Feedforward Mapping for Engine Control

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1 Feedforward Mappg for Ege Cotrol Volka ARAN Faculty of Egeerg ad Natural Sceces Sabac Uversty & FORD OTOSAN Product Developmet Istabul, Turkey Mustafa Uel Faculty of Egeerg ad Natural Sceces Sabac Uversty Istabul, Turkey Abstract-Feedforward cotrol s wdely used electroc cotrol uts of teral combusto eges besdes feedback cotrols. However, almost all feedforward cotrol values are used table form, also called maps, havg ege speed ad ege torque ther aes. Table approach lmts all teractos two put dmesos. Ths paper focuses o applcato of Gaussa process modellg of errors of verse parametrc model of the valve posto. Valdato results based o real ege data are preseted for steady ad dyamc codtos. Keywords Gaussa process regresso; desel ege ar path; ope loop cotrol; ege mappg; EGR I. INTRODUCTION Icreasgly strget emsso regulatos of the desel eges created the eed for better ege out emsso cotrol. Desel ege emsso cotrol ca be eamed uder two ttles: Ar path ad Fuel path. Ar path cotrol cossts of maly regulatg followg three actuators: throttle valve, ehaust gas recrculato valve, varable geometry turbe vae or waste gate. Traset cotrol of desel ege ar path s focused o traset emssos ad torque buld up. Oe of the most mportat ehaust emsso gases s Ntrous Ode. Ehaust gas recrculato EGR) system s the maor NO reducto system for ege out emssos [1]. Commo cotrolled outputs of the desel ege ar path are the fresh arflow to the ege MAF) ad take mafold pressure MAP). Ths study focusses o cotrol of MAF va EGR valve posto. Regardless of type of the valve poppet or butterfly) flow cotrol wth a valve s a o-lear cotrol problem. Desel ege ar path has bee a plat for olear cotrol research for decades. Wth the varatos the applcato PID cotrol s oe of the stadard methods the ar path cotrol lterature [2], [3], [4], [5], [6], [7], [8]) besdes creasgly popular model predctve cotrol [9], [10], [11], [12], [13], [14], [15]). Other advaced cotrol methods such as: Sldg mode cotrol [16], [17], [18], [19]), H fty cotrol [20]) LQG LTR[21]), Adaptve Cotrol [22]) ad Lyapuov cotrol methods [23]) are also foud the ar path cotrol lterature wth lower frequecy. Although a varety of cotrol approaches ca be foud the lterature commercal desel ege commercal cotrollers stll uses feedforward cotrol ad basc PID s as well as verse models for determg feedforward valve postos. Recet ar path feedforward cotrol studes are dyamc feedforward cotrol wth predetermed optmum tables [24]) ad adaptve feedforward wth reset cotrol [25]). Map or table structure ege cotrol algorthms uses ege speed ad ege torque or fuel quatty) as aes desred values sce all the eteral demads to the ege are defed terms of ege speed drectly vehcle speed) ad ege torque related to the drver throttle pedal posto). Commo practce s usg same parameters for mappg of feedforward cotrol values. However, moder eges have to adapt dfferet operato modes ad evrometal codtos. Thus, the real feedforward cotrol values are dfferet for the same ege speed ad torque values for dfferet operato modes or evrometal codtos. Addtoal maps for dfferet operato modes ad evrometal codtos are solvg ths problem. Although ths soluto works real lfe applcato, umber of ecessary parameters for the tables s growg ad the related developmet effort s beg tred to de reduced. I recet years, there s a growg terest Gaussa Process modelg approaches. Iverse model wth Gaussa process regresso s especally prased for accuracy ad smoothess [26]. Am of ths work s to use Gaussa process models for feedforward mappg of ar path cotrol actuators. There are parametrc verse models commercal desel ege cotrol softwares. They have good performace for most of the ege operato pots. However, certa errors at crtcal operato pots may become uacceptable. Retug of parametrc verse models wthout alterg the whole behavor of the model s ot possble. Ths causes repetto of the whole valdato cycle. Gaussa process regresso offers a good alteratve for both map ad correctos logc of commercal ege cotrol ut structure ad parametrc model error correctos. Combed modelg of feedforward maps of the desel ege ar path actuators wth both parametrc ad oparametrc models s the ma cotrbuto of ths study. Forward system detfcato of the EGR le s preseted the et secto. Physcal sghts ad system detfcato methods are show. Later, verse actuator posto modelg wth parametrc ad oparametrc models are troduced. Performaces of both models are compared o steady state real ege for both trag ad valdato tests. Fally traset characterstcs of the steady state traed

