Optimization of Heavy Truck s Driveline Performance via Model Predictive Control rated by a Comfort Evaluation Algorithm

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1 Proceeding of the 7th World Congre The International Federation of Automatic Control Optimization of Heav Truck Driveline Performance via Model Predictive Control rated b a Comfort Evaluation Algorithm L. Weberinke D. Feth M. Hertweck A. von Vietinghoff U. Kiencke Intitute of Indutrial Information Technolog, Univerität Karlruhe (TH), German DaimlerChrler AG, German Abtract: Finding the bet compromie between comfort and dnamic during Tipin/out operation in heav truck i the aim of thi project. Therefore, in thi paper a new control concept i introduced baed on model predictive control. The main part of thi concept are a fuion of the two different control target comfort and dnamic to one reulting control variable and the deign of a model predictive controller. Thi controller provide an optimal tracking of the predicted control target. Due to the ubjective perception of the driver, evaluating the comfort of a driving ituation i not a ea a to decribe the dnamic. Therefore, an online comfort evaluation algorithm baed on objective meaurement data i developed. The ver good performance of the developed control concept can be confirmed b thi evaluation algorithm. Copright c 8 IFAC. Keword: tem with time-dela, optimal control theor, control problem under conflict and/or uncertaintie, automobile powertrain, vehicle dnamic tem. INTRODUCTION High dnamic driving behavior, which i imilar to fat acceleration, i conflicted with comfortable driving experience without driveline ocillation. However, olvingthi conflict ha been conidered for a long time. Epeciall in heav truck the impact of fater acceleration on the comfort of the vehicle i ver ditinct. Therefore, finding the bet compromie between comfort and dnamic i indipenable for a good driving behavior. Due to the aim to optimize the acceleration of a heav truck, the driving operation of a Tipin and a Tipout i conidered for further invetigation. An evaluation concept baed on comfort and dnamic mut be conidered, due to be able to evaluate the behavior of the controlled vehicle. To benchmark the dnamic objective meaurement like the acceleration of the vehicle can be conidered. However, the evaluation of the comfort of the truck i dependent on the ubjective perception of the paenger and not on objective data. Therefore, an online comfort evaluation algorithm mut be developed to benchmark the reult of the controlled tem. Some controller concept to find the bet compromie have alread been conidered in thi project. A common olution of thi problem i to limit the gradient of the engine torque a it can be een in figure. However, although the dnamic of the vehicle i reduced the comfort i unacceptable. Regarding the ocillation in the driveline a ramp-haped engine torque i not able to increae the comfort. Me in Nm t in n in rad/ Fig.. A Tipin/out and it impact on the driveline; engine torque, difference of rotational peed of engine and wheel Therefore, in a firt tep an advanced PD-Controller wa developed in (Weberinke, L. et al. 7) to increae the comfort. The teting reult how that the controller i able to minimize the ocillation in the driveline while the dnamic i of the ame ize a in the common olution. However, finding a compromie with a higher dnamic i not poible. Therefore, a new concept baed on tate pace controller wa developed in (Weberinke, Lena et al. 8a). Thi concept include two LQG-controller, each of them upporting onl comfort or dnamic behavior. B a fuzz fuion with repect to the driving ituation and the drive input the manipulated variable of both controller are merged in a uitable manner. The reulting algorithm i able to compromie dnamic and comfort with focu /8/$. 8 IFAC /876-5-KR-.36

2 7th IFAC World Congre (IFAC'8) on one of both target. However, having two controller, which work at the ame time, can caue a conflict during a witching phae. Additionall, the parametrization of the algorithm to follow the deired compromie i difficult and the reult of the controller are not optimal. Therefore, in thi paper a new controller concept i introduced, which allow an optimal tracking of the control target a well a an ea wa of parametrization. Thi concept i baed on a imple driveline model which i decribed in ection. Due to the optimal tracking, the implemented controller i baed on the theor of model predictive control (MPC) (ee ection 3). However, finding the bet compromie between