ENGINE NET TORQUE COMPENSATION THROUGH DRIVELINE TORQUE ESTIMATION IN A PARALLEL HYBRID VEHICLE

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1 Internatinal Jurnal f Autmtive Technlgy, Vl.?, N.?, pp.??(year) Cpyright 2000 KSAE Serial#Given by KSAE ENGINE NET TORQUE COMPENSATION THROUGH DRIVELINE TORQUE ESTIMATION IN A PARALLEL HYBRID VEHICLE Jinrak Park 1), Seibum Chi 1)*, Jiwn Oh 2), and Jengs E 2) 1) Department f Mechanical Engineering, KAIST, Daejen 34141, Krea 2) Research and Develpment Divisin, Hyundai Mtr Grup, 150 Hyundaiyengus-r, Namyang-eup, Hwaseng-si, Gyenggi-d 18280, Krea (Received date ; Revised date ; Accepted date ) * Please leave blank ABSTRACTIn recent years, interest in smart and green vehicles has increased. There are many cases where engine net trque related cntrl is perfrmed when building smart and green car systems. Speed tracking cntrl in autnmus driving, r ptimal transmissin shift cntrl is an example. The engine net trque is the sum f the engine indicated trque, accessry lad trque, and frictinal trque, and the starter mtr trque in the case f a parallel hybrid vehicle. Hwever, the estimatin errr f these trque items can cause the estimatin errr f the engine net trque. In this paper, a cmpensatin methd fr the slwly varying uncertainty f the engine net trque in a parallel hybrid vehicle using a multiplicative cnstant is prpsed. The adaptatin f the multiplicative cnstant is cnducted using the amunt f change in the engine net trque estimated in the backward directin f the driveline. The prpsed algrithm is verified based n prductin vehicle data. KEY WORDS : Engine trque estimatin, Engine net trque estimatin, Engine trque cmpensatin, Engine net trque cmpensatin, Vehicle driveline mdel, Parallel hybrid vehicle NOMENCLATURE T e : engine net trque, N m T e.n : nminal engine net trque, N m T ec : engine clutch trque, N m T m : mtr trque, N m T c : transmissin clutch trque, N m T : utput shaft trque, N m T L : lad resistance trque, N m J e : engine inertia, kg m 2 J m : mtr inertia, kg m 2 J c : clutch inertia, kg m 2 J v : vehicle inertia, kg m 2 J mc : mtr and clutch inertia, kg m 2 i t : transmissin gear rati, - i f : final gear rati, - l: trque cnstant, - L 1 : lwer bund f actuatr displacement, mm L 2 : upper bund f actuatr displacement, mm d a : actuatr displacement, mm ω e : engine angular speed, rad/s ω m : mtr angular speed, rad/s ω c : clutch angular speed, rad/s * Crrespnding authr. sbchi@kaist.ac.kr ω w : wheel angular speed, rad/s θ c : rtatinal angle f the transmissin shaft, rad θ w : rtatinal angle f the wheel, rad λ : adaptatin gain, - ε : adaptatin errr, N m : the amunt f variatin, - V x : vehicle lngitudinal velcity, rad/s t s : gear hlding time, s α : lwer bund f engine trque mm β : lwer bund f vehicle lngitudinal velcity, rad/s γ : lwer bund f gear hlding time, mm δ : upper bund f gear hlding time, mm 1. INTRODUCTION Drivers expectatins fr car cnvenience are increasing and autmbile exhaust gas regulatins are being strengthened cntinually. Thus, research n intelligent vehicles and ec-friendly vehicles has been actively cnducted recently. Engine net trque is ne f the mst imprtant cntrl variable t realize a smart and green car system. Fr example, precise cntrl f engine net trque is required in a system f vehicle dynamics cntrl, active engine cntrl, ptimal pwertrain cntrl, predictive energy management, etc.

