J. Software Engneerng & Applcatons, 009, : 309-315 o:10.436/jsea.009.5040 Publshe Onlne December 009 (http://www.scrp.org/journal/jsea) 309 Responsveness Improvement of Ilng Spee Control for Automotve Usng SMC Yang ZHANG 1, Nobuo KURIHARA, Hroyuk YAMAGUCHI 3 1 Doctor of Scence Program n Mechancal Systems, Hachnohe Insttute of Technology, Hachnohe, Japan; Grauate School of Engneerng, Hachnohe Insttute of Technology, Hachnohe, Japan; 3 Department of System an Informaton, Hachnohe Insttute of Technology, Hachnohe, Japan. Emal: kurhara@h-tech.ac.jp Receve August 8 th, 009; revse September 8 th, 009; accepte September 15 th, 009. ABSTRACT To mprove the responsveness of engne spee control to sturbances, robust controls were nvestgate by smulaton. The ntake ar control system of a gasolne engne s a typcal nonlnear system, an the sturbances an parameter perturbatons are generally regare as beng the unstable factors wth regar to engne control. In ths paper, a Mean-Value Engne Moel (MVEM) wth sturbances an parameter perturbatons s nvestgate usng Slng Moe Control (SMC), whch s a form of varable structure control, wth a vew to aress nstablty n the le spee control process. The smulaton results confrme that, compare wth a conventonal PI (Proportonal-Integral) controller, the stablty of the le spee for an engne that s beng subjecte to sturbances, parameter varatons an backgroun nose s greatly mprove by the applcaton of SMC. Keywors: Gasolne Engne, Intake Ar Control, Slng Moe Control, Smulaton 1. Introucton Snce the begnnng of the 1st century, envronmental an energy problems have been becomng ncreasngly serous. A lack of fuel economy for automobles s consere to be the man cause of the global energy crss, an ths ssue nees to be aresse. Ile spee s the mnmum operatng spee of a combuston engne [1]. The pero at le occupes 30% of rvng tme for urban traffc. Furthermore, f the le spee can be reuce to 100 rpm (revolutons per mnute) by mprovng the control metho, fuel consumpton wll be reuce by to 5%. Therefore, sgnfcant fuel economy an emssons mprovements can be acheve by lowerng the le spee of an engne. In orer to acheve a relatvely lower le spee whle at the same tme preventng the engne from stallng, t s necessary to mantan a stable le spee n the presence of both known sturbances (e.g. statonary steerng an evaporaton-gas purge) an unknown sturbances. The automotve engne s a typcal nonlnear, tme-elay, tme-varyng parameter system. Recently there are many stues that apply control theores such as LQG, PID, an aaptve control to le-spee control []. In partcular, because Varable structure control s sutable for lnear an nonlnear, contnual an screte, certan an uncertan systems, the applcaton of slng moe control s regare as the soluton to the problem of mprovng the le-spee control. Nevertheless there are some stues are applyng ths theory [3,4]. However, le-spee control s suppose to be nvestgate practcally. In ths paper, le spee control was stue base on a non-lnear gasolne engne moel. As the PID (proportonal ntegral ervatve) controller s usually use for le spee control, the PID control an slng moe control (SMC) were employe to mprove le-spee control. The several sturbances such as control nput sturbance, torque sturbance an fuel sturbance were ae n the engne moel to certfy the responsveness an stablty of two control methos. An the operaton of the suen start also was also stue uner the fuel sturbance. The system s smulate by MATLAB /Smulnk. Relyng on result of smulatons, the robustness of le-spee control was mprove by usng SMC.. Ile Spee Control System In ths paper, we use an le spee control system whch was bult base on the mean value engne moel (MVEM) [5]. The moel conssts of three unts: an ntake manfol unt, a fuel mass unt, an a crankshaft unt. Because le spee control s the subject of ths stuy, an electronc Copyrght 009 ScRes
