Air-to-Fuel and Dual-Fuel Ratio Control of an Internal Combustion Engine

Transcription

1 Downloaded from SAE International by Brought o You Michigan State Univ, hurday, April, Air-to-Fuel and Dual- Control of an Internal Combution Engine Stephen Pace and Guoming G Zhu Michigan State Univerity Copyright 9 SAE International ABSRAC Air-to-fuel (A/F) ratio i the ma ratio of the air-to-fuel mixture trapped inide a cylinder before combution begin, and it affect engine emiion, fuel economy, and other performance Uing an A/F ratio and dualfuel ratio control oriented engine model, a multi-inputmulti-output (MIMO) liding mode control cheme i ued to imultaneouly control the ma flow rate of both port fuel injection () and direct injection () ytem he control target i to regulate the A/F ratio at a deired level (eg, at toichiometric) and fuel ratio (ratio of fueling v total fueling) to any deired level between ero and one A MIMO liding mode controller wa deigned with guaranteed tability to drive the ytem A/F and fuel ratio to the deired target under variou air flow diturbance he performance of the liding mode controller wa compared with a baeline multi-loop PID (Proportional-Integral-Derivative) controller through imulation and howed improvement over the baeline controller Finally, the engine model and propoed liding mode controller are implemented into a Hardware-In-the-Loop (HIL) imulator and a target engine control module, and HIL imulation i conducted to validate the developed controller for potential implementation in an automotive engine INRODUCION Increaing concern about global climate change and ever-increaing demand on foil fuel capacity call for reduced emiion and improved fuel economy Vehicle equipped with fuel ytem have been introduced to market globally In order to improve engine full load performance at high peed, oyota introduced an engine with a toichiometric injection ytem with two fuel injector for each cylinder, ee [] One i a injector generating a dual-fan-haped pray with wide diperion, while the other i a port injector he dual-fuel ytem introduce one additional degree of freedom for engine combution optimiation to reduce emiion with improved fuel economy Uing gaoline and ethanol dual-fuel ytem to ubtantially increae gaoline engine efficiency i decribed in [] he main idea i to ue a highly booted mall turbocharged engine to match the performance of a much larger engine Direct injection of ethanol i ued to uppre engine knock at high engine load due to it ubtantial air charge cooling reulting from it high heat of vaporiation he control of A/F ratio i an increaingly important control problem due to federal and tate emiion regulation Operating the park ignited internal combution engine at a deired A/F ratio i due to the fact that the highet converion efficiency of a three-way catalyt occur around toichiometric A/F ratio here have been everal fuel control trategie developed for internal combution engine to improve the efficiency and to reduce exhaut emiion A key development in the evolution wa the introduction of a cloed-loop fuel injection control algorithm [], followed by a linear quadratic control method [4], and an optimal control and Kalman filtering deign [5] Specific application of A/F ratio control baed on oberver meaurement in the intake manifold were developed in 99 [6] Another approach wa baed on meaurement of exhaut gae by an oxygen enor and the throttle poition [7] Hedrick alo developed a nonlinear liding mode control of A/F ratio baed upon the oxygen enor feedback [8] he conventional A/F ratio control for automobile ue both cloed-loop SAE Int J Engine Volume Iue 45