2 Figure 1. Methds f engine net trque estimatin The engine net trque mentined in this paper refers t the trque that can be transmitted frm the engine crankshaft end flywheel. A trque sensr that can measure driveline trque, e.g., the engine net trque n the engine flywheel shaft, is nt installed in a real car due t their high cst and spatial limitatin (Yi et al., 2000, Kim et al., 2018, Ga et al., 2011). Therefre, the engine net trque must be estimated withut accurate measurement, even thugh it is imprtant infrmatin in varius cntrl systems. Fig. 1 shws a lumped driveline mdel f a parallel hybrid vehicle and methds f engine net trque estimatin. The engine net trque can be calculated by accurately estimating and summing the engine indicated trque generated by fuel cmbustin, the accessry lad trque, the frictinal trque, and the starter mtr trque in the case f a parallel hybrid vehicle: this is knwn as the frward directin estimatin methd. When estimating the engine indicated trque, a map whse inputs are thrttle angle and engine speed, and whse utput is the engine indicated trque is ften utilized (Rajamani, 2011). On the ther hand, when the altitude f the envirnment in which a vehicle is traveling changes, the atmspheric pressure als changes, and the amunt f air sucked int an engine with respect t the same thrttle angle and engine speed is als changed. Additinally, when the intake line is mdified, the amunt f intake air can als be changed. The engine indicated trque map f thrttle angle and engine speed will then be changed frm the riginal map, and as a result the engine indicated trque can be inaccurately estimated. Als, if an additinal accessry is installed fr the user's cnvenience, the errr f the accessry lad trque can ccur. In additin, it is difficult t estimate the frictin trque since it varies depending n the type f engine il and the engine wear. Therefre, when estimating the engine net trque in the frward directin, uncertainty n the engine indicated trque, the accessry lad trque, and the frictinal trque causes uncertainty in the engine net trque. The engine indicated trque can be estimated based n a trque mdel instead f a trque map (Guzzella and Onder, 2009, Erikssn and Nielsen, 2014), and sme studies have been cnducted t imprve the accuracy f the trque mdel in the engine transient state (Smith et al., 1999, Chevalier et al., 2000). Als, the engine indicated trque was estimated as a functin f crankshaft speed and the amplitude f crankshaft speed fluctuatin (Sttsky, 2009, Sttsky, 2005) (Rizzni, 1989), derivative terms f crankshaft angle (Lee et al., 2001), crankshaft speed and engine blck vibratin (Azzni et al., 1998), and crankshaft speed and an index that was newly prpsed in the papers (Jianqiu et al., 2002b, Jianqiu et al., 2002a). The sum f the frictin trque and the accessry trque was estimated using the engine indicated trque when an engine is idling (Sttsky, 2009). The secnd way f estimating the engine net trque is the backward directin methd. This methd estimates the utput shaft trque r rad lad trque, and calculates the engine net trque in the backward directin cnsidering the inertia effect. By using this backward engine net trque estimatin methd, it is pssible t crrect the uncertainty f the engine net trque in the afrementined engine net trque estimatin methd in the frward directin. Hwever, little research n the backward engine net trque estimatin methd using a vehicle driveline mdel has been cnducted. In sme papers (Rizzni and Zhang, 1994, Chi and Hedrick, 1996), the engine net trque was estimated based n the engine lad trque which is assumed t be measured using a dynammeter. Hwever, the engine lad trque cannt be measured and als cannt be estimated easily in a real vehicle. Furthermre, the adaptatin methd f the engine net trque was studied in (Oh et al., 2013). An additive cnstant, which represents the engine net trque

3 uncertainty, and the utput shaft trque were estimated simultaneusly using the nminal engine net trque and a driveline mdel. Hwever, the cnvergence speed can be prblematic when tw parameters are estimated simultaneusly in ne mdel equatin. Als, in many studies, the utput shaft trque is mdeled using the shaft cmpliance mdel (van Berkel et al., 2014, Oh et al., 2014, Oh et al., 2017a, Jeng and Lee, 2000b, Glielm et al., 2006). Hwever, in a prductin vehicle, the shaft angle cannt be measured and therefre shuld be calculated by integratin f the shaft speed. Hwever, the shaft angle can drift due t the nise f the shaft speed. Als, the shaft cmpliance mdel cannt describe the backlash f shaft jints. Thus, the estimate f the