310 Responsveness Improvement of Ilng Spee Control for Automotve Usng SMC Fgure 1. Engne moel for le spee system throttle s necessary. The usual control process for le spee s llustrate as follows. The ntake ar flow s ajuste to acheve the set pont for the engne spee by ajustng the angle an poston of the electronc throttle. The crank angle sensor etects the engne spee, an the angle of the electronc throttle epens on the controller n the engne control unt. Next, the amount of ar supple to the cylner s ajuste usng the electronc throttle. Once that has been one, an amount of fuel proportonate to the ar flow s njecte nto the cylner. Thus, the torque prouce by fuel combuston mantans a constant engne spee. A moel of an le spee control system s shown n Fgure 1. Next, we wll escrbe the three parts of the engne moel by provng the equatons we use. The man ntal parameters of the engne moel were as follows: the engne splacement (V ) s 1.3 L; the fuel energy constant (H u ) was 43000 K J/kg; the gas constant of ar (R) was 0.0087 mbar/k.kg; the atmospherc temperature (T a ) was 93 K; the ntake manfol volume V was 0.000564 m 3 the atmospherc pressure (P a ) was 1.013 bar; an the moment of engne nerta was 5.638 kgm. Here we consere four factors that can easly make le spee control unstable: torque sturbance, fuel vapor sturbance, control nput sturbance, an parameter errors..1 Crankshaft Block n = H m In P P P In (1) u f f p The varable n n Equaton (1) s the engne spee (the unt use was set at rpm/1000); η s the thermal effcency; an P f, P p an P b are frctonal power, pumpng power, an loa power, respectvely. = n p n= 0.015+0.558 10.39 n 036 p=0.87+0.58p 0.39P = 0.01711.740.745 =0.7+0.04 0.00048 mbt P f, P p an P b are calculate usng the three emprcal equatons below. 3 P 1. 673n 0. 7n 0. 0135n f p 0969nP 006. n P 3 b Mbn 60 Kbn P. P Here, P s the manfol pressure; θ s the gnton angle; θ mbt s the mean best torque spark avance; λ s the excess ar coeffcent; an Mb an K b are both for the torque loa.. Fuel Block m ff X m f m ff f m fv 1 Xm f X 0. 7P 0. 055n 0. 68 mbt f 1. 35 0. 067n 1. 68 P 0. 85 0. 06n 0. 15 0. 56 (3) Here, m ff s the evaporaton fuel n the cylner; m f s the njecte fuel; m fv s the gasfe fuel; m f s the total amount of fuel n the cylner; X s the coeffcent of the fuel epost; an f s the tme constant for fuel evaporaton..3 Manfol Block at ap () P RT m m V PT /T (4) Here, T s the temperature n the manfol; m at s the ntake ar whch passes through the throttle; an m ap s the cylner ntake ar. m m m (5) at s a m s where s the ntake ar that passes through the by-pass valve m 0. 3988 u P 0. 01 (6) a m a 1 Here, s the ntake ar that passes through the throttle. 1 u 11. 4073cos u 180 0. 4087cos u 180 P r 0415. 1 P r 0. 415 P r 1 0. 415 0 P r 0. 415 r (7) Copyrght 009 ScRes
Responsveness Improvement of Ilng Spee Control for Automotve Usng SMC 311 Here, u s the openng of the throttle an Pr s the rato of P to P a. Where s the engne volumetrc effcency. v 095. 0075. P v T R 0. 4m m T 14. m T T PV 3. Lnearzaton ap at at a As s well known, the engne moel s a typcal non- near system. For the followng esgn for SMC, we neee to lnearze the engne moel to a state-space equaton at the operaton pont. In ths case, we selecte an engne spee of n an manfol pressure of P as two states. Here, u s the nput of avance angle gnton an u s the nput of the throttle, an both were provsonally consere as control nputs. x1 n u x u x P u A1 x B1 x 0 Ax Bx A 0 B x x A x B x u 1 x A x 0. 1841P 0. 039nP 0. 3178 0. 0516n 0. 006n A x 61. 895 1 18nP 15. 5 1. 397n B x m 680. 7 n B x RT V 1 n p ap (8) Havng sorte out the affne non-lnear equatons as state above, we then aresse the target operaton pont (x ), whch s gven as follows: x n P Therefore, the engne moel s lnearze n the vcnty of x. x xx u uu x AxBu 1 1 (9) a11 a1 b11 b1 (10) A B a a b b Next, we substtute the tangent lne for the curve lne accorng to the affne non-lnear equaton. f1 f1 x1 x n f A x x,u fn fn x1 x n f1 f1 u1 u n f B u x,u fn fn u1 u n a 11 0. 039 0. 0516 0. 005n a 1 0. 18410. 0039n a 1 0. 039 0. 0516 0. 005n a 61. 895 18n P x b1 b1 0 b1 n pm ap 680. 7 n b 155 (11) As a result, we were able to obtan the fnal matrces for A an B of the lnearze moel at two certan values of the abovementone states. 4. PID Control Desgn In the paper, we employe PI controller shown n Fgure. The gan of Kp an K are etermne by the Zegler- Nchols metho. 5. Slng Moe Control Desgn SMC s a type of varable structure control n whch the ynamcs of a nonlnear system are altere by the applcaton of a hgh-frequency swtchng control [6]. In other wors, SMC uses practcally nfnte gan to force the trajectores of a ynamc system to sle along the re- mportant, ro- strcte slng moe subspace. Ths s an bust control approach that proves an aaptve approach to tacklng the parametrc system, uncertan parametrc system, an uncertan sturbance system. If a swtchng surface s approprately esgne wth esrable characterstcs, the system wll exhbt esrable behavor when confne to ths swtchng surface. To pursue the target value, le-spee control can be shown as a servo system. Thus, the slng moe for a sngle-nput sngle-output Fgure. Block agram of PI controller Copyrght 009 ScRes