2 Downloaded from SAE International by Brought o You Michigan State Univ, hurday, April, 5 feedback and feed forward control to achieve good teady tate and tranient repone he control trategie, mentioned above, were mainly for ytem Mitubihi began to invetigate combution control technologie for direct injection engine in 996 [9] Due to the introduction of internal combution engine with dual-fuel ytem ( and ), control of both A/F ratio and fuel ratio (ratio of fueling v total fueling) became part of a combution optimiation problem in [] In thi paper, a control oriented model of a dual-fuel ytem i developed for control development and evaluation purpoe, and a MIMO liding model controller i developed to regulate the engine A/F and fuel ratio to target level he control trategy i validated in imulation baed upon the developed dualfuel ytem model Furthermore, the engine model and propoed liding mode controller are implemented into a Hardware-In-the-Loop (HIL) imulator and a target engine control module, and HIL imulation i conducted to validate the developed controller for potential implementation in an automotive engine hi paper i organied a follow It begin by preenting a implified A/F and fuel ratio control oriented model, followed by a ection that decribe an innovative liding mode controller that regulate both A/F and fuel ratio to deired nonero target and imulation reult are hown Next, a tate etimator will be preented for a fixed engine operation condition and the HIL environment etup will be decribed Finally, HIL imulation reult are preented and concluion are dicued A/F RAIO AND FUEL RAIO ENGINE MODEL he control problem of thi work i to vary both fuel ma injection rate ( m and m ) o that the engine A/F ratio i regulated at a deired level (eg, toichiometric) and the fuel ratio of effective fueling, m _, to total fueling, E m total m E m, i _ maintained at a deired value a hown in Figure Note that the effective fueling for i equal to the injected fuel A/F Ratio toich - F/R deired - A/F Ratio F/R m Controller _ E m m air A/F Ratio F/R Engine Model FIGURE : AGRAM OF A/F AND FUEL RAIO CONROL PROBLEM A nonlinear model for thi problem, uing implified engine dynamic to model both the engine A/F and fuel ratio, i to be dicued below he air flow, m air, i model a m, () air where i the nominal air flow and i the air flow diturbance due to the engine operational condition change he fuel flow for wall-wetting dynamic from the port fuel injector i modeled by the following tranfer function m _ E ( ), () m ( ) where and are elected to be 5 and 8, repectively, in thi model he fuel flow from the direct injector contain negligible dynamic Due to the three-way catalyt ued for emiion control, mot engine are deign to achieve a target A/F ratio around toichiometry For thi reearch, we ue a normalied target A/F ratio, target, which i defined a deired air-to-fuel ratio divided by toichiometric air-tofuel ratio (46 for gaoline) Note that at toichiometry the normalied target A/F ratio i equal to one he normalied A/F ratio can be expreed a: m air () 46 m total Now, the engine equivalence ratio i defined a the invere of relative A/F ratio and can be approximated uing equation () and () below 46 m, total (4) where equation () i approximated by a firt order aylor expanion For the ret of the paper, we conider only equivalence ratio control intead of A/F ratio he fuel ratio of the dual-fuel ytem i defined a the effective fueling divided by total fueling, where m E m E R fuel (5) m m m _ E total Similarly, fuel ratio, R fuel, can be approximated by ubtituting equation (4) into (5), replacing the engine equivalence ratio with the target ratio herefore, R 46m fuel / _ E t arg et (6) he equivalence and fuel ratio model, operating at a fixed engine peed (5RPM), include wall-wetting dynamic of fuel ytem, average fuel injection delay (5m), oxygen (A/F ratio) enor delay (4m), and air flow travel delay from engine throttle to cylinder (m) hee time delay are approximated by unitary gain firt order tranfer function he complete model i divided into three ubytem, a hown in Figure, where the oxygen enor dynamic are denoted a G, the air flow dynamic a G, and the fuel flow dynamic a G he tate pace equation of the three ubytem are hown in equation (7), (8), and (9) x A x Bu (7) y Cx x A x Bu (8) y C x D u C [ C C ], 46 SAE Int J Engine Volume Iue

