Energy Fuels 2009, 23, 6026–6032 Published on Web 09/30/2009
: DOI:10.1021/ef900736e
Lean Limit and Emissions Improvement for a Spark-Ignited Natural Gas Engine Using a Generalized Predictive Control (GPC)-Based Air/Fuel Ratio Controller Xiaojian Mao,* Du Wang, Wenyong Xiao, Zhiyuan Liu, Junxi Wang, and Hangbo Tang School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200240, People’s Republic of China Received July 16, 2009. Revised Manuscript Received September 7, 2009
The effects of the different air/fuel ratio (AFR) controller on lean limit and emission characteristics of a compressed natural gas (CNG) engine have been studied. The CARIMA model for the CNG engine was established, and a generalized predictive control (GPC)-based adaptive AFR controller was built by Matlab/Simulink. A simulation model of the engine was established by GT-Power. The experimental investigation was conducted on a six-cylinder multipoint injection lean-burn turbocharged spark-ignition (SI) CNG engine. The results of the simulation and experiment show that, in comparison to the proportional-integral-derivative (PID) algorithm, the GPC algorithm has not only better dynamic behavior but also better adaptability to the disturbances of the system, especially at transient conditions. Using the GPC controller, the lean misfire is improved because of the smaller overshoot of the excess air ratio and the operating range of the engine is extended. As a result, the emissions decrease slightly.
In comparison to the stoichiometric engine, the lean-burn engine presents a new set of challenges to the engine control community. The main challenge is that, under lean-operating conditions, there is a wide range of AFR references and it is more difficult to control accurately. However, the AFR is one of the most important engine parameters and directly affects the lean limit, fuel economy, and emissions. Therefore, it is necessary to design a controller to regulate the tailpipe AFR to follow the reference value for the objectives of optimizing fuel economy and satisfying emission constraints. A number of publications have described various designs of AFR controllers for the stoichiometric AFR control.4-7 Related work in the AFR control for lean burn is limited. In the literature,8 an adaptive-feedforward model-based AFR controller was developed for a four-cylinder, 2.2 L MercedesBenz lean-burn engine. The control performance is largely dependent ipon the control-oriented engine model. However, it is very difficult to establish an accurate “outer-feedback loop” emission model covering all operating conditions over the engine life cycle. In addition, there is significant open-loop uncertainty in the fuel injection and exhaust system, which cannot be handled by the feedforward control. Therefore, feedback control is necessary to maintain accurate AFR control. The most common closed-loop controller is based on a proportional-integral-derivative (PID) algorithm, which is used in most production engines. Although the PID controller
1. Introduction In 2008, global proven oil reserves fell by 3 billion barrels to 1258 billion barrels, with a reserves/production (R/P) ratio of 42 years.1 Because of limited reserves of oil, development of alternative fuel engines has attracted more and more concern in the engine community. Natural gas is considered to be one of the favorable alternative fuels for engines and is beneficial to help alleviate the fuel shortage and reduce engine exhaust emissions. Lean-burn technology for engines has drawn great attention during the past decade, largely because of its potential for improving fuel economy and reducing emissions.2 A leanburn engine is designed to operate at high intake manifold pressure with an excess air ratio greater than 1. Consequently, combustion efficiency can be improved through reduced pumping losses and enhanced thermodynamic efficiency. Moreover, the leaner mixture slows down the burn as well as decreases in-cylinder pressure and temperature, which decreases the possibility of the auto-ignition of end gas and will result in a lower chance of knocking and lower NOx emissions.3 However, lean-burn technology may bring with it some negative effects for engine performance, such as the increasing chance of misfire, especially at transient operating conditions. With poor combustion quality, as in the case of partial burning and misfire, engine efficiency drops and hydrocarbon (HC) and CO emissions increase, thereby defeating the purpose of lean-burn operation. Therefore, the air/fuel ratio (AFR) should follow accurately the given set point, for avoiding mixtures leaner than the lean limit.
(4) Jones, V. K.; Ault, B. A.; Franklin, G. F.; Powell, J. D. IEEE Trans. Control Syst. Technol. 1995, 3 (1), 14–21. (5) Bidan, P.; Boverie, S.; Chaumerliac, V. IEEE Trans. Control Syst. Technol. 1995, 3 (1), 4–13. (6) Guzzella, L. Models and model-based control of IC engines;A nonlinear approach. SAE Tech. Pap. 950844, 1995. (7) Turin, R. C. Model-reference adaptive A/F ratio control in an SI engine based on Kalman-filtering techniques. In Proceedings of the American Control Conference, Seattle, WA, 1995; pp 4082-4089. (8) Fekete, N. P.; Nester, U.; Gruden, I.; Powell, J. D. Model-based air-fuel ratio control of a lean multi-cylinder engine. SAE Tech. Pap. 950846, 1995.