2 models are shared. Strog ad weak pots of combed modelg s dscussed. II. FORWARD SYSTEM IDENTIFICATION A. EGR System defed as flow from ehaust to take drecto ad tally t s assumed postve oly. B. System Idetfcato Prevous secto preseted olear ature of the system. I order to facltate traset data for the EGR flow model. For the detfcato of the forward dyamc system, same tests wth NO detfcato method wth ovel chrp sgals s used [28]. Model puts are selected as P3, P2, T3, Total flow eterg tot the ege Fresh Arflow MAF) + EGR flow) ad modelled output s selected as MAF. The test desged to ecte chaels VNT posto, EGR posto, Ege Speed ad Iecto quatty wth Chrp sgals as descrbed [28]. Total flow through the ege s modelled as fucto of ege volume take mafold pressure ad temperature ad volumetrc effcecy of the ege. Hammerste model structure No output olearty) s selected for the detfcato of the system. MATLAB System Idetfcato Toolbo [29] s used for creatg the models. Regardg equato 1 polyomal oleartes of order 2 are selected for all put chaels. Fg. 1 Desel Ege Ar Path Scheme [20] Ehaust gases from ehaust mafold are fed to the take mafold for reducto of the ege out NO emssos moder desel eges. Ths cofgurato s called hgh pressure EGR system Fg. 1). Ma drvg force s the pressure dfferece betwee two eds of EGR le. Here forward system modelg s amed to estmate the mass flow o the le based o the kow pressure ad temperature parameters. I Desel Ege Ar Path Cotrol lterature EGR flow s modelled as compressble flow uder varable restrcto of the flow area. A eample of smplfed physcal system model equato s preseted [27]. Oe-le compact verso of the relato ca be wrtte as the followg: 1) where P2 s take mafold pressure or MAP), P3 s ehaust mafold pressure, T3 s ehaust mafold temperature, ad R e s gas costat, p opt s the model tug parameter, whch s added for low-pressure rato alog the le. Area s a fucto of actuator valve posto ad geerally dfferet from geometrc area ad tued wth test data. Postve flow s Fg. 2 Hammerste Modelg Results o Trag ad Valdato Data

3 As see Fg.2 valdato results of MAF smulato o World Harmozed Test Cycle WHTC) s promsg, however hgher accuracy valdato tha accuracy of trag remds the lower complety of valdato test wth respect to the trag test. Fg. 3 EGR chael olearty Forward system ca be modelled wth certa accuracy but feedforward cotrol requres verse model of the system amely, model output of valve posto wth respect to other put parameters preseted. However, wth the same type of the model verse model accuraces were very poor. Oe eplaato for ths result may be the o-vertble ature of the EGR olearty foud by forward model system detfcato. I Fg. 3 t s clearly see that resultat system polyomal olearty of EGR chael s ot oe to oe. III. INVERSE ACTUATOR POSITION MODEL Here two modelg stage s beg preseted as the Fg. 4. Frst, olear verse system s modelled wth parametrc model ad output errors of the parametrc model s covered wth Gaussa Process Regresso. GPR). Ths approach s vestgated o steady ad traset data sets followg two subsectos. Fg. 4 Model Iput - Output Scheme A. Gaussa Process Regresso for Parametrc Model Error Although Gaussa Process Model accuracy ad ease of mplemetato are favorable, computatoal cost s hgh for commercal ege cotrol uts ad t s the ma drawback of the method for the dustry. Regardg curret commercal ege electroc cotrol ut resources, a relatvely smple model s developed whle keepg the essetal beefts of the Gaussa Process Regresso GPR). Parametrc