3 Downloaded from SAE International by Brought o You Michigan State Univ, hurday, April, 5 Air In In x A x B (9) y Out Out Fuel Flow Dynamic (G) In Out Air Flow Dynamic (G) C x arget Eq Ratio 4 6 Gain In Out Oxygen Senor Dynamic (G) FIGURE : EQUIVALENCE AND FUEL RAIO MODEL he entire ytem can be expreed by the following tate-pace model A B x A x CCxx B u () A B and the output equation for the equivalence and fuel ratio uing () can be approximated by y EqRatio 46C C x x () y 46 C x ( C x 65u ) / FuelRatio t arg et () he value for the matrice of the engine model are A 5; B 46; C 5; A 5; B ; C 5; A - ; B ; -5 C ; D 65 he nonlinear tate pace engine model mut be tranformed into the regular form [] below to apply liding mode control f a (, (, ; () f (, G(, u, b (4) where the forcing term of equation (), (,, contain the diturbance input and f a (, contain the nonlinear portion of () A change of variable, x (5) tranfer the original tate vector, x x x x x x (6) into the regular form coordinate, where the tranformation matrix i choen uch that x x x 65x ] (7) [ [ x x ] (8) hu, the original ytem (repreented in the regular form) i hown in (9) and () It can be een that the model contain two control input correponding to and fueling and one ma air flow diturbance input h(, where f a (, -5 u - u f b (, h(, 46 ( 65 ) SLING MODE CONROL SRAEGY G (, (9) () Exiting liding mode A/F ratio control application in [] and [] utilied the binary nature of a HEGO (Heated Exhaut Ga Oxygen) enor to reduce it ocillation reulting from the time delay by uing a dynamic, one dimenional liding urface In thi paper, a two dimenional liding urface i elected to control both equivalence and fuel ratio of the dual-fuel ytem he liding urface i defined a (), () where the control objective i to regulate to ero by deigning a feedback () uch that it tabilie equation (9) Letting 6 ( ) () - - reult in the aymptotic tability at the origin for (9) and decouple the nonlinear dynamic contained in f a (, from the remaining equation Alo, () doe not contain the tate and remove it from having any affect on the ytem, which i ignificant becaue the tate contained the input diturbance, Differentiation of the liding urface yield fb (, G(, u f a (, (, () Selecting the control u to cancel the known term of () u G (, fb (, f a (, G (, v (4) where v i the control input to be defined hu, and v (,, (5) 6 (, (6) herefore (5) become v (7) he elected v need to force toward ero and uing V = / a a Lyapunov function candidate for (5) then V v v (8) SAE Int J Engine Volume Iue 47

4 Downloaded from SAE International by Brought o You Michigan State Univ, hurday, April, 5 Selecting v a v gn( ), where b, for ome b (9) lead to V () and therefore guarantee aymptotic tability he reulting control force the ytem tate onto the liding urface in finite time and eventually bring thee tate on the liding urface to ero o achieve the deired nonero equivalence and fuel ratio, conider ( ) () ( ) () where and go to ero, leading and converging to the target tate and a time goe to infinity ince the liding mode controller regulate the tate,,, and to the liding manifold = Uing thee target tate, and can bring the equivalence ratio and fuel ratio to any deired value Uing () and (), (9) and () become ( 65 ) ( 65 ) - 46 ( 65 ) () -5 u 5 (4) - u o invetigate the tability of the ytem with thee new target tate, () from () i ued and by ubtituting () into (), the final ytem become ( 65 ) ( 65 ) (5) -5 u 5 (6) - u It can be een that the nonlinear term of equation of () i now eliminated, leaving a linear term with contant matrice plu the forcing term, and equation (4) remain linear For entire ytem tability analyi, the characteritic equation of the linear matrix A * i * det( I A ) ( 5)( 5)( )( 5)( ) with all eigenvalue in the left half plane, where ( 65 ) -5 A* Note that the target tate and can be determined with the given input air diturbance and deired equivalence and fuel ratio he following output equation are the reult of coordinate tranformation of () and () (uing (5)) ~ y EqRatio 5 5 ( 65 ) (7) ~ y 46 5 ( u ) / FuelRatio t arget (8) Conider the tate equation (9) and () at teady tate by etting derivative term equal to ero, leading to y~eqratio (9) 5 ( ) (4) (4) u 5 (4) u (4) Uing (8), (4), and (9), we have ~ y arg FuelRatio t et (44) 46 5 ( ) (45) herefore, the ytem teady-tate tate and can be expreed a a function of the deired output ratio and input diturbance he target tate and can be obtained with given target ratio and diturbance he ero target tate liding mode control trategy i modified uch that the cloed-loop ytem converge to the deired target tate, ee Figure m air m m Figure : Schematic diagram of liding mode control trategy o improve the performance of the liding mode controller, the tabiliing function () can be generalied a follow 6 ( ), (46) SAE Int J Engine Volume Iue

