advanced direction, the seeking and instant correction actions of the advanced controller will adjust the advanced limit online. Figure 10 shows simulation results of closed loop knock limit control using the proposed stochastic limit control strategy shown in Figure 9. It is clear that the knock intensity stays below the desired knock intensity level of 0.4 volts, and the ignitiontiming limit stays close to constant level instead of varying over a certain range. EXPERIMENT SETUP AND RESULTS A 3.0L V6 engine was used for prototyping tests. The dynamometer controls the engine (such as throttle, fueling, EGR, etc.) except for the engine ignition system, which is controlled by a rapid prototyping system. The architecture of the prototyping stochastic knock limit management system is shown in Figure 11. The ionization feedback signals of all cylinders are fed into the "Knock Intensity Box". The ionization current signals are merged, conditioned, and used to generate an analog knock intensity signal to be sampled for closed loop control. Ionization detection Ion ignition coils Signals Dwell CMD Signal Conditioning Ignition Control Signal Generation Knock Intensity calculation Stochastic Knock Limit Control Knock Intensity Box Baseline Ignition Control Strategy Prototype Unit Figure 11: CL knock limit control system architecture The knock intensity signal is sampled every combustion event and fed into the stochastic knock limit controller described in Figure 9. The stochastic limit controller computes the final ignition command based upon the desired ignition timing from the baseline ignition control strategy and the determined ignitiontiming limit for knock avoidance. Although it's not shown in Figure 11, the baseline ignition strategy can also use ionization signal feedback (see reference 5). The stochastic knock limit controller shown in Figure 9 computes the stochastic parameters from the sampled ionization knock intensity signal at each combustion event. Based upon these parameters, the controller provides a closed loop limit value for the ignition timing in the advanced direction. Figure 10: Stochastic limit control results The ideal action of the stochastic knock limit controller can be explained as follows: suppose that we want to make sure that the knock intensity will not go beyond a given value, say 0.1 volt. This value is then the desired confidence level target. Using the standard deviation of the measured data, one can backcalculate a nominal target for the regulation controller by subtracting a certain multiple of the standard deviation of the

8 measured data in the buffer (the action of nominal mean target computation block). That initial mean target is then increased by the adaptive seeking loop slowly if the resulting confidence level number computed from the measured data (say 90%) is less than desired confidence level target of 0.1 volt. That way, if the initial mean target was too conservative; i.e., the confidence level number is well below 0.1 volt, then the mean target will be increased. On the other hand, the instant correction feedback acts as a safety since whenever the feedback goes beyond 0.1 volt it will instantaneously retard the advanced limit. Then the seeking will start again to push the advanced limit as long as the things are favorable. Since the mean and stochastic properties are used as feedback signals, the controller will not react aggressively to each combustion variation, which would be the case if the feedback signal from each cycle were used directly. Figure 13: Knock intensity distribution locations The knock intensity distribution locations at 95%, 98%, and 100% confidence level are shown in Figure 13. The distribution locations increase as the spark timing advances. The criterion used for adaptive seeking is the distribution location with certain confidence level for stochastic limit control. This adaptive seeking control loop adjusts the reference signal for mean control loop such that the given confidence level percentage of knock intensity signal stays below the confidence target level. Figure 12: Knock intensity statistics Before discussing closed loop control of knock limit, knock controllability, using ionization knock intensity feedback, is studied. As described in the previous section, the stochastic limit control strategy utilizes the mean and standard deviation information of the ionization knock intensity signal as well as the evolution of its stochastic distribution. Due to the highresolution knock intensity signal obtained from incylinder ionization signals, both mean and standard deviation of the knock intensity signal show high correlation to engine spark timing, see Figure 12. When the engine spark timing varies from 10 DATDC to 26 DATDC, both mean and standard deviation increase. This demonstrates good controllability using the knock intensity obtained from ionization signals. The mean and standard deviation data was obtained from a 3.0L V6 engine operated at 1000 RPM with WOT. The mean and standard deviation data is processed using 300 cycles ionization data. Similar results are obtained over the whole speed and load range of the engine. Figure 14: Comparison of conventional and stochastic knock limit control The architecture of the knock limit control is shown in Figure 9 and Figure 11. The closed loop control results, comparing conventional and stochastic knock limit controller, are shown in Figure 14. The conventional knock limit control used is the same as the countup/down controller described in Equation (2) and the calibrations, used to obtain the simulation results shown in Figure 7, are used for real time control.