comfort and dnamic with an ea wa of parametrization wa not poible in the former concept. Therefore, an optimal control target i predictedbaedonthe fuionofbothconflictedgoal. The calculationofthi targeti introducedinection4. Afirt evaluation of the imulation reult i dicued in ection 5. However, decribing the comfort behavior b objective meaurement i not poible. Therefore, in ection 6 the online comfort evaluation algorithm i introduced. After etting up a comfort model an implementation with the help of neuronal net work theor i decribed in ection 7. Section 8 evaluate the comfort of the reult of the controllerconceptbaedonthe evaluationalgorithm. The paper i ummarized with a concluion.. Drive-Shaft Model. DRIVELINE MODEL Ever MPC ue an explicit model of the proce conidered. Here, with repect to computing time a well a reproduction of the tem dnamic, a imple linear tate-pace model of 3rd order, the o-called drive-haft model, i choen (ee (Kiencke, Uwe and Nielen, Lar 5)). M e J d n c i = i d i t Fig.. The drive-haft model k d J n w d Therefore, the driveline i aumed to conit of two rotating inertia connected via a pring-damper element a hown in figure. The left inertia J combine the engine, the clutch, the tranmiion (with ratio i) and the propeller haft. The pring-damper element, decribed through it damping coefficient d d and it tiffne k d, repreent the drive haft. The econd inertia J model the wheel. The vicou friction of the two rotational inertia i taken into account through the damping coefficient d and d, repectivel. J i affected b the engine torque M e and J b the load l coniting of air drag, rolling reitance, and vehicle ma. Neglecting the engine friction, the engine torque M e i the um of the driver torque M d = u d and the controller torque M c = u c. l Baed on the drive-haft model, a linear 3rd order tatepace model canbe derivedb uing Newton generalized econd law. Defining the tate vector x and the input vector u ext to be [ ] α [ ] ud x = n e, u ext =, () l n w where n e and n w are the rotational peed of the engine andthe wheel, repectivel, and α i the torionbetween thee two component, lead to ẋ(t) = A x(t) + b c u c (t) + B ext u ext () (t) = C x(t) (3) where i A = k d (d + dd i ) d d, (4) ij J ij k d d d (d d + d ) J ij J b c =, B J ext = J, C = [ ( i) ] (5) J The controller can onl influence u c but not u ext. For ever gear the unknown parameter of thi timecontinuou model are etimated b uing meaured data and an appropriate identification algorithm (Weberinke, Lena et al. 8b). For the MPC algorithm a time-dicrete model i required and the Tutin approximation reult in x(k + ) = A di x(k) + b c,di u c (k) + B ext,di u ext (k) (6) (k) = C x(k). (7). Drive-Shaft Model with Time Dela Engine Engine u d z z u re + u c (k ) u c (k ) u c (k) Driveline MPC x, n, ldata Preproceing n ref Reference Computation Fig. 3. Block diagram of the cloed-loop tem The drive-haft model i ued b the MPC. However, there i an additional dead-time not conidered et. Figure 3 how a block diagram of the cloed-loop control. In imulation, u d i meaured at the output of the engine, wherea u c till ha to be proceed b the engine. Thi reult in a dela of approximatel two ample time between the two ignal. Due to the prediction of the MPC, thi time dela can be conidered. x 759

3 7th IFAC World Congre (IFAC'8) Therefore, the tate vector of the drive-haft model i extended to α n e x td (k) = n w (8) u c (k ) u c (k ) and the dicrete tate-pace repreentation i of the form with x td (k + ) = A td x td (k) + b c,td u c (k) + B ext,td u ext,td (9) (k) = C td x td (k) () A di A td = B ext,td = B ext,di b c,di, b c,td =, (), C td = [ C ] () A MPC i deigned uing the drive-haft model with and without time dela and the reult are compared. 3. THEORY OF MPC In the MPC algorithm, the tem behavior i predicted over a certain period of time, the prediction horizon p, at ever ample time k. Uing equation (6) and (7) the output of the tem i predicted for the ample time (k+i) to be [ ((k+i) k)= n((k+i) k)= C b uc u c (k )+ i A i di x(k) + ( h= A (i ) di h u c (j) +B ext u ext. (3) j= The cot function to be optimized i p ( J = wi+,j n ( n(k + i + k) r(k + i + )) i= wi+,j n and wuc i + w uc i u c (k + i i) ) (4) are the weight of the cot function and thu, the adjutable parameter of the MPC. r i the reference trajector defining the target of the output variable n (ee ection 4). Additionall, contraint of the form u min u u max, min max (5) are et up to take the tem contraint into account. Thi reult in a Quadratic Programming Problem