*To whom correspondence should be addressed. Telephone: þ86-2134206138. E-mail:
[email protected]. (1) BP Statistical Review of World Energy. 2009 (6). (2) Heywood, J. B. Internal Combustion Engine Fundamentals; McGraw-Hill: New York, 1988. (3) Wang, D.; Mao, X. J.; Wang, J. X.; Zhuo, B. Energy Fuels 2009, 23 (6), 3054–3062. r 2009 American Chemical Society
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Energy Fuels 2009, 23, 6026–6032
: DOI:10.1021/ef900736e
Mao et al.
is able to meet the given set point and keep the system stable around it, some advantages are expected from the use of advanced control algorithms. However, it is always considered that all control algorithms should be programmable in a standard electronic control unit (ECU), with changes only in the software. In the literature,9 eight different control algorithms were investigated: PID, fuzzy PID (FPID), generalized predictive control (GPC), and dynamic matrix control (DMC), together with the equivalent versions with feedforward, namely, PID(ff) and FPID(ff), or considering a measurable disturbance, namely, GPCDM and DMCDM. The test results indicated that the predictive control GPC algorithm based on the CARIMA model was most robust to system nonlinearities. In the paper, the generalized predictive control algorithm for AFR is established. To reduce the development process, the model of a turbocharging multi-point injection compressed natural gas (CNG) engine is built and the combined GTPower/Simulink simulation is used. Finally, some experiments are performed for evaluating the control performance of AFR, emissions characteristic, and lean limit improvement.
Figure 1. GPC algorithm principle.
where ξ=e- T/τe and T is the sample time. 2.4. CARIMA Model. The simultaneous eqs 1-23 can describe the engine model λs ðtþ1Þ ¼ ξλs ðtÞ þ ð1 -ξÞðA=FÞs
where ma(t - 1) is the air mass, w(t) is system disturbance and is zero-mean discrete random quantity, and {A/F}s is stoichiometric. For the AFR model, the input, u(t), is (tinj - td) and y(t) is the output, λs(t). Therefore, eq 4 can be written as
2. Controller Design As discussed above, the GPC algorithm is based on the CARIMA model. The engine model for AFR control includes the injector model, AFR transport model, and AFR measure model. Because of the low system model required for GPC, using the three models, the CARIMA model for the controller can be established. 2.1. Fuel Injector. The fuel injector is simply a solenoidactuated valve supplied with CNG. The amount of fuel injected is more or less linearly proportional to the duration of the current pulse that excited the solenoid coil. mf ¼ KðTinj -Td Þ
yðtÞ - ξyðt -1Þ ¼
ð1 -ξÞðA=FÞs K uðt -2ÞþwðtÞ ma ðt -2Þ
ð5Þ
Equation 5 is changed into discrete difference form, and the CARIMA model of the engine is derived Aðz-1 ÞyðtÞ ¼ Bðz-1 Þuðt -1ÞþCðz-1 ÞwðtÞ=Δ
ð6Þ
where Δ=1 - z-1 and
ð1Þ
Aðz-1 Þ ¼ 1 -ξz-1
where mf is the amount of fuel injected, tinj is the fuel pulse width, and td is the injector no-flow period. 2.2. AFR Transport. At the controlled modeling process, it is assumed that the in-cylinder combustion is complete and the AFR transport process is regarded as a delay between when the fuel injection occurs and when the corresponding exhaust gas reaches the universal exhaust gas oxygen (UEGO) sensor. It has been found by experiment that this delay is very close to one full engine cycle.10 Although it is not necessary to limit this delay to an even cycle, doing so simplifies the model considerably. The excess air ratio (λs) is delayed relative to the in-cylinder excess air ratio (λm) by one cycle and is expressed as λe ðtþ1Þ ¼ λm ðtÞ
KðTinj ðt -1Þ -Td Þ þwðtÞ ma ðt -1Þ ð4Þ
Bðz-1 Þ ¼
ð1 - ξÞðA=FÞs K -2 z mac ðt -2Þ
Cðz-1 Þ ¼ 1 - z-1 -1
ð7Þ -1
-1