5 Downloaded from SAE International by Brought o You Michigan State Univ, hurday, April, 5 where i a poitive contant Subtituting (46) into (9) yield, - 5 d - 5 (47) where d = 95 Equation (47) can be viewed a A g(, ) (48) where, - 5 d A( ) - 5, (, ) g It can been een that A() i Hurwit if > and alo d d (49) Let Q = I and define X() > a the olution of the Lyapunov equation auming > A ( ) X ( ) X ( ) A( ) Q he maximum and minimum eigenvalue of X() are plotted a function of in Figure min of X() > for all time, where i a poitive contant, and can be retated a: ( X ( ))d (5) max Figure 4 how that max (X()) = for all >, thu (5) d Equation (5) how that if i mall, then there exit an > with guaranteed tability SIMULAION RESULS A MIMO PID controller wa deigned for comparion purpoe to the MIMO liding mode controller hi controller cacaded two PID controller uch that the firt PID i ued to control the equivalence ratio and the econd PI i ued to reduce the fuel ratio error, ee Figure 5 he controller gain for both PID and PI controller are hown in able Eq Ratio error Kd Ki Kp Kd Ki error Ki Kp x m m 5 max of X() Kp PID Controller PI Controller Figure 5: Schematic diagram of PID controller > Figure 4: Maximum and minimum eigenvalue of X() Define the Lyapunov function V() = X(), leading to the following propertie: min ( X ( )) V ( ) max ( X ( )), V A - Q -min ( Q), (5) V X X max ( X ) he derivative of V() atifie V ( ) ( A ( ) X ( ) X ( ) A( )) d ( ) X - ( Q) ( X ( )) d min herefore the origin i exponentially table if V ( ) or ( X ( )) d (5) max max he tability condition will hold auming All controller gain parameter were tuned uch that the repone of the cloed-loop ytem wa table and had a fat a repone a poible Simulation of the liding mode controller under different air flow input diturbance were conducted and compared to the PID controller able : PID and PI controller parameter K p = K p 5 K p 5 K i = K i K i 5 K p = K p 7 he gain matrix in the liding mode controller for each imulation wa tuned uch that the tranient repone wa acceptable and it wa elected a 6 7 (54) A unitary target equivalence ratio and 6% (6) target fuel ratio were choen for each imulation Figure 6 how the cloed-loop repone of the PID controller and liding mode controller for Simulation # he imulation ue a contant input diturbance of plu 5 percent noie, adding a tep input of 5 to the contant diturbance at the 6th econd It alo ha a fuel ratio reduction from 6 to 4 at the 9th econd, and SAE Int J Engine Volume Iue 49

6 Downloaded from SAE International by Brought o You Michigan State Univ, hurday, April, 5 how that the controller reject the diturbance quickly Figure 6 alo how the and fuel control input for both PID and liding mode controller It can be oberved that the liding mode controller provide quick fueling input of both and ytem, leading to better diturbance rejection and tranient repone over the PID repone able ummarie the overhoot and ettling time for both PID and liding mode controller able : Comparion of controller for Simulation # % Overhoot (after 6 th econd) Settling ime (after 9 th econd) e (after th econd) PID Sliding Mode PID Sliding Mode PID Sliding Mode Eq Ratio 59% 44% 6 ec < 5 ec 6 % 6% 9 ec ec Sliding Mode Fueling PID Fueling 5 Sliding Mode PID Sliding Mode PID Figure 6: Cloed loop repone of imulation # ABLE : COMPARISON OF CONROLLERS FOR SIMULAION # % Overhoot (after 6 th econd) Settling ime (after 9 th econd) e (after th econd) PID Sliding Mode PID Sliding Mode PID Sliding Mode Eq Ratio 99% 5% 45 ec 9 ec 8 7 9% 7% 5 ec < ec 4 5 Figure 7 how the cloed-loop repone of both PID and liding mode controller for Simulation # hi imulation decreae the target equivalence ratio from