A New Generalized Controller for Engine in Idle Speed Condition

Transcription

1 J. Basc. Appl. Sc. Res., 2() , 22 22, TextRoad Publcaton ISSN Journal of Basc and Appled Scentfc Research A New Generalzed Controller for Engne n Idle Speed Condton * Mohammad Reza Gharb, 2 Majd Moavenan, 2 Department of Mechancal Engneerng, Ferdows Unversty of Mashhad, Mashhad, Iran ABSTRACT The man objectve of ths paper s to use a robust controller based on quanttatve feedback theory on vehcle to control engne at dle speed. There are dfferent parameters affectng vehcle fuel consumpton, fuel effcency, exhaust emsson reducton and better power delvery from whch Changes n engne works condton. In ths paper, the varous steps of controller desgn are undertaken and an optmal robust controller s desgned. Ths controllng approach, proposes a transparent and practcal controller desgn methodology for uncertan sngle-nput sngle-output and multvarable plants. In engne, Throttle Valve dynamc has multvarable nonlnear transfer functons. For ths reason n ths paper QFT technque s used for desgnng the proposed controller. After lnearzaton a robust controller s desgned for trackng problem. Next, smulaton for trackng problem has been carred out whch ndcates successful desgn of controller. The smulaton results show very good engne behavour under controlled actons n stuatons where the uncontrolled throttle has undesred behavour. It s also shown that wth the presence of dfferent uncertantes, the controller s able to produce accurate desred responses. KEYWORDS: Robust, Controller, QFT, Idle Speed, Throttle Valve. INTRODUCTION An mportant motvaton behnd ths study s that automatc control of nternal combuston engnes leads to several benefts such as reducton n emssons, mprovement n fuel effcency and power delvery. The ar qualty n many ctes falls consderably below the standards set by the World Health Organzaton as well as the Natonal Ambent Ar Qualty Standards []. One of the most mportant parameters n fuel consumpton and also emsson n engne s Ar-Fuel rato. It s the mass rato of ar to fuel present durng combuston. AFR s a sgnfcant measure for ant-polluton and performance tunng Procedures. Fgure shows emssons n dfferent AFR. Fg. Emssons n the dfferent AFR Lean mxtures, when njected n an nternal combuston engne, produce a smaller amount power than the stochometrc mxture. In the same way, rch mxtures return of poorer qualty fuel effcency than the stochometrc mxture. (The mxture for the best fuel effcency s somewhat dfferent from the stochometrc mxture). There are some modes whch engne works on them. When the engne s cold, t s cold speed. The engne makes so emsson especally harmful gases n ths condton. When the engne works dle, t emts also dangerous products but not as hazardous as cold speed. Fgure 2 shows them clearly [2]. *Correspondng Author: Mohammad Reza Gharb, PhD canddate, Department Mechancal Engneerng, Ferdows Unversty of

2 Gharb and Moavenan 22 Fg.2 Ar-Fuel Rato n engne modes There are some Standards for emssons. One of the most famous standards s Euro. Fgure 3 shows the amount of some dangerous combuston products n Euro 5. Fg.3 Emsson n Euro 5 For havng an obvous study n estmatng fuel consumpton, t s needed to test every vehcle. These tests are done n a same standard n every country. The protocol used for ths named drvng cycle. Drvng cycle s a seres of data shows the speed of vehcle versus tme. They are dfferent n dfferent regons. Some of them lke European are smooth. In fgures 4 and 5 one of the famous European drvng cycles and Amercan drvng cycles are demonstrated respectvely. Fg.4 One of the European drvng cycles Fg.5 One of the Amercan drvng cycles