where the coefficients of A(z ), B(z ), and C(z ) are variable; therefore, the adaptive algorithm is adopted to estimate the parameters of the GPC algorithm. 2.5. GPC-Based Adaptive Algorithm. The GPC-based adaptive algorithm combines the adaptive and predictive controls. The parameter required for the AFR controller is less. Through the CARIMA model of the engine obtained above, the AFR adaptive algorithm can be realized. The GPC-based adaptive algorithm adopts a multi-step predictive method, can modify in time the error of the predictive model because of slow time-varying parameters, and has robustness and the ability of compensation for the change of time delay. The algorithm principle is shown in Figure 1. 2.6. Algorithm Realization. After the operating state of the engine changed, the pretuning control parameters may be no longer efficient. Then, the optimizing process begins to search the optimal parameters. From eq 7, it can be seen that the order of A(z-1) and B(z-1), na and nb, is separately 1 and 2. C(z-1) equals 1. Therefore, eq 6 can be written as
ð2Þ
2.3. AFR Measure. For multicylinder engines, the mixing of the exhaust from the different cylinders in the exhaust manifold is modeled as a recursive average of the sequential λm outputs from each cylinder. The UEGO sensor is modeled as a first-order lag with a time constant (te). The state element associated with the sensor measurement (λs) is updated once per engine cycle ð3Þ λs ðtþ1Þ ¼ ξλs ðtÞ þ ð1 -ξÞλe ðtÞ (9) Luj an, J. M.; Climent, H.; Guardiola, C.; Garcı´ a-Ortiz, J. V. Proc. Inst. Mech. Eng., Part D 2007, 221, 629–640. (10) Powell, J. D.; Fekete, N. P.; Chang, C.-F. Observer-based air-fuel ratio control. IEEE Control Syst. Mag. 1998, 18 (5), 72–83.
ΔyðtÞ ¼ Xðt -1ÞT θ0 þ ωðtÞ 6027
ð8Þ
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: DOI:10.1021/ef900736e
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Figure 2. Engine simulation model in GT-Power.
where X(t - 1)T=[-Δy(t - 1), ..., -Δy(t - na), Δu(t - 1), ..., Δy(t - nb)] and θ0 =[a1, ..., ana, b0, ..., bnb]T. a1(t), ..., Let ε(t)=Δy(t) - X(t - 1)Tθˆ (t - 1) where θˆ (t)=[^ a^na(t), b^0(t), ..., b^nb(t)]T. Use the recursive least-squares method with a forgetting factor θðtÞ ¼ θðt -1Þþ "
Pðt -1Þ ¼
Pðt -2ÞXðt -1ÞεðtÞ FþXðt -1ÞT Pðt -2ÞXðt -1Þ T
The implementation steps of the GPC algorithm are listed blow. ^ -1) and B(z ^ -1) online using eqs 9 and Step 1: Estimate A(z 10. j using Diophantine Step 2: Calculate E^j, F^j, G^j, and H function ( 1 ¼ Ej ðz-1 ÞAðz-1 ÞΔþz -j Fj ðz-1 Þ ð11Þ Ej ðz-1 ÞBðz-1 Þ ¼ Gj ðz-1 Þþz -j Hj ðz-1 Þ
ð9Þ
1 Pðt -2ÞXðt -1ÞXðt -1Þ Pðt -2Þ Pðt -2Þ F FþXðt -1ÞT Pðt -2ÞXðt -1Þ
where j=1, ..., N1 and A(z-1) and B(z-1) should be replaced ^ -1) and B(z ^ -1). by A(z Step 3: Calculate the matrix G^ and (G^TG^ þ λI)-1. Step 4: Solve the control output u(t) using eqs 12 and 13
#
ð10Þ where F is the forgetting factor and equal to between 0.95 and 1 and P(-1) is a positive definite matrix. Given F, P(-1), the initial value of θˆ (t) (θˆ (0)), the timedomain of prediction N1, the time-domain of control Nu, and the weighted constant R F=0.95 2 3 1 0 0 Pð-1Þ ¼ 4 0 1 0 5 0 0 1 θˆ (0)=[0.01, 0.01, 0.01] N1 =3 Nu =3 R=0.1
ΔuðtÞ ¼ PT ½yr -FyðtÞ -HΔuðt -1Þ
ð12Þ
uðtÞ ¼ uðt -1ÞþuðtÞ
ð13Þ
where PT is the first line of the matrix (G^TG^ þ λI)-1GT. Step 5: t=t þ 1 and return to step 1. 3. Integrated Simulation Model On the basis of Matlab/Simulink, the GPC-based controller is built. For the purpose of evaluating accurately the control algorithm and replacing some test bench tests, the engine model with a turbocharger, throttle, UEGO, injector, and spark coil should be built. The engine system is becoming very complex and more difficult to build/maintain in Simulink. 6028
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Therefore, it is proposed to replace the existing engine models built in Simulink with those in GT-Power for both pure