which i to be olved. In order to obtain an optimal equence u opt = [u opt (k) u opt (k + )...u opt (k + p)] (6) the Active Set Method ((Camacho, E.F. and Bordon, C. 4)) i ued and the firt value u c (k) = u opt (k) of thi vector i paed through a manipulated variable. Conidering the principle of receding horizon, the algorithm i carried out at ever ample time anew. 4. CALCULATION OF TARGET In figure n i hown during a Tipin/out operation without feedback control of the torque. Due to the driveline ocillation, driving comfort i poor. n i not onl an indicator for comfort but alo for dnamic. The higher the amplitude of the firt ocillation after a Tipin/out the higher the dnamic but the le the comfort. The decreae of n after the firt maximum alo ha a great influence on comfort. Lat but not leat, trong and long-lating ocillation are perceived a jerking b the driver and caue a reduced comfort. Hence, with repect to the control target, a reference trajector r = n ref with amplitude n (ee figure 4) i defined for n to reduce the ocillation and keep the maximal jerk under a certain limit. n, M k k TI f f (k) n M max k TO n max Fig. 4. Reference trajector n ref with parameter; u d Adjuting the following parameter comfort and dnamic can be influenced. f i the frequenc at the tart of the Tipin/out and f (k) = f m(k) = f (7) m (k k TI ) i the frequenc after n ref ha reached n. m(k) i the decreae in frequenc after n. n i not a parameter that can be et but i dependent on the driver torque M d. The maximum abolute value M max of M d i determined at the tart of ever Tipin/out operation. Auming an approximatel contant frequenc of the ocillation, n predict = n(k + k k) i predicted appling equation 3. k i the number of ample tep between the tart of the Tipin/out operation and the firt maximum of the ocillation of n. However, to guarantee acceptable comfort, n mut not be larger than n max. { npredict if n predict n max n = (8) n max ele Uing thi bounded amplitude n the reference trajector for a Tipin operation i Θ {}}{ n in(πf (k k TI )) if TI and (Θ π ) n ref = (9) ( ( )) (m(k) ) n in πf (k) k k TI + 4 f if TI and (Θ > π ) k 76

4 7th IFAC World Congre (IFAC'8) In analog, n ref for the Tipout operation i computed. In Figure 4 the influence of the parameter on the reference i illutrated for the Tipout operation. The reference trajector combine the two target high dnamic and high comfort and can be parameterized eail. The imulation reult of a MPC uing thi reference are preented in the next ection. 5. SIMULATION RESULTS In order to demontrate the good performance of the MPC, it i teted in imulation examining variou parametrization of the controller and of the algorithm computing the reference trajector. Therefore, two different MPC are implemented. One uing the drive-haftmodelwhichneglect the time dela (MPC) and the other one which conider the time dela (MPC). The reult are compared. The tem work with a ample time of T =.. The prediction horizon i et to be 5. ure in Nm n in rad ax in rad ȧx in rad time in Fig. 5. Simulation reult of MPC in gear ; high comfort, high dnamic, n ref, common olution The weight of the MPC determine whether the emphai of the control i on n to follow n ref or u re to become. The latter correpond to a retricted controller intervention. Thu, the torque i expected to follow u d. Thi can be achieved eail without an control action. A thi ection i uppoed to illutrate the performance of the controller, the weight wi, n (i =...p) of n are choen relativel large. The main target of the controller i to find a good compromie between comfortanddnamic during a Tipin/out operation. Figure 5 how an adjutment of the parameter for high comfort and one for high dnamic. The main difference with repect to the parameter i in n max. n max = 5rad/ allow a higher dnamic than n max = 3rad/. Furthermore, the decreae in the frequenc f (k) i higher for the comfortable etting than for the dnamical one. However, even the comfortable etting of the parameter improve the dnamic and vice vera. ure in Nm n in rad ax in rad ȧx in rad time in Fig. 6. Simulation reult of MPC in gear 4; - MPC, common olution, n ref Due to the different number of tate of the model implemented in MPC and MPC it i difficult to compare the performance of thee two controller directl. One et of parameter cannot be ued for both controller. Figure 6 how the imulation reult for MPC in gear 4. The parameter are aiming for a high dnamic. Furthermore, the ocillation are reduced. Hence dnamic and comfort are increaed. MPC permit a higher