3 J. Basc. Appl. Sc. Res., 2() , 22 Because of some reasons lke traffc, the engne should work n the dle speed condton. Ths study s devoted to control the engne n ths mode. Nomenclature: Symbol Quantty Parameter Value m α(t) Fllng rates of ar mass Angle, α.39 radans m β(t) Emptyng rates of ar mass Dameter, d th (58.). -3 m R Gas constant for ar Leakage area, A leak (5.3). -6 m 2 T m The manfold temperature Gas constant, R 28 J/Kg K V m The manfold volume Ambent temperature, T amb 298 K d th Dameter of crcular Ambent pressure, P amb (.98). 5 N/m 2 P atm Atmospherc pressure Isentropc exponent, γ.35 T atm Atmospherc temperature Volume, V m (5.8). -3 m 3 C d Dscharge coeffcent for the flow Ar temperature, T m 34 K γ Specfc heats of ar rato Coeffcent, γ.45 ρ m (t) Densty of ntake manfold ar Coeffcent, γ (3.42). -3 s ω(t) Engne speed n rad/s Coeffcent, γ 2 (-.). -6 s 2 η vol (t) Volumetrc effcency of the engne Stroke volume, V d (2.). -3 m 3 V d(t) Stroke volume of the engne cylnder Clearance volume, V c (.2). -3 m 3 m f Mass flow rate of fuel delvered by the fuel njector Exhaust gas pressure, P ex (.8). 5 N/m 2 X The fracton of the fuel that mpnges on the wall Parameter, η.6 J/Kg m ff The mass of the manfold fuel flm Parameter, η (2.2). -3 J s/kg τ ff Tme constant for the frst order evaporaton mode Parameter, β 5.6 N m λ Ar fuel rato Parameter, β 2 (.5). -3 N m s 2 T L Load torque and of the engne Transport delay from sucton to.25 s power stroke J Rotatonal nerta of the engne Inerta, J.2 Kg m 2 α Throttle angle when the throttle s fully closed A leak Flow area when the throttle angle s α δ suct pow Tme delay between sucton phenomenon and torque producton P(s,α) Uncertan plant G(s) Compensator N Engne speed Idlng The engne operates n ths mode f the clutch s dsengaged; the accelerator pedal s not pressed by the drver and the engne s n the dle speed range (typcally8-5 rpm). A separate dle speed controller takes over control of the engne. The reference speed for ths mode s set equal to mnmum possble speed such that the engne does not shut off. When the clutch s n dsengaged condton, the net power-tran nerta s very low. As a result, the cyclc fluctuatons n torque may cause undesrably large speed fluctuatons. Also the engne load durng dlng s of varable nature and could be a source of sudden drop or rse n the engne speed. When at dle, the engne s at the lowest extreme of ts speed range, pston speeds are low and the ar mass flow s mnmal thus turbulence and swrl are low. The valve overlap used to enable effcent engne breathng at hgher engne speeds means that at dle there s a large amount of resdual (burnt) gas present n the cylnder wth the charge, up to 3-4% at low ar flows ([FC99]).These factors mean that combuston qualty s generally poor, the non-homogeneous nature of the charge meanng that the varablty from cycle to cycle s larger than at hgher mass flows. The smaller system nerta durng the dle mode (compared to when the clutch s engaged and the nerta s comprsed of the whole vehcle) means that cyclc varatons n engne torque can sgnfcantly affect the engne speed on a cycle by cycle bass. Although the system s nherently stable n a nonlnear sense, see appendx C, cyclc varablty can stll cause sgnfcant speed varatons whch wll detrmentally affect customer percepton of vehcle qualty. The control objectves durng dlng mode are: Mantanng the mean engne speed equal to the reference value 2 Mnmzng speed fluctuatons. The work apples only to gasolne, spark gnted, port fuel njected (PFI) engnes. The work presented here s developed for an engne wth manual throttle and CU controlled ar bypass valve, however t s straghtforward to translate the work to engnes wth the ar path controlled by electronc throttle. Quanttatve Feedback Theory (QFT) There are dfferent methods to control engne at dlng speed. Amongst these methods, QFT s appled for controllng the engne at dlng speed condtons. In the 96s, Horowtz contnued the poneerng work of Bode and ntroduced a frequency-doman desgn methodology that was refned n the 9s to ts present form, commonly referred to as the quanttatve feedback theory (QFT) [3, 4]). 6598