simulation and real-time hardware in the loop simulation (HILS), which can bring about many advantages, such as more continuity between engine cycle simulation and engine system simulation, arbitrarily complex systems being built, and simpler model calibration processes.11 The integrated model incorporates a mean value engine model in GT-Power, which can capture dynamics over one or more engine cycles, and the run speed is close to or faster than real time. Figure 2 shows the engine model that includes the engine, turbocharger, intercooler, injectors, throttle, intake and exhaust system, and other necessary components for simulation. Engine specifications are listed in Table 1. Figure 3 shows the integrated engine and control system simulation model, which includes the excess air ratio reference series prediction module. GPC module calculates
Table 1. Specifications of the Experimental Engine parameter
definition
engine type aspiration intercooler fuel type bore stroke (mm) compression ratio displacement (L) rated power (kW)/speed (revolutions/min) maximum torque (N m)/speed (revolutions/min) combustion chamber
in-line six cylinders, spark ignition turbocharger air/water compressed natural gas 112 132 11 7.8 191/2300 980/1400 ω type
Figure 3. Integrated engine and control system simulation model.
Figure 4. Experimental setup.
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Table 2. Components of CNG component methane ethane propane 2-methylpropane n-butane 2-methylbutane n-pentane 2,2-dimethylbutaan nitrogen
chemical formula
proportion
CH4 C2H6 C3H8 i-C4H10 n-C4H10 i-C5H12 n-C5H12 C6H14 N2
91.68 4.64 1.09 0.19 0.23 0.08 0.07 0.28 1.69
Figure 5. Response of the excess air ratio controlled by PID and GPC algorithms during simulation and experiment.
GPC adaptive parameters by referring the recent injection mass and excess air ratio and then calculates the next injection mass using the excess air ratio reference series λr(t þ j), which are the function of the excess air ratio set point, engine speed, and intake manifold absolute pressure (MAP). λr ðtþjÞ ¼ f ðλr ðt -jÞ, λr ðt -jþ1Þ, :::, λr ðtÞ, n, MAPÞ
ð14Þ
where j=1, 2, .... 4. Experimental Setup The experiments were carried out on a six-cylinder, multipoint injection, spark-ignition (SI) CNG engine (see Table 1 for specifications). The experimental engine was coupled to an eddy-current dynamometer for engine speed and load measurement and control. An electronic control system acquired the sensor signal, controlled the actuators, and provided access to all calibration parameters, allowing the user to set the desired equivalence ratio (by adjusting fuel injection duration), throttle position, ignition timing, and boost pressure. The wastegate on the turbocharger was designed to dump exhaust pressure around the turbine to reduce boost. Therefore, ECU could set the boost pressure by controlling the opening of the wastegate. In-cylinder pressure is the most important classical diagnostic in engine studies, providing information on the burn rate and overall engine performance. In knock studies, in particular, cylinder pressure also provides measures of knock intensity. Such knock indicators include the amplitude of the pressure fluctuation, the rate of the pressure rise, the third derivative of pressure, the burn duration, and the rate of change of the net heat release rate.12 In-cylinder pressure data were taken with a watercooled piezoelectric pressure transducer (Kistler6125A) and indicator system (AVL Indimeter619). Exhaust gases were measured online by an AVL exhaust analyzer, in which HC was analyzed with a flame ionization detector (FID), CO was analyzed with a nondispersive infrared analyzer (NDIR), and NOx was measured with a chemiluminescent detector (CLD). CO, HC, and NOx emissions were the average values of acquired data at each steady state of operating conditions. All of the tests were repeated. The AFR was monitored by an ETAS wide range λ meter. Figure 4 shows the experimental setup consisting of several main subsystems, namely, the CNG engine system, an electronic control system and the calibration tools, the λ meter and the exhaust analyzers, and a PC system equipped with an in-cylinder pressure monitor system. The dynamometer is not presented at Figure 4. CNG composition varies drastically with location, time of year, and time of day. Table 2 shows the components of CNG in this study.
Figure 6. Desired excess air ratio.