utput shaft trque itself can be inaccurate due t these reasns. This paper prpses a cmpensatin methd fr the slwly varying uncertainty f the engine net trque estimated in the frward directin f the driveline in a parallel hybrid vehicle using a multiplicative cnstant, which is called the trque cnstant in this study, and mainly addresses the adaptatin algrithm f the trque cnstant. The adaptatin f the trque cnstant is cnducted using the amunt f change in the nminal engine net trque estimated in the frward directin f the driveline and the amunt f change in the engine net trque estimated in the backward directin. The reasn why the amunt f change in the engine net trque is utilized instead f the engine net trque itself is due t the drift issue f the utput shaft trque which is used t estimate the engine net trque in the backward directin. The utput shaft trque is mdeled using the shaft trque cmpliance mdel in this study. The remaining part f this paper is rganized as fllws. Sectin 2 intrduces the cmpensatin methd fr the uncertainty f the nminal engine net trque and the adaptatin algrithm f the trque cnstant. Sectin 3 addresses the experiment results in a parallel hybrid prductin vehicle. Sectin 4 cncludes this paper 2. ENGINE NET TORQUE COMPENSATION METHOD In this sectin, the cmpensatin methd fr the slwly varying uncertainty f the engine net trque estimated in the frward directin f the driveline in a parallel hybrid vehicle using a multiplicative cnstant (which is referred t as the trque cnstant in this paper), and the adaptatin algrithm f the trque cnstant are addressed. The adaptatin f the trque cnstant is perfrmed using the amunt f change in the nminal engine net trque estimated in the frward directin f the driveline and the amunt f change in the engine net trque estimated in the backward directin. Hereinafter, the engine net trque estimated in the frward directin f the driveline is called the nminal engine net trque and the engine net trque estimated in the backward directin is called the estimated engine net trque. A driveline mdel f a parallel hybrid vehicle and an engine net trque estimatin methd in the backward directin f the driveline are intrduced in subsectin 2.1. In additin, the adaptatin algrithm f the trque cnstant is dealt with in subsectin 2.2. Lastly, the applicatin cnditin f the adaptatin algrithm is mentined in subsectin Driveline mdel Fig. 1 shws a lumped inertia driveline mdel f a parallel hybrid vehicle. In this study, the methd f estimating the engine net trque frm the utput shaft trque in the backward directin f the driveline is utilized and the utput shaft trque is estimated using the trque cmpliance mdel like belw. t t T b ( w) k ( w) (1) i i i i The trque cmpliance mdel cnsists f a trque spring cnstant and damping cnstant f a shaft, and the trque mdel is thereby nt affected by the external envirnment f the vehicle such as inclinatin, cmpared with the lad trque mdel. The mathematical driveline mdel f a parallel hybrid vehicle using a lumped inertia is as fllws, referring t the driveline mdel f ther studies (Oh et al., 2017b, Oh and Chi, 2015, Ni et al., 2009, Jeng and Lee, 2000a). Jee Te Tec (2) J T T T (3) m m ec m c J T cc Tc (4) J T T (5) v w L In this study, it is cnsidered that the adaptatin f the trque cnstant, and transmissin gear shift cntrl are nt perfrmed at the same time. S, it is assumed that the transmissin clutch is fully engaged during the adaptatin perid f the trque cnstant. Equatins (3) and (4) can then be expressed as fllws. J T T mcm ec m (6) J J J (7) mc m c Furthermre, the engine net trque can be estimated using the utput shaft trque in a backward manner in T

4 the driveline as fllws by summing equatins (2) and (7). T T T J J (8) e m e e mc m Here, it is assumed that the engine speed and mtr speed in the right side are measurable, and that the mtr trque is als measurable by current measurement Adaptatin algrithm f trque cnstant In equatin (1), the trque cmpliance mdel f the utput shaft trque is expressed with the rtatinal angle f the transmissin and the wheel. Hwever, in a prductin vehicle, the rtatinal speed f shafts is measured rather than the rtatinal angle, and therefre equatin (1) shuld be mdified as given belw fr applicatin t a prductin vehicle. T b ( ) k ( ) dt t t t w 0 w iti f iti f (9) Hwever, the rtatinal angle f the transmissin and the wheel is integrated frm the rtatinal speed. Thus, the estimated value f the utput shaft trque may becme inaccurate ver time if the small errr f the rtatinal angle f the transmissin and the wheel is accumulated by sensr nise. Als, due t the backlash f shaft