models o eges are geerally physcs based emprcal models as descrbed prevous secto. However, these models are geerally vald uder certa assumptos I our eample: o reverse flow). Obvously, real physcal system s more comple tha smplfed parametrc models ad the real physcal system models cossts of dfferetal equatos that caot be solved faster tha real tme sde the embedded cotroller. Although smplfed parametrc models ca be tued for certa trag data ad model accuracy values terms of errors ca be far for test data average, t may be ecessary to have better accuracy at certa operato codtos. Oce model s tued parametrc models caot be easly altered for better accuracy at ths certa pot whle keepg same model performace for the rest. Retug all the model may requre repeated valdato the whole space ad ths may be very costly terms of both tme ad moey a automotve ew model developmet cycle. However, ths correcto of the parametrc model fuctoalty s atural for GPR ad f dstace parameters are tued accordgly GPR does ot chage output values of the tal parametrc model where ts pror performace s already good. Assumg that the parametrc model s a determstc mea fucto for Gaussa Process of the verse model error. Gaussa Process: A Gaussa process s a collecto of radom varables, ay fte umber of whch has a ot Gaussa dstrbuto. [30]). Assume that the ose s addtve depedet ad detcally dstrbuted, ad y s the error of the parametrc model. I the sequel, we wll follow the formulato detaled [30]. Let the fuctoal relatoshp betwee puts ) ad the output y) be gve as: 2 y = f) +ε, ε N0, σ ) 2) Pror covarace o the osy observatos y ad y s defed as cov y, y ) = k ) + δ 3) σ 2 where k, ) s a covarace fucto defed over put samples ad, ad δ s the Kroecker delta fucto. k, ) s defed as: d 0.5 T l l k ) =σ e 4) where σ s the horzotal scale parameter ad d s a scaled l put sample gve by l 1 2 =... l1 l2 where l s the legth scale parameter. l T 5)

4 Cosderg samples of trag puts, oe ca costruct the followg covarace matr that wll be used subsequet aalyss: K X, X) = k 1, 1) k 1, 2)... k 1, ) 6) k ) k, ) Legth scale l ad horzotal scale σ d are called hyper parameters. These parameters wll be optmzed for model trag. I Gaussa process modelg there are two values so-called trag ad test values). Trag values are used for fdg hyper parameters ad also they become part of the model tself. The test values are the smulato puts whose outputs are calculated. Test puts are deoted by. * The covarace vector betwee smulato pot ad the trag pots s defed as: [ k ) k )... k ] T k ) * 1 * 2 * *= 7) Fally, the predctor equato s gve as: f T 2 1 = k K+ σ I y 8) * * ) The cost fucto log lkelhood) for the Mamum Lkelhood hyper parameter estmato s gve as: T log p y X) = 0.5y α tracelog L)) / 2log2π) 9) where s the umber of trag puts ad Fg. 5 Trag data pots selecto IV. SIMULATION RESULTS Parametrc model s ftted to steady state ege data of 524 pots wth R-square value of For the trag data, top 60 hghest error pots are selected. Mamum lkelhood estmato s doe va optmzato of GPR hyper parameters. Combed model reached a R-square value of 0.91 See Fg. 6). The am of correctg the parametrc model wthout makg trade-offs from ts geeral performace s acheved. α = L T L\ y) 10) L= cholesky K +σ 2 I) 11) Note that L s obtaed through the Cholesky decomposto. There are two challeges Gaussa process modelg: Fdg the hyper parameters ad selectg the trag pots. I ths work smple methods are carred out to overcome these two problems. Frst, hyper parameters are foud by umercal optmzato. Local mmums are foud wth gradet based optmzato wth MATLAB s fmco fucto. Ths was possble because of the lmted umber of trag pots. Remember trag of the model eeds verse of the K matr whch s by ). Wth creasg umber of, optmzato tme wll be loger. Latter challege s solved wth selectg trag pots havg error values of hgher tha certa threshold see Fg. 5). Parametrc Model Fg. 4 s selected as a secod degree polyomal wth 6 parameters: EGR = c EGR + c P3 P2) + c EGR P3 P2) posto 1 flow 2 3 flow + c EGR + c P3 P2) + c 4 flow ) Fg. 6 Combed model results as: measuremet ad y as: model) The am of the study was fdg better feedforward cotrol values. Model s et valdated o a traset ege cycle. Frst steady state ege operato pots ege speed ad total ecto quatty) of the ege are smulated wth parametrc model ad R-square value of 0.55 s obtaed. Error modelg wth GPR rased the ft value to I order to see traset geeralzato performace of the steady tued verse model, WHTC smulatos are compared wth