5. Results and Discussion In the paper, the simulation and experiment are implemented. To verify the control effect of the GPC-based controller, the PID control algorithm is introduced and its response is taken as the baseline. 5.1. Control Result with Steady Condition. First, the engine is at steady condition, and the desired excess air ratio is manually changed with a single step. Figure 5 shows the response of the excess air ratio controlled by PID and GPC algorithms during simulation and experiment. In comparison to the PID controller, as can be seen in Figure 5, the GPC controller offers a smaller overshoot. However, the difference of the response time is not obvious. Because the engine is at steady condition and the disturbance does not exist. 5.2. Control Result with Transient Condition. The desired excess air ratio of the lean-burn CNG engine varies with operating conditions. Figure 6 shows that the desired excess air ratio is decided to MAP and engine speed. In addition, at cold environment or transient conditions, the desired excess air ratio is affected by the engine temperature and operating conditions. For a natural gas engine, the European transient cycle (ETC) test should be used to test the control effect of the transient condition. Figure 7 shows the engine speed and torque range of the ETC cycle. Figures 8 and 9 show the response of the excess air ratio with PID and GPC algorithms between 200 and 400 s during the ETC cycle. In comparison to PID, the overshoot and regulation time of the excess air ratio are obviously smaller when using the GPC algorithm, because of the faster response and better adaptability. At the transient condition, the throttle often makes a sudden quick open or close and then the air mass flow rapidly increases or decreases. Because of the measurement
(11) Narula, M.; Olikara, C. Implementation of a Real Time GTPOWER Model for HIL Simulation; Cummins, Inc.: Columbus, IN, Nov 15, 2005. (12) Puzinauskas, P. V. Examination of methods used to characterize engine knock. SAE Tech. Pap. 920808, 1992.
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Figure 7. ETC transient cycle: engine speed and torque.
Figure 8. Test results of AFR control with the PID algorithm.
Figure 10. Effects of PID and GPC algorithms on the lean limit.
Figure 9. Test results of AFR control with the GPC algorithm.
delay of the excess air ratio and air mass flow and the calculation error of the fuel mass, the excess air ratio may deviation from the desired value. As can be seen in Figures 8 and 9, the GPC algorithm is more robust. 5.3. Effects of Different Algorithms on the Lean Limit. Because of the density of the charge and the conductivity of natural gas, lean-burn turbocharged CNG engines have more chances of lean misfire. Therefore, it is necessary to keep some lean misfire margin. However, if the overshoot of the excess air ratio occurs frequently, the lean misfire margin should be extended to avoid misfire. With the GPC algorithm, the overshoot of the excess air ratio decreases; therefore, a smaller misfire margin can be kept and the operating range of the engine can be extended. The effects of PID and GPC algorithms on the lean limit are showed in Figures 10 and 11, which show the engine operating range and the extended lean boundary. 5.4. Effects of Different Algorithms on Emission Characteristics. Figure 12 shows the effects of an excess air ratio on
Figure 11. Extended lean boundary.
Figure 12. Effects of an excess air ratio on emissions.
emissions. With the increase of an excess air ratio, NOx decreases and HC and CO increase. The oxidation catalytic 6031
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comparison to PID, the overshoot and the regulation time of an excess air ratio are obviously smaller when using the GPC algorithm. (3) With the GPC algorithm, a smaller misfire margin can be kept because of the decreasing overshoot of the excess air ratio and the operating range of the engine can be extended. (4) When the GPC controller is used, the emissions decrease slightly because of the increase of the excess air ratio of the lean limit. Acknowledgment. This study is supported by the National 863 Project of China (2006AA11A1A9). The authors acknowledge the colleagues at Shanghai Jiaotong University and Guangxi Yuchai Machinery Co. Ltd. for their help with the experiment and preparation of the manuscript.
Figure 13. Effects of different algorithms on emissions.
converter is installed in the exhaust pipe, and HC and CO can be maintained at a low level. Therefore, the increase of an excess air ratio is beneficial to decreasing emissions. As discussed above, the lean limit is extended using the GPC algorithm. As a result, the emissions decrease, which is showed in Figure 13.
Nomenclature AFR=air/fuel ratio CNG=compressed natural gas ECU=electronic control unit ETC=European transient cycle MAP=manifold absolute pressure n=engine speed PC=personal computer rpm=revolutions per minute SI=spark ignition UEGO=universal exhaust gas oxygen λ=excess air ratio
6. Conclusions In this research, the GPC-based controller is built for improving the accuracy of AFR control. The main conclusions can be summarized as follows: (1) At the engine steady operating condition, there is no significant difference between PID and GPC for the response of the step change of the desired excess air ratio. (2) At the transient condition, in
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