jints, the estimate f the utput shaft trque may becme inaccurate. In the case f a vehicle equipped with a dual clutch transmissin(dct), it is difficult t determine the shaft speed and the shaft gear rati when the transmissin gear shift is perfrmed, and discntinuity f the utput shaft trque ccurs befre and after the shift. Fr these reasns, the estimated utput shaft trque can drift, and this value cannt be used t cmpensate fr the uncertainty f the engine net trque directly. Further details f the drift issue f the utput shaft trque are discussed in the results sectin. On the ther hand, the amunt f change in the utput shaft trque during a specific perid f time can be mre accurate than the value f the utput shaft trque itself. Therefre, in this study, the amunt f change in the engine net trque is estimated using the amunt f change in the utput shaft trque ver a specific perid f time and the adaptatin f the trque cnstant is cnducted using the amunt f change in the nminal engine net trque and the amunt f change in the estimated engine net trque instead f using the estimated engine net trque itself. Further details f the specific perid f time is addressed in the next subsectin. By mdifying equatin (8), the fllwing trque variatin frmula can be btained. T Te ( Tm Jee Jmcm ) (10) Applying the trque cnstant t the engine net trque, the fllwing equatin can be btained. T e lt e. n (11) Als, the estimate f the trque cnstant can be expressed as fllws. ˆ ˆ T Te ( Tm Jee Jmcm ) (12) T ˆe lˆ T e. n (13) In rder t cnsider bth situatins where the engine net trque increases r decreases, the adaptive errr is defined as fllws by taking the abslute value f the engine net trque in equatins (11) and (13). T Tˆ ( l lˆ ) T e e e. n T ( T J J ) lˆ T t f m e e mc m e. n (14) Finally, the adaptive law f the trque cnstant is defined as fllws using a simple gradient methd (Sastry and Bdsn, 2011, Iannu and Sun, 1996). l ˆ T, 0 en (15). the adaptatin f the trque cnstant is cnducted at the end f each specific perid f time using the amunt f change in the engine net trque. Figure 2. Experimental vehicle Figure 3. Schematic diagram f the engine clutch actuatr

5 Figure 4. Output shaft trque accrding t gear shift The amunt f change in the nminal engine net trque satisfies the persistence f excitatin (PE) cnditin, and the errr f the trque cnstant will cnverge t zer Applicatin cnditin Figure 5. Enlarged figure f utput shaft trque accrding t gear shift T prve the stability f the errr dynamics during the adaptatin, the estimatin errr f the trque cnstant is defined as fllws. l l lˆ (16) Als, the estimatin errr dynamics f the trque cnstant is given as fllws. 2 l l T en., 0 (17) The stability f the errr dynamics then can be prven using a simple Lyapunv functin as fllws. Vl () 2 l 2 (18) 2 2 V l T en. 0 (19) In the previus subsectin, it was nted that the adaptatin f the trque cnstant is perfrmed at the end f each specific perid f time using the amunt f change in the engine net trque ver the specific perid f time. Hereinafter, the specific perid f time when the amunt f change in the engine net trque is calculated is called applicatin perid. Als, it was mentined that the utput shaft trque which is estimated using the shaft trque cmpliance mdel can becme inaccurate if the small errrs f the transmissin input shaft and wheel speed are accumulated due t the integratin f the rtatinal speeds. Thus, the engine net trque which is calculated using the estimated utput shaft trque drifts as well ver time and the errr f the amunt f change in the engine net trque wuld be large when an applicatin perid is lng. Als, the amunt f change in the engine net trque ver an applicatin perid shuld be large cnsidering the errr f the amunt f change. Therefre, it is nticed that an applicatin perid shuld be shrt and the amunt f change in the engine net trque ver an applicatin perid shuld be large. In the case f a parallel type hybrid vehicle, the engine net trque changes greatly and mntnically when the engine clutch is engaged and disengaged, that is discussed in the result sectin. Thus, this study prpses t use the perid, when the engine clutch is engaged and disengaged, i.e., when the driving mde f