intervention of the controller in the tem behavior. Furthermore, there are le ocillation than uing MPC. In previou control trategie the performance of the controller wa onl atifing for low gear. However, the imulation reult in figure 6 demontrate, that the MPC produce contantl good performance, even for higher gear. Although n i ued to control dnamic and comfort, it i onl an indicator for comfort and dnamic. Due to evaluate the controller performance with repect to comfort and dnamic an appropriate algorithm ha to be defined. The dnamic of the controlled tem can be rated eail b evaluating the acceleration a x of the truck. However, the evaluation of the comfort i more complex. Therefore, an online algorithm for comfort evaluation i derived in the next ection. 6. ALGORITHM FOR COMFORT EVALUATION In literature a lot of work can be found concerning the evaluation of driving comfort in paenger car (ee (Gebert )), but hardl anthing concerning the driving comfort in truck. Becaue of the truck upenion thee two kind of vehicle cannot be treated the ame wa. Thu, an online algorithm for evaluation of the driving comfort in 76

5 7th IFAC World Congre (IFAC'8) heav truck during Tipin/out operation i preented in thi ection. gear back ret eat z z x x z pitch aw x feet Fig. 7. Coordinate tem to decribe human perception of acceleration and jerk in different direction n i a reaonable indicator for the driving comfort but it doe not allow a reliable, objective evaluation due to the vehicle upenion and the ubjective impreion of the driver. Hence, an online comfort evaluation algorithm i implemented uing the acceleration of the different direction of motion meaured at the driver cabin (ee figure 7). In (Int 997) filter are defined to model human perception of ocillation. Generall, the vehicle occupant perceive ocillation of the frequenc interval from approximatel Hz to Hz mot. ax in m time in 3 ax,filt in m.5.5 time in 3 Fig. 8. a x of driver cabin meaured (left) and filtered with filter according to (Int 997)(right) Figure 8 illutrate the difference between the actual meaured acceleration at the driver cabin a x and the filtered acceleration a x,filt perceived b the driver. In order to obtain an objective comfort evaluation the filtered acceleration of four different direction of motion (x, z, pitch and roll) and the jerk ȧ x (t) are ued to define characteritic c i (i =...n). The higher a characteritic the wore the comfort. Therefore, feature of the ignal are conidered like e.g. it energ or the amplitude of the ocillation. A an example, one of the characteritic i preented. The evaluation of the height of the edge running in oppoite direction of a x,filt are evaluated after ever Tipin/out operation. That i ever ection where (ȧ x,filt < ) or (ȧ x,filt > ) for a Tipin or Tipout, repectivel. In order to obtain thi characteritic the weighted um i computed c = M [ ( ) ] w c (t) max N (a x,filt) min (a x,filt) j. ȧ x,filt < ȧ x,filt < j= N i the total duration of the edge in oppoite direction and M i their number. The weight w c (t) i increaing with time. Similarl, the other characteritic are defined. Thee parameter are ummarized in one comfort characteritic value C that can be interpreted according to table. Hence, C can be computed online for ever Tipin/out operation. C Interpretation ver good acceptable inufficient Table. Interpretation of the comfort evaluation value C However, before thi comfort evaluation can be applied, the unknown function C ha to be etimated. Therefore, a neural network i applied. 7. NEURAL NETWORK A neural network i conidered, due to the aim to approximate human feeling. Thi neural network i able to approximate unknown nonlinear function depending on the input of the net. For further detail to neural network ee (Braue, Rüdiger 995). Decribing the comfort of a heav truck the characteritic c i are proceed in two hidden laer and one output laer and reult in a poitive mark. However, the weight of each interconnection in thi network mut be adjuted. Therefore, the ubjective feeling of driver during Tipin/out operation expreed in mark on a cale from one to ix (one - ver good, ix - ver bad) wa recorded. The correponding characteritic c i could be calculated out of the meaured data of the CAN-bu. Hence, a training et exiting of the net input c i and the net output (ubjective mark) i available. The neural network i trained with thi et via backpropagation algorithm. The cot function of the quadratic error between the calculated net output and the target mark i minimized b an optimization