31 Responsveness Improvement of Ilng Spee Control for Automotve Usng SMC Fgure 3. Block agram of SMC system has been mae nto the block agram shown n Fgure, whch llustrates a close-loop SMC. The control nput s the sum of the lnear an non-lnear nputs. Here, n s the target engne spee, n s the actual engne spee, an the four kns of sturbances we have consere n ths paper have also been ae n the Fgure 3. 5.1 Controller In ths paper, we are only conserng the angle of the throttle as the control nput. Consequently, the followng system s consere. x 1 a11 a1 x1 b1 u x a1 a x b (1) a a n b u 11 1 1 a1 a P b In orer to apply SMC to the servo system, an expanson system s use n whch a new state, z, s assume as the value for the ntegraton of the fference between the target value an nput. The varable z s efne n Equaton (13) below. z rx n n (13) 1 The expanson servo system s gven n Equaton (14) below. z 0 1 0 z 0 1 x 1 0 a11 a 1 x1 0 u 0 r (14) x 0 a1 a x b 0 Equaton (14) can be rewrtten as follows: x Ax Bu Er (15) The swtchng functon s as follows: z x x Sx S x1 (16) The esgn for the swtchng surface s escrbe late. When the system s n slng moe, the swtchng functon s as follows: x 0 (17) When the system s n slng moe state, the ynamc characterstc s exhbte. When above the swtchng hyper-plane, the system mantans 0. Hence, by usng S x, substtutng Equaton (15) nto 0 gves: 0 SAx SBueq SE r (18) Takng the control law as: eq 1 u SB SAx SE (19) Equaton (19) gves the equvalent lnear control of a servo system wth slng moe. 5. Hyper-Plane For the system stablty margn, plane S s gven as follows: T r the swtchng hyper- S B P (0) where P s the postve efnte soluton of the Rccat equatons, so that: T PA A P PBB P Q 0 A A I Where s the stablty margn coeffcent, >0 s assume. To etermne the swtchng law, the Lyapunov func- ton canate wth s efne as follows: T (1) V 1 x () If the frst-orer ervatve V of the Lyapunov functon s a negatve efnte functon, can converge to 0. So the control nput s the sum of the lnear an non-lnear nputs. u u u (3) eq Here, non-lnear nput u nl s obtane as follows: u 1 nl k SB nl (4) If k >0, >0, k s the non-lnear nput swtchng gan an t s effcent n compensatng for unknown sturbances. To allevate chatter n the control output of the slng moe controller, we use as the output alteraton, whch s generally calle the smooth functon Copyrght 009 ScRes
Responsveness Improvement of Ilng Spee Control for Automotve Usng SMC 313 for replacng a conventonal sgnal functon. V k 0 (5) Accorng to Lyapunov s secon theorem on stablty, the hyper-plane measures the exstence of the slng m oe an reachablty. 6. Smulaton In orer to confrm robustness wth respect to a loa change sturbance urng le spee, the system was smulate uner the contons below. Frst, the ntal le spee of the engne was 700 rpm, gven the exstence of sturbances such as fuel purges an power wnow, a unt step nput was ae for the sturbance that results from an evaporaton-gas purge n the fuel moule an another unt step nput was ae for the sturbance that results from statonary steerng or other types of torque varatons n the crankshaft moule. The smulaton results are shown n Fgure 4. Secon, we consere the varable factors n a real engne, allowng us to nput the engne moel error, the Fgure 4. Responses for two sturbances Fgure 5. Responses for nput error an parameter pertur- batons control nput error, the gnton angle error, an the A/F (ar/fuel) rato nto the engne moel. Fgure 5 shows the results. From Fgure 4, we can see that f two entcal sturbances are loae at 5 secons an 1 secons, the control system s force to spen a conserable amount of tme reachng the target spee agan when