6 applicatin perid. Hereinafter, this applicatin perid is called applicatin perid2. T, V, t (21) e x s 3. EXPERIMENT RESULTS Figure 6. Engine clutch trque and actuatr psitin while the engine clutch is engaged r disengaged Figure 7. Driveline speed while the engine clutch is engaged r disengaged a parallel hybrid vehicle is transferred frm the electric vehicle(ev) mde t the hybrid electric vehicle(hev) mde and frm the HEV mde t the EV mde, as an applicatin perid. Hereinafter, this applicatin perid is called applicatin perid1. Referring t the schematic diagram f the engine clutch actuatr f the experimental vehicle like Fig. 3, In this study, the pistn psitin signal f the engine clutch actuatr is utilized t check the engagement r disengagement f the engine clutch. Thus, the applicatin perid1 is defined as the perid when the pistn psitin f the engine clutch actuatr is in a specific range like belw. L d L (20) 1 a 2 Als, t cmpare the adaptatin perfrmance f the trque cnstant in the envirnment f the applicatin perid1 with the perfrmance in the envirnment f anther applicatin perid, the perid, when the amunt f change in the engine net trque is nt large and the cnditin belw is satisfied, is defined as anther In this paper, the adaptatin algrithm f the trque cnstant described abve was verified based n the daily driving data f an riginal prductin hybrid vehicle. The schematic diagram f the experimental vehicle s pwertrain is shwn in Fig. 1. Fig. 4 shws an example f the estimated utput shaft trque and the estimated engine net trque using equatin (8) and (9). Fig. 5 is an enlarged figure f Fig. 4 fr a certain perid. Fr a vehicle equipped with a DCT, as described in subsectin 2.2, the engaged shaft s gear rati must be determined in rder t estimate the utput shaft trque befre and after the transmissin gear shift. On the ther hand, since it is difficult t determine the engaged shaft and the engaged shaft s gear rati during the shift, the utput shaft trque estimatin is suspended during the shift and the estimatin starts again after the shift is cmpleted. In this case, the utput shaft trque des nt change after the shift but T i i shws a discntinuity befre and after the shift since the speed rati is changed. Als, angular velcity nise, and backlash between the shaft jints als cause errr in the utput shaft trque estimatin. This can be seen in Fig. 4 and Fig. 5. Fig. 6 shws examples f the applicatin perids when the amunt f change in the engine net trque is calculated. The experimental vehicle is equipped with a nrmally clsed engine clutch, which is pen when the value f the actuatr psitin is large and clsed when the value f the actuatr psitin is small. Als, Fig. 7 shws examples f the driveline speed during the applicatin perids. In Fig. 6, it is nticed that the engine net trque is changed greatly and mntnically during the applicatin perid1, which is the perid when the engine clutch is engaged and disengaged, r the engine clutch actuatr pistn psitin is within a certain level. In cntrast, the engine net trque is nt changed greatly during the applicatin perid2, which is the perid when the cnditin f the inequality (21) is satisfied. The adaptatin perfrmance f the prpsed algrithm was verified by investigating whether the trque cnstant tracks the reciprcal f the cnstant, which is multiplied t the engine net trque intentinally, assuming that there is uncertainty in the nminal engine net trque. Fig. 8(a), and (b) shws the estimated trque cnstant in the envirnment f the applicatin perid1 and the

7 (a) (b) Figure 10. Estimated trque cnstant in the envirnement f the applicatin perid1 when the nminal engine net trque was multiplied by 1.5 Figure 8. Estimated trque cnstant in the envirnement f (a) the applicatin perid1 (b) the applicatin perid2 when the nminal engine net trque was multiplied by 1 (a) (b) Figure 9. The amunt f change in the estimated engine net trque and the nminal engine net trque ver (a) the applicatin perid1 (b) ver the applicatin perid2 when the nminal engine net trque was multiplied by 1 applicatin perid2, respectively when the prpsed algrithm was applied t the experimental data fr 600 secnds, assuming that there is n uncertainty in the nminal engine net trque, which is when cnstant 1 Figure 11. The amunt f change in the estimated engine net trque and the nminal engine net trque ver (a) the applicatin perid1 when the nminal engine net trque was multiplied by 1.5 was multiplied t the nminal engine net trque. The trque cnstant in the prpsed algrithm musllw the reciprcal t cancel the multiplied cnstant. Fig. 8 (a) shws that the trque cnstanllwed 1 and the errr cnverged t within 0.1. Hwever, Fig. 8 (b) shws that the trque csntant did nllw 1 and the errr was getting bigger. Fig. 9(a), and (b) shws the amunt f change in the estimated engine net trque and the nminal engine net trque ver the applicatin perid1, and the applicatin perid2, respectively. In Fig. 9(a) shws that the amunt f change in the estimated engine net trque and the nminal engine net trque ver the applicatin perid1 shw a similar tendency t each ther, and the trque cnstant is estimated by cmparing the tw amunts f change. Hwever, Fig. 9(b) shws that the amunt f change in the estimated engine net trque and the