4 Gharb and Moavenan 22 The QFT s consdered as a practcal engneerng method for the robust controller desgn of contnuous tme feedback systems, based on frequency-doman desgn methodologes [5, 6,, 8]. The quanttatve approach provdes a desgn methodology whch enables the desgner to observe clearly the lmtatons and trade-off n ts desgn. However, to use ths flexblty n an optmal compromse between dfferent practcal desgn requrements would requre much experence and expertse and s manly based on a tme consumng tral-and-error procedure [9, ]. Port Fuel Injecton System and Control System Fgure 6 shows a sketch of a drve-by-wre port fuel njecton engne. The engne control unt (ECU),controls ar/fuel rato and gnton tmng. Fg.6 drve-by-wre PFI engne Modellng Intake Ar Path Dynamcs In ths part, a dynamc model for ntake ar path n PFI engnes s derved.the resultng model s sutable for ntal analyss and desgn of a robust controller based on Quanttatve Feedback Theory on vehcle to control engne at dle speed. Fgure llustrates schematc of the ntake ar path. Fg. schematc of the ntake ar path One smple model of the ar flow n an ntake manfold s the fllng and emptyng model. The throttle admts ar flow from one end of the manfold, whle the cylnder draws ar out from the other. Assumng no leaks, the mass flow rate ( ) through the throttle and the mass flow rate ( ) out of the manfold are dentcal only n steady state. The rate of change of the ar mass wthn the ntake manfold equals the dfference between these two flows. = = Assumng that the manfold pressure ( ) s unform and the ntake manfold temperature ( yelds an expresson of ar path dynamcs n terms of manfold pressure. = () 2 ) s constant, deal gas law (2)

5 J. Basc. Appl. Sc. Res., 2() , 22 The ar mass flow rate past the throttle secton s a functon of followng two varables: area for the flow, and pressure rato across the throttle secton. m (t) = C P Area(t) ψ P (t) (3) RT P (t) Fg.8 Ar flow past the throttle plate The avalable cross sectonal area whch the flow has to pass can be expressed as: Area(t) = d [ cos(α(t))] ψ ( ) = ( ) γ[ ] ( ( ) ( ) ) [ ( ( ) ( ) ) for ] for ( ) < [ ] ( ) ( ) [ ] ( ) (4) (5) The throttle body control block s shown n Fgure 9. Fg.9 Throttle body control block As a consequence, two approxmate results could be observed. Frst, the equalty of temperature before and after orfce T atm (t) = T m (t) and Second, the equalty of downstream pressure, P m (t),and the pressure at the narrowest ponts of valve. By Modellng ar nducton we can come nto the assumpton that engne s a volumetrc pump. m β (t) = ρ m (t) V (t) (6) Cylnder ar nducton control block s shown n Fgure. Fg.. Cylnder ar nducton control block Assumng (η ) as a statc functon of manfold pressure and engne speed, a typcal expresson for mass flow rate s as follows: m β(t) = ρ m (t) η vol (P m (t), ω(t)) V d ω(t) 2π Torque Producton Three dmensonal thermodynamc smulaton of the combuston process s requred for accurate estmaton of torque. The engne torque s usually formulated as a statc functon of the nfluencng varables to obtan modelng. Varous approaches have been proposed to obtan the statc torque functon [, 2]. From one of these approaches that use the noton of mean effectve pressures the followng expresson s drven []: () T (t) = ( ( ), ( )) ( ) H ( ). ( ) ψ(ω(t), P (t)). (8) Lnearzaton The man objectve durng the dlng mode s to mantan a constant engne speed rrespectve of engne loadng. It s assumed that the ar-fuel rato s held at stochometrc value by a separate controller. It s also assumed that the spark