PID s use. In other wors, the response tme s long an the compensaton effect s weak. In contrast, the sturbances were almost compensate for because of the relatvely large value of the compensatng gan k we use n the nonln- ear nput. A ±3% ranom error was ae n front of the engne moel as a control nput error. In aton, ±3% an ±1% ranom errors were ae to the stochometrc fuel ar rato an the gnton angle, respectvely. The results were as follows. From Fgure 5, we can see that there s lttle fluctuaton when PID s use, an the use of SMC oes not change the results. Thr, Moreover, as backgroun nose, the engne spee fluctuatons measure on an actual engne was ae to the engne moel, meanwhle, two sturbances as same as those n Fgure 4 were loae. The smulaton result s Copyrght 009 ScRes
314 Responsveness Improvement of Ilng Spee Control for Automotve Usng SMC shown n Fgure 6. The control system wth the slng moe controller s clearly more effectve aganst both of the two sturbances as f backgroun nose was loae. Fnally, we consere the responsveness an tracng ablty when the engne s mae a suen start from a lower le spee to a hgher spee such as 000rpm. As far as we know, there s usually lttle fuel loss n the suen start conton ue to some of fuel rops attache to the manfol, whch sometmes leas to the unesrable spee own. So we assume the suen start occurre at 6 secons an a step sturbance as fuel loss was loa at the tme. The smulaton results are shown n Fgure 7. Apparently, the transton of the suen start by SMC s faster than that by PI although the sturbance s loae. Base on the aforementone smulaton results, we can see that a control system wth a slng moe controller s more effectve wth respect to ether of the two sturbances, as well as to some errors n the actual en- provng the robustness of SMC. In aton, the gne, tracng ablty of le spee also appears to be mprove Fgure 7. Responses for a suen start from 700 rpm Fgure 6. Responses for loang engne-spee sgnal n the work conton uner the suen start wth the fuel sturbance. 7. Conclusons In ths paper we aresse the ssue of le spee control n orer to mprove the stablty of an engne s le spee an mprove ts fuel economy. To acheve hgh stablty an robustness for the le spee control system, the electronc throttle (whch regulates the ntake ar flow when an engne s lng) was taken as the control object, the engne was moularze by MATLAB/SIMULINK, an gven that the engne system s a typcal nonlnear system, the moel was lnearze at the operatng pont. Usng a lnearze state-space moel, we bult a hy- per-plane whch s aaptve to the controlle plant, after whch we also esgne a control nput for a controlle plant whch s the sum of the nonlnear an lnear nputs, so the SMC s constructe n m-fle. To prouce comparatve results, PI control was use, an n accorance wth Zegler-Nchols, the parameters of proporton an ntegral were ajuste on the ntal engne spee of 700 rpm. By usng SMC, the swtchng hyper-plane was esgne base on system zeros, an the system was esgne as a servo system n orer to acheve the target value. Compare wth conventonal PI control, the stablty aganst sturbances was mprove. Furthermore, the Copyrght 009 ScRes
Responsveness Improvement of Ilng Spee Control for Automotve Usng SMC 315 relatve robustness of SMC was confrme when an engne system was smulate uner parameter perturbatons an backgroun nose. Above all, t s much more potental to mprove le spee control an pursue low spee of the le spee by slng moe control. REFERENCES [1] H. Ano, Gasolne rect njecton engnes-present an future, Journal of Software Engneerng an Applcatons, Vol. 53, No. 9, 1999. [] F.-C. Hseh an B.-C. Chen, Aaptve Ile-spee control for spark-gnton engnes, SAE paper: 011197, 007. [3] B. Kwak an Y. Park, Robust vehcle stablty controller base on multple slng moe control, SAE paper: 011060, 001. [4] Y. Zhang, T. Koorkawa an N. Kurhara, Evaluaton of slng moe Ile-spee control for SI engnes, Journal of Software Engneerng an Applcatons, Vol. 40, No. 4, pp. 997 100, 009. [5] E. Henrcks, A. Chevaler an M. Jansen, et al., Moelng of the ntake manfol fllng ynamcs [J], SAE960037, pp. 1 5, 1996. [6] K. Nonam an H. Tan, Slng moe control of nonlnear robust control theory, Chapter 3, Corona publsher, Tokyo, 1994. Copyrght 009 ScRes