8 nminal engine net trque ver applicatin perid2 des nt shw a similar tendency t each ther. This shws that the utput shaft trque which is calculated based n the trque cmpliance mdel can becme inaccurate ver time due t the integratin f the transmissin input shaft speed and the wheel speed and the specific perid f time that the amunt f change in the engine net trque is calculated shuld be shrt enugh and the amunt f change in the engine net trque shuld be large ver the specific perid. Furthermre, Fig. 10 shws the estimated trque cnstant in the envirnment f the applicatin perid1 when the nminal engine net trque was multiplied by the cnstant 1.5. In Fig. 10, t cancel the multiplied cnstant, the trque cnstant cnverged t 1/1.5 within errr f 0.1. Fig.11 shws the amunt f change in the estimated engine net trque and the nminal engine net trque ver the applicatin perid1. It is shwn that the amunt f change in the nminal engine net trque is larger than that f the estimated engine net trque since the nminal engine net trque is multiplied by 1.5. The prpsed algrithm adapts the trque cnstant using the difference f the tw variatins. Hwever, in Fig. 9(a), it can be seen that the amunt f change f the estimated engine net trque smetimes differs greatly frm that f the nminal engine net trque. This is due t the errr f the amunt f change in the utput shaft trque. Therefre, the trque cnstant shuld be averaged ver a lng perid f time t reduce the effect f this errr, while the estimated and nminal engine net trque data are accumulated. 4. CONCLUSION This paper prpsed a cmpensatin methd fr the slwly varying uncertainty f the nminal engine net trque estimated in the frward directin f the driveline in a parallel hybrid vehicle using a multiplicative cnstant which was called the trque cnstant. The adaptatin f the trque cnstant was cnducted using the amunt f change in the nminal engine net trque and the amunt f change in the estimated engine net trque instead f the estimated engine net trque value itself due t the drift issue f the utput shaft trque, which is mdeled using the shaft trque cmpliance mdel. The amunt f change in the engine net trque was estimated in the backward directin f the driveline using the amunt f change in the utput shaft trque. Furthermre, the perid when the engine clutch is engaged and disengaged was cnsidered as the specific perid f time when the amunt f change in the engine net trque is calculated. The adaptatin perfrmance f the trque cnstant was verified using the daily driving data f a prductin parallel hybrid vehicle. In future wrk, rbustness f the prpsed algrithm will be investigated and refined using mre vehicle data in many different envirnmental cnditins. ACKNOWLEDGEMENT This research was partly supprted by Hyundai Mtr Cmpany, a Natinal Research Fundatin f Krea (NRF) granunded by the Krean gvernment (MSIP) (N. 2017R1A2B ), and the BK21+ prgram thrugh the NRF funded by the Ministry f Educatin f Krea. REFERENCES AZZONI, P., MORO, D., PONTI, F. & RIZZONI, G Engine and lad trque estimatin with applicatin t electrnic thrttle cntrl. SAE technical paper. CHEVALIER, A., M LLER, M. & HENDRICKS, E On the validity f mean value engine mdels during transient peratin. SAE transactins, CHOI, S.-B. & HEDRICK, J Rbust thrttle cntrl f autmtive engines: Thery and experiment. Jurnal f dynamic systems, measurement, and cntrl, 118, ERIKSSON, L. & NIELSEN, L Mdeling and cntrl f engines and drivelines, Jhn Wiley & Sns. GAO, B., CHEN, H., MA, Y. & SANADA, K Design f nnlinear shaft trque bserver fr trucks with Autmated Manual Transmissin. Mechatrnics, 21, GLIELMO, L., IANNELLI, L., VACCA, V. & VASCA, F Gearshift cntrl fr autmated manual transmissins. IEEE/ASME transactins n mechatrnics, 11, GUZZELLA, L. & ONDER, C Intrductin t mdeling and cntrl f internal cmbustin engine systems, Springer Science & Business Media. IOANNOU, P. A. & SUN, J Rbust adaptive cntrl, PTR Prentice-Hall Upper Saddle River, NJ. JEONG, H.-S. & LEE, K.-I. 2000a. Frictin cefficient, trque estimatin, smth shift cntrl law fr an autmatic pwer transmissin. KSME internatinal jurnal, 14, JEONG, H.-S. & LEE, K.-I. 2000b. Shift characteristics analysis and smth shifr an autmatic pwer transmissin. KSME internatinal jurnal, 14, JIANQIU, L., MINGGAO, Y., MING, Z. & XIHAO, L. 2002a. Advanced trque estimatin and cntrl algrithm f diesel engines. SAE Technical Paper.

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