6 Gharb and Moavenan 22 advance s affected by a separate controller. Therefore, for the purpose of controllng dlng speed, throttle angle (α) s the only control nput that nfluences engne torque producton, and thus engne speed. The model has two state varables manfold pressure (P m ) and engne speed (ω). Equaton (4) for the throttle area s modfed to the followng form: Area(t) = d ( ) + A ( ) (9) In dlng condton, the manfold pressure (P m ) s always less than the crtcal pressure lmt (P cr ) defned as : [ ] P (t). In ths case, equaton (3) for mass flow rate across the throttle secton s approxmated n equaton (): m (t) = Area(t) ( ) () Substtutng equaton (9) nto () gves the followng statc relatonshp between the mass flow rate and the throttle angle. ( ) ( ) + A = m (α(t)) () m (t) =. ( ) d The mass flow rate of ar enterng the cylnder may be expressed as a statc functon as follows [2]. m (t) =. η P (t). η ω(t) V ( ) = m P (t), ω(t) (2) Thus, from equatons (2), () and (2) the rate of change of manfold pressure P (t) can express as a nonlnear functon of α (t), P m (t) and ω (t) as follows: P (t) = f (P (t), ω(t), α(t)) (3) Evoluton of the engne speed happens as expressed by equatons (4): δ (t) = ( ) (4) It s assumed that the ar-fuel rato s held tghtly at the stochometrc value. The tme delay from sucton to power stroke s neglected. Then from equaton (8) the engne torque can expressed as a nonlnear statc functon of engne speed (ω) and the ntake manfold pressure (P m ). Ths n-turn allows rate of change of engne speed to be expressed n the followng form: ω (t) = f (P (t), ω(t), T (t)) (5) State matrx s chosen to have two elements vz. manfold pressure (P m ) and engne speed (ω). The nput to the control system s throttle angle (α). Load torque (T L ) s the dsturbance for the system. The nonlnear system expressed by equatons (3) and (5) s lnearzed and expressed n the followng state-space form: P ω =. P ω +. α +. T (6) The coeffcent matrces must be evaluated at a gven operatng pont defned by combnaton of (P m, ω) or (α, T L ). For the purpose of smulatons, engne specfcatons for a 2.8 ltter port fuel njecton engne are taken from [3]. These specfcatons and values of varous other engne parameters for the engne at dlng state are mentoned n Appendx A. The desred dlng speed s chosen as rad/s. The ntal load torque s taken as 5 Nm, requred throttle angle and the ntake manfold pressure were found usng equatons (3) and (5). They came out to be.598 radans and N/m2 respectvely. The coeffcent matrces were evaluated at the operatng pont to gve followng state-space equaton. P = ω P ω e. α + 5. T () Quanttatve Feedback Theory (QFT) QFT desgn ncludes three man steps whch are computng the robust performance bounds, desgnng the robust controller and f necessary proper pre-flter. At the end, analyss of the desgn s requred. In Fgure transfer functons G(s) and F(s) are compensator (strctly proper) and pre-flter (proper) respectvely. Also these two transfer functons are 66

7 J. Basc. Appl. Sc. Res., 2() , 22 checked to be stable. P(s) s uncertan plant belong to a set of P(s) {P(S, α); α P}where α s the vector of uncertan parameters for uncertanty structured of P(s) whch to take values n P; also R(s) are reference nput sgnals. Fg. Feedback Control System Confguraton for QFT Trackng Problem The specfcatons overshoot and the settlng tme are gven n the form of upper and lower bounds n frequency doman, usually based on smple second-order models to represent under damped and over damped condtons. P(j )G(j ) a( ) <F(j ) b( ) P(j )G(j ) Where a( ) and b( ) are postve real valued functons of. Robust Margns The two condtons for robust stablty are: () stablty of the nomnal system and (2) the Nchols envelope does not ntersect the crtcal pont q (whch s the (-8, db) pont n a Nchols chart or the (-, ) pont n the complex plane). The second condton s equvalent to placng a magntude constrant on the complementary senstvty functon. l ( j ) l For all > and p where: L(s) = P(s) G(s) (9) Robust Performance Bounds Havng obtaned the robust-performance bounds nclude trackng problem and robust stablty bounds (U-contour) the overall bounds of the desgn can be calculated by combnng approprately the ndvdual bounds for each pont of the phase-grd. Loop Shapng Employng the uncertanty templates n the desred frequency doman and by satsfyng the robust stablty and performance bounds s acheved. Loop shapng s performed to produce a loop gan whch satsfes the correspondng bounds at all frequences. The compromse between performance and cost of feedback, compensator order and bandwdth s clearly seen n the loop-shapng process. Ths process s, however, very much dependent on the experence and ngenuty of the desgner [3, 4, 6, ]. The trackng specfcaton s translated to certan condton on the nomnal open loop frequency responsel (s) = P (s)g (s)wherep (s) denotes the nomnal plant, defned for any P the trackng specfcatons wll be satsfed []. (8) L ( j ) max p P ( j ) L ( j ) P( j, ) db ( ) b( ) a( ) (2) Desgn of Robust Controller Template Generaton Fgure 2 shows the model of Yaw channel throttle valve. TF =. a= [.,.4] b= [3.3, 3.6] (2) Trackng Problem The overshoot lmt n specfcatons (M P = 2%) and the settlng tme (T S =. s) are gven n form of upper and lower bounds n frequency doman, Robust trackng bounds for yaw channel are shown n Fgure3.