to 9 at the 6 th econd, and increae it back to unity at the 9 th econd Again, the contant input diturbance wa plu 5 percent noie Figure 7 alo diplay both fueling input of PID and liding mode controller Although the PID controller ha a fater equivalence ratio repone than the liding mode one, it i under the penalty of the fuel ratio control accuracy (huge pike during the tranition) On the other hand, the liding mode controller provide mooth tranition for both equivalence and fuel ratio herefore, the liding mode control repone are more favorable over the PID one able ummarie the overhoot and ettling time for both PID and liding mode controller for Simulation # It i worth to noting 9% fuel ratio overhoot for the PID controller while the liding mode controller only ha % Sliding Mode Fueling PID Fueling 5 Sliding Mode PID Sliding Mode PID FIGURE 7: CLOSED LOOP RESPONSE OF SIMULAION # 5 SAE Int J Engine Volume Iue

7 Downloaded from SAE International by Brought o You Michigan State Univ, hurday, April, 5 SAE ESIMAOR DESIGN he liding mode control trategy wa implemented uing tate feedback, but thi tate information will not be available for cloed loop control ince in practice only ome of the tate variable are meaurable In ome cae, even though they are meaurable, high cot prohibit utiliing tate feedback herefore, to implement the liding mode control cheme, a tate etimator mut be deigned to obtain tate information in real-time from the available meaurement hey are the equivalence and fuel ratio output, and the and fueling input Conider the nonlinear ytem decribed in equation (), (), and () Since tate x can be etimated from the ma air flow enor ignal equipped on the engine, auming that x i known, the ytem can be rewritten a x x 46 ~ x ~ x 65 u (55) - -5 ~ 46x 46x y 4875x / u x 85 / t arg et where t arg et ~ x (56) ~ x x x x4 x5 and note that the ytem i now linear hu a linear tate etimator can be contructed a xˆ A xˆ Bu L ( ~ y yˆ ) (57) yˆ C xˆ Du he matrix L i deigned uch that ALC i table he etimated ytem can be rewritten a u xˆ ( A LC) xˆ B LD L~ y yˆ Cxˆ Du hi etimator i known a the Luenberger oberver [4] and the error between the actual tate ~ x ( t ) and the etimated tate xˆ i given by e ~ x x ˆ Ax ~ Bu Axˆ Bu LC~ x xˆ Since the eigenvalue of ALC are in the left half plane, e ~ x xˆ( t), e a t For a fixed air flow diturbance of, the teady tate value of x = 8 and uing the linear ytem etimation equation (57), a linear tate etimator can be deigned with the following ytem parameter matrice: L, A, C, B, D 85 HIL SIMULAION SEUP he A/F and fuel ratio engine model wa implemented into an Opal-R HIL ytem uing MALAB/Simulink he engine model wa running on the Opal-R HIL imulator at a ample period of milliecond Similarly, the liding mode controller, along with tate etimator, wa dicretied with a five-milliecond ample period ( = 5) and implemented in Simulink Due to dicretiation, communication, and computational delay (ee Figure ), the ytem repone ocillate In the HIL imulation, the gain defined in (54) wa tuned for minimal ettling time without ocillation Figure 8 how the repone of the equivalence and fuel ratio for different value It turn out that when HIL = 4, the HIL imulation provide the bet repone for the dicretied liding mode controller Figure 8: Repone of ratio for different ampling period he dicrete Simulink model wa then implemented into a Mototron Engine Control Module (ECU) ampled every 5 milliecond he Opal-R HIL imulator communicate with the Mototron ECU controller through the high peed controller-area network (CAN), where ignal were ent and received with minimal delay he HIL imulation cheme i hown in Figure 9 SAE Int J Engine Volume Iue 5