5 measured valve postos. Here parametrc model has ft value of 0.39 where combed model has 0.46 Fg. 7). The gap betwee combed ad parametrc models became arrower as show above. However, there are apparet accuracy crease especally steady sectos of the test as see Fg. 8. models wth feedback cotrol wll be cosdered as a future work. ACKNOWLEDGMENT Authors would lke thak colleagues from Calbrato & Cotrols ad Test & DV departmets of FORD OTOSAN for ther support o coductg epermets ad collectg real ege data. Ths study s fuded by FORD OTOSAN Product Developmet. REFERENCES Fg. 7 Iverse model o traset cycle Fg. 8 Valve posto vs. Tme V. CONCLUSION Gaussa process error modelg s successful for mprovg model accuracy of the verse valve posto model wthout worseg the behavour o the already accurate pots. Sce the umber of trag pots s lmted, fast smulato ad trag s possble whle geeralzato performace o the traset test was lmted. For the better traset verse modelg, adaptato of trag pots or usg addtoal flterg may be ecessary. I addto to the verse model mprovemet, ths type of [1] Heywood, J. 2000). Iteral Combusto Ege Fudametals. McGraw-Hll Book Co. [2] M. J. Va Neuwstadt, I. V. Kolmaovsky, P. E. Moraal, a. Stefaopoulou, ad M. Jakovc, EGR-VGT cotrol schemes: epermetal comparso for a hgh-speed desel ege, Cotrol Syst. IEEE, vol. 20, o. 3, [3] G. Stefaopoulou, I. Kolmaovsky, ad J. S. Freudeberg, Cotrol of varable geometry turbocharged desel eges for reduced emssos, Proc Am. Cotrol Cof. ACC IEEE Cat No98CH36207, vol. 3, o. 4, pp , [4] J. Chauv, G. Corde, ad N. Pett, Traset cotrol of a desel ege arpath, Proc. Am. Cotrol Cof., pp , [5] R. Omra, R. Youes, ad J. C. Champouss, Optmal Cotrol of a Varable Geometry Turbocharged Desel Ege Usg Neural Networks: Applcatos o the ETC Test Cycle, IEEE Tras. Cotrol Syst. Techol., vol. 17, o. 2, pp , [6] J. Wahlström, L. Erksso, ad L. Nelse, EGR-VGT cotrol ad tug for pumpg work mmzato ad emsso cotrol, IEEE Tras. Cotrol Syst. Techol., vol. 18, o. 4, pp , [7] S. Formet, S. M. Savares, ad L. Del Re, No-teratve drect data drve cotroller tug for multvarable systems: theory ad applcato, IET Cotrol Theory Appl., vol. 6, o. 9, p. 1250, [8] I. Park, S. Hog, ad M. Suwoo, Robust Ar-to-Fuel Rato ad Boost Pressure Cotroller Desg for the EGR ad VGT Systems Usg Quattatve Feedback Theory, vol. 22, o. 6, pp , [9] P. Orter ad L. del Re, Predctve Cotrol of a Desel Ege Ar Path, Cotrol Syst. Techol. IEEE Tras., vol. 15, o. 3, pp , [10] H. J. Ferreau, P. Orter, P. Lagthaler, L. Del Re, ad M. Dehl, Predctve cotrol of a real-world Desel ege usg a eteded ole actve set strategy, Au. Rev. Cotrol, vol. 31, o. 2, pp , [11] G. Stewart ad F. Borrell, A model predctve cotrol framework for dustral turbodesel ege cotrol, th IEEE Cof. Decs. Cotrol, pp , [12] T. Maruyama, T. Shmura, A. Er, Y. Ika, ad K. Shmota, Model Predctve Cotrol Appled to a Desel Ege Ar-Path System wth Dead Tme, o. 2, pp , [13] J. Wahlstrom ad L. Erksso, Output selecto ad ts mplcatos for MPC of EGR ad VGT desel eges, IEEE Tras. Cotrol Syst.Techol., vol. 21, o. 3, pp , [14] A. Murlo, M. Alamr, ad D. Alberer, A Geeral NMPC Framework for a Desel Ege Ar Path, It. J. Cotrol, o. Jue 2015, pp. 121, [15] M. Huag, Robust Rate-Based Model Predctve Cotrol of Desel Ege Ar Path, pp , [16] V. I. Utk, H.-C. Chag, I. Kolmaovsky, ad J. a Cook, Sldg Mode Cotrol, Amerca Cotrol Coferece ACC), 2000, 2000, o. Jue,pp [17] D. Upadhyay,V. I. Utk, G. Rzzo Multvarable Cotrol Desg for Itake Flow Regulato of a Desel Ege Usg Sldg Mode, IFAC Proceedgs Volumes Volume 35, Issue 1, 2002, Pages

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