8 Gharb and Moavenan 22 Robust Trackng Bounds Magntude (db) Plant Templates (parametrc part w/o hardware) Magntude (db) Phase (degrees) Fg.2 Uncertanty templates Phase (degrees) Fg.3 Robust Trackng Bounds Robust Margns For our QFT desgn, the followng robust stablty margn constrant s added. Robust Margn: l + (jω) < (22) Fgure 4 shows the Robust Margns Bounds. Robust Performance Bounds The robust performance bounds for Throttle Valve are obtaned by ntersecton bounds from robust margns and trackng bounds. You can observe the robust performance bounds n Fgure 5. Robust Margns Bounds All Bounds Magntude (db) Magntude (db) Phase (degrees) Fg.4 Robust Margns Bounds Phase (degrees) Fg.5 Robust performance bounds Loop Shapng By usng the elements of the QFT toolbox we desgn the controller so that the open loop transfer functon exactly les on ts robust performance bounds and does not penetrate the U-contour at all frequency values (ω ). Fgure 6 demonstrates the Loop-shapng n Nchols chart. The optmal s desgned and gven as below: Fg.6 Loop-shapng n Nchols chart

9 J. Basc. Appl. Sc. Res., 2() , 22 s G(s) =.465 s (23) Analyss of Desgn The tme doman closed loop response wth controller s shown n Fgure whch ndcates our desgn s accurate. Concluson Fg. Step response and control effort of system wth G(s) Automatc control of engne's throttle valve has many advantages such as reducton n emssons, mprovement n fuel effcency and power delvery. In ths paper, after obtanng model of system wth uncertanty, QFT s used n order to desgn a robust controller for engne at dle speed. The basc desgn steps can be summarzed as lnearzaton of Throttle body dynamcs, desgn of sutable robust controller for stablty and trackng problems. Fnally, smulaton of control ndcates that applyng the proposed technque successfully overcomes obstacles for robust control of engne at dle speed. REFERENCES [] Zhong Y., T. Fang, and K.L. Wert, 2. An adsorpton ar condtonng system to ntegrate wth the recent development of emsson control for heavy-duty vehcles. Energy, 36 (): [2] Ohata, A., M. Ohash, M. Nasu, and T. Inoue, 995. Model based ar fuel rato control for reducng exhaust gas emssons. SAE Internatonal Congress and Exposton, Techncal Paper, No [3] Horowtz, I.M., 99. Survey of Quanttatve Feedback Theory. Int. Journal of Control, 53(2): [4] Horowtz IM, O. Yanv, 985. Quanttatve cascade mult-nput mult-output synthess by an mproved method. Internatonal Journal of Control, 42(2): [5] Yang, S.H, 29. An mprovement of QFT plant template generaton for systems wth affnely dependent parametrc uncertantes. Journal of the Frankln Insttute, 346(): [6] Gharb, M.R., S. Kamelan, S.A. S. Mousav, and I. Dabzadeh, 2. Modellng and Lnear Multvarable Robust Control for a Power Plant. Internatonal Journal of Advance Mechatronc Systems, 3(2): [] Chat, Y., and O. Yanv, 993. Mult-nput/sngle-output computer aded control desgn usng the Quanttatve Feedback Theory. Internatonal Journal of Robust and Non-lnear Control, 3 ():4-54. [8] Yanv, O., 998. Quanttatve Feedback Desgn of lnear and non-lnear control systems. Kluwer Academc Publshers, Norwell. [9] García-Sanz, M., I. Egaña, and M. Barreras, 25. Desgn of Quanttatve Feedback Theory Non-Dagonal controllers for use n uncertan multple-nput multple-output systems. IEEE Proceedngs-Control Theory and Applcatons, 52 (2): -8. [] Amr-M., Amr-A, M.R. Gharb, and M. Moavenan, 29. Modellng and Control of a SCARA Robot Usng Quanttatve Feedback Theory. Proc. IMechE Part I: J. Systems and Control Engneerng, 223 (): [] Ford, R.G., 2. Robust Automotve Idle Speed Control n a Novel Framework. Ph. D, Dssertaton, Darwn College, Unversty of Cambrdge. [2] Guzzella, L., C. Onder, 24. Introducton to Modelng and Control of Internal Combuston Engne Systems. Sprnger, Berln. [3] Pushkaraj, A.P., 25. Dynamc Modelng and Control of Port Fuel Injecton Engnes. Thess for Master of Technology, Indan Insttute of Technology, Bombay.