8 Downloaded from SAE International by Brought o You Michigan State Univ, hurday, April, Figure 9: HIL engine model and controller etup he Opal-R imulation tep ie of milliecond wa choen in order to emulate a real-world continuou time engine Similarly, the Mototron data ampling rate of 5 milliecond wa the controller updating peed ued in many production engine control ytem he CAN communication between Opal-R and Mototron had a time delay between the time when ignal were ent from Mototron and the time when they were received by Opal-R, and vice vera hi delay wa le than milliecond for our etup PI Fueling Figure : HIL timing cheme HIL SIMULAION RESULS For the HIL imulation, a fixed air flow diturbance,, of wa ued throughout the entire imulation A unitary target equivalence ratio and 6% (6) target fuel ratio were choen to begin the imulation he equivalence ratio and fuel ratio repone of both HIL imulation and pure imulation are hown in Figure, which how a fuel ratio reduction from 6 to 4 at the 5 th econd Figure alo how the and fuel control input for both imulation environment It can be oberved that the HIL imulation repone i lightly lower than the pure imulation, which i due to both the feedback and control time delay between the HIL imulator and engine controller Figure how an equivalence ratio increae from unity to at the 4 th econd and alo the correponding fueling input Again the HIL imulation ha a lower repone than the pure imulation For both the fuel ratio reduction and the equivalence ratio increae, the real-time liding mode controller in the HIL environment wa able to achieve the deired ratio value very well Fueling Figure : Cloed-loop repone of HIL for fuel ratio reduction CONCLUSION A multi-input-multi-output liding mode controller wa developed baed upon the A/F and fuel ratio model to achieve nonero deired equivalence and fuel ratio target he liding mode controller wa validated with the developed imple nonlinear dual-fuel ytem model and compared to the multi-loop PID controller Furthermore, the controller wa implemented in a realtime Hardware-In-the-Loop (HIL) environment and the reult how that it i feaible to be implemented in a production engine control module controller 5 SAE Int J Engine Volume Iue

9 Downloaded from SAE International by Brought o You Michigan State Univ, hurday, April, 5 PI Fueling Fueling Figure : Cloed-loop repone of HIL for eq ratio increae REFERENCES akuya Ikoma, Shiuo Abe, ukihiro Sonoda, Hiao Suuki, Yuichi Suuki, and Maatohi Baaki, Development of V-6 5-liter Engine Adopting New Direct Injection Sytem, SAE Lelie Bromberg, Daniel Cohn, and John Heywood, Optimied Fuel Management Sytem for Direct Injection Ethanol Enhancement of Gaoline Engine, US patent application 6/6 J G Rivard, "Cloed-loop Electronic Fuel Injection Control of the IC Engine," in Society of Automotive Engineer, 97 4 J F Caidy, et al, "On the Deign of Electronic Automotive Engine Control uing Linear Quadratic Control heory," IEEE ran on Control Sytem, vol AC-5, October 98 5 W E Power, "Application of Optimal Control and Kalman Filtering to Automotive Sytem," International Journal of Vehicle Deign, vol Application of Control heory in the Automotive Indutry, 98 6 N F Benninger, et al, "Requirement and Performance of Engine Management Sytem under ranient Condition," in Society of Automotive Engineer, 99 7 C H Onder, et al, "Model-Baed Multivariable Speed and Air-to- Control of an SI Engine," in Society of Automotive Engineer, 99 8 S B Choi, et al, "An Oberver-baed Controller Deign Method for Automotive Fuel-Injection Sytem," in American Control Conference, 99, pp Kume, et al, "Combution echnologie for Direct Injection SI Engine," in Society of Automotive Engineer, 996 G Zhu, et al, Combution Characteritic of a Single-Cylinder Engine Equipped with Gaoline and Ethanol Dual-Fuel Sytem, SAE H Khalil, Nonlinear Sytem, ed: Prentice Hall, M Won, et al, Air to Control of Spark Ignition Engine Uing Dynamic Sliding Mode Control and Gauian Neural Network, in American Control Conference, 995, pp J Souder, et al, Adaptive Sliding Mode Control of Air- in Internal Combution Engine, International Journal of Robut and Nonlinear Control, vol 4, 4 4 D G Luenberger, "Oberver for Multivariable Sytem," IEEE ran on Automatic Control, vol AC-, pp 9-97, 966 CONAC Stephen Pace, Electrical Engineering, Michigan State Univerity, Engineering Building, Eat Laning, MI 4884, USA pacete@muedu ( ) Guoming (George) Zhu, PhD, Mechanical Engineering, Michigan State Univerity, 48 ERC-South, Eat Laning, MI 4884, USA hug@egrmuedu ( ) SAE Int J Engine Volume Iue 5