algorithm baed on the gradient method. Due to get reaonable reult a lot of tet data of different driver i necear. However, ever driver ha a different notion of a comfortable behavior. Additionall, ome ubjective mark could be incorrect a the driver ha to make hi deciion ver fat. The net hould be trained to the correcttendenc andnotto the abolutcorrectvalue, due to get an average comfort mark. Therefore, the training of the net mut be topped before the cot function i too mall. 8. COMFORT EVALUATION OF MPC For validation of the performance of the MPC two objective mut be conidered: the comfort and the dnamic. The comfort can be decribed b the algorithm for comfort evaluation a decribed in chapter 6. The time difference to reach a change in the acceleration in the direction of motion of rad i ued to evaluate the dnamic. Baed on thee evaluation algorithm the MPC wa teted and compared with the former LQG-concept and the common olution introduced in ection. The following figure 9 and how the reult of a imulationwithintegratedcalculationofthe neededcharacteritic (e.g. pitch) for the comfort evaluation. The olid line repreent the MPC and the dotted line the 76

6 7th IFAC World Congre (IFAC'8) n in rad ax in rad Me in Nm nw in rad time in Fig. 9. The reult for gear : common olution, MPC n in rad Me in Nm ax in rad nw in rad time in Fig.. The reult for gear 4: common olution, MPC common olution (CS). Both conidered adjutment of the predictive controller lead to nearl the ame comfort a in the common olution, due to get comparable driving ituation. Hence, the ocillation in the difference of rotational peed i nearl the ame for both tem. The reult of validation of both objective comfort and dnamic are ummarized in table. The evaluation for lower gear repreented b gear (figure 9) and for higher one repreentedb gear4(figure ) will be dicued in the following. However, although the comfort i nearl the ame the dnamic according to the characteritic of the lateral acceleration a x i enhanced b the MPC. The conidered time for acceleration i reduced b 5% for a Tipin in gear and b nearl 85% in gear 4. The former LQGgear TI comf TI dn TO comf TO dn CS MPC CS MPC Table. The evaluation. CS: common olution, TI: Tipin, TO: Tipout concept i not able to enhance the dnamic for higher gear a time dela and active contraint preponderate there. Thi large improvement b the MPC how the ver good performance of the preented algorithm. 9. CONCLUSION The model predictive controller conidering the time dela of the engine with combination of the control target calculation i able to increae the performance during accelerationphae verwell. The eawato parameterize thi algorithm and the new definition of the control target enable a high dnamical and comfortable behavior of the heav truck. Up to now it wa not poible to increae the dnamic while the comfort remain acceptable for higher gear, too. Hence, uing the decribed algorithm the dnamic can be increaed up to 85% compared with the common olution. A comfort validation of the different control concept uing the developed comfort evaluation algorithm help to optimize the performance and to give ignificant evaluation reult. In future work an adaptive algorithm hould be included into the model predictive concept to enhance the performance of the tem and to adapt it to other driveline configuration. REFERENCES Braue, Rüdiger (995). Neuronale Netze. B.G.Teubner Stuttgart. Camacho, E.F. and Bordon, C. (4). Model Predictive Control.. ed.. Springer-Verlag London Berlin Heidelberg New York. Gebert, J. (). Adaptive Parametervariation bei Getriebeteuerungen zur Optimierung de Schaltkomfort. number 44 In: Reihe, Fortchritt-Berichte VDI. VDI Verlag. Deldorf. Int (997). ISO 63-:997 Mechanical vibration and hock - Evaluation of human expoure to whole-bod vibration Part : General requirement. nd ed. Kiencke, Uwe and Nielen, Lar (5). Automotive Control Stem for Engine, Driveline, and Vehicle.. ed.. Springer-Verlag Berlin Heidelberg New York. Weberinke, L., Hertweck, M., Holl, J. and Kiencke, U. (7). An advanced pd-controller for tipin/out control of a heav truck. In: Proceeding for the 5th IFAC Smpoium on Advance in Automotive Control. Weberinke, Lena, Augentein, Lutz, Hertweck, Mario and Kiencke, Uwe (8a). Adaptive linear quadratic control for high dnamical and comfortable behavior of a heav truck. In: SAE World Congre. Weberinke, Lena, Herder, Stephan, Hertweck, Mario and Kiencke, Uwe (8b). Advanced technique for offand online-identification of a heav truck driveline. In: SAE World Congre. 763