9 Figure 15: IMEP variations of conventional and stochastic knock limit control Figure 15 shows the IMEP variation due to two different knock control schemes. It can be observed that the covariance of IMEP using proposed stochastic controller is about 20 percent lower than the one using conventional control scheme, indicating that the proposed control scheme provides a smoother engine operation than the conventional one when the engine is operated at its knock limit. The closed loop control results of knock intensity control, using the proposed stochastic limit control, are shown in Figure 16, where the top plot shows both actual mean knock intensity and confidence level knock intensity; the second plot from top shows spark advance limit and actual spark timing; the third shows the instantaneous knock intensity signal and the target confidence level knock intensity at 0.1 volt; and the bottom plot shows the percentage of over the 0.1 volt threshold. During the first 18 seconds, the closed loop knock limit control is not active, baseline spark timing starts at around 13 DATDC and the knock intensity mean is relatively low (around 0.1 volt). At the 16 th second, the baseline spark timing is manually advanced to 20 DATDC and mean and confidence level knock intensity increases to over 0.4 volt and 1.4 volt respectively right before the closed loop knock limit control is activated. After the knock limit control is enabled at 18 th second, knock intensity is reduced to desired mean knock intensity level (0.1 volt) and the advanced limit, generated by the closed loop knock limit controller, moves back to 11 DATDC. Note that the advanced spark is digitized from the advanced limit with onedegree resolution due to the control hardware limitations. Between the 18 th and 60 th second, the bottom plot shows that there is about 5% of the actual knock intensity staying beyond 0.1volt confidence level target. At the 60 th second, the adaptive seeking algorithm is enabled with a 90% actual confidence level target and the percentage over 0.1volt target increases to around 10% (or 90% confidence level). The spark timing is further advanced to between 14 and 13 DATDC. Figure 16: CL knock limit control (1000 RPM, WOT) Figure 17 shows the test results of the closed loop knock limit controller when the engine is operated at 1500 RPM with 8.5 bar BMEP. The confidence level target is selected as 0.2 volt since a lower number generates a more conservative limit control at the new operating point. As shown in Figure 17, the spark is manually advanced while the initial knock limit was 40 DATDC. After a certain transient behavior, the knock limit controller pushes the advance limit back to around 23 DATDC, for which the 90% confidence level was around 0.2 volt as desired. The percentage above 0.2 volt is around 10% from the bottom plot of Figure 17. Note that the slow transition of the percentage curve shown in the bottom plot of Figure 17 is due to the number of points used for calculating the percentage. Figure 17: CL knock limit control (1500 RPM, 8.5 bar) CONCLUSION A closed loop stochastic knock limit management system is proposed in this paper. A simple nonlinear dynamic model is developed to study stochastic nature of the knock limit control feedback signal: knock intensity. Simulation results show that the conventional

10 deterministic knock limit control techniques are not able to operate IC engine at its borderline limit smoothly. With the proposed stochastic knock limit control strategy, utilizing stochastic information of the knock intensity signals, the control can seek, maintain and limit the spark timing at a desired userspecified level of knock intensity using the feedback signal derived from incylinder ionization signals. The proposed knock limit control system also utilizes an adaptive control architecture. The stochastic limit control strategy is applied to closed loop knock (advanced) limit control using incylinder ionization feedback signals successfully. The system is currently being evaluated in terms of its projected benefits on knock control quality. REFERENCES 1. Yoshiaki Kawamura, Mamoru Shinshi, Hiroshi Sato, Nobutaka Takahshi, and Masahiro Iriyama, "MBT control through individual cylinder pressure detection", SAE paper , Mark C. Sellnau, Frederic A. Matekunas, Paul A. Battiston, ChenFang Chang, and David R. Lancaster, "Cylinderpressurebased engine control using pressureratiomanagement and lowcost non Intrusive cylinder pressure sensor", SAE paper , L. Eriksson, and L. Nielsen, "Closed Loop Ignition Control by Ionization Current Interpretation", SAE paper , Guoming G. Zhu, Chao F. Daniels, and James Winkelman, "MBT timing detection and its closedloop control using incylinder pressure signal", SAE paper , Guoming G. Zhu, Chao F. Daniels and Jim Winkelman, "MBT Timing Detection and its Closedloop Control Using InCylinder Ionization Signal", SAE paper , R. J. Hosey and J. D. Powell, "Closed loop, knock Adaptive Spark timing control based on cylinder pressure", Transaction of ASME, Vol. 101, March, Kunifumi Sawamoto, Yoshiaki Kawamura, Toru Kita, and Kenjiro Matsushita, "Individual cylinder knock control by detecting cylinder pressure", SAE paper , Chao F. Daniels, Guoming G. Zhu and Jim Winkelman, "Inaudible Knock and Partial Burn Detection Using InCylinder Ionization Signal", SAE paper , Ibrahim Haskara, Guoming Zhu, and Jim Winkelman, "IC Engine Retard Ignition Timing Limit Detection and Control using InCylinder Ionization Signal", SAE paper , CONTACT Guoming (George) Zhu, Ph.D., Visteon Corporation, One Village Center Drive, Van Buren Township, MI , USA. gzhu1@visteon.com ( ) DEFINITIONS, ACRONYMS, ABBREVIATIONS IC: IMEP: COV: MBT: PDF: RPM: WOT: DATDC: PI: : CL: Internal Combustion Indicated Mean Effective Pressure Covariance Maximum Brake Torque Probability Density Function Revolutions Per Minute Wide Open Throttle Degrees After Top Dead Center Proportional and Integral Knock Intensity Closed Loop