Transmission control for power-shift agricultural tractors Design.pdf
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Transmission control for power-shift agricultural tractors: Designand end-of-line automatic tuningMara Tanellia, Giulio Panzania, Sergio M. Savaresia, Carlo PirolabaDipartimento di Elettronica e Informazione, Politecnico di Milano, Piazza L. da Vinci, 32, 20133 Milano, ItalybSAME Deutz-Fahr Group, Viale F. Cassani, 15, 24047 Treviglio (Bergamo), Italya r t i c l ei n f oArticle history:Received 24 May 2010Accepted 14 November 2010Available online 8 December 2010Keywords:Power-shift transmissionAgricultural tractorsAutomotive systemsEnd-of-line tuninga b s t r a c tThis paper addresses the analysis and design of the transmission control system for a high-powerpower-shift agricultural tractor. Specifically, all the criticalities involved with the correct managementof both single clutch and double clutch gear shifts are investigated, and a control system capable ofproviding good shifting performance in all operating conditions is proposed. Further, to comply withcomponents tolerances and spreads in the production line, an automatic procedure for the end-of-linetuning of the transmission control system is proposed to objectively classify the quality of the gear shiftand automatically optimize it. The suitability of the proposed approach is thoroughly tested on an instru-mented vehicle.? 2010 Elsevier Ltd. All rights reserved.1. Introduction and motivationAgricultural vehicles have to cope with working conditionswhich are more complex and demanding than those experiencedby other ground vehicles, 10. In fact, agricultural vehicles areessentially designed to work at low speed while providing largetraction forces. Moreover, their ease of moving on uneven soilmakes them suitable also for heavy trailers transportation. To en-sure the maximum flexibility of use at each speed and to exploitthe maximum engine power available in all working conditions,nowadays agricultural vehicles are often equipped with a so-calledpower-shift transmission. This kind of transmission has a largenumber of gears available (typically from 9 to 30) and it allowsto perform a gearshift with no (or at least with a minimum) lossof power from the engine to the driving wheels.Usually, a power-shift transmission is characterized by thepresence of two or more (depending from the number of gearsand the overall mechanical architecture of the gearbox) wetclutches connected to an hydraulic circuit, whose pressure can beregulated by a proportional solenoid valve. Considering the largenumber of gears available and the fact that to achieve an optimalgear shift it is necessary to correctly manage several control vari-ables, this kind of transmission needs to be properly controlled.The design of such a control system is not a trivial task. In thescientific literature, some works dealing with power-shift or dualclutch transmissions control for ground vehicles are available,see e.g., 38,15, but very little has been done on specific solutionsfor agricultural tractors. This is mainly due to the fact that agricul-tural vehicles have very specific performance specifications due tothe very broad range of working conditions and variability of thevehicle load, which make the gear shift optimal performance defi-nition different from that of ground vehicles. As a matter of fact,the main constraints are the repeatability of the manoeuvre andthe comfort of the driver on all working grounds, which vary fromasphalt roads to rough off-road terrains. Also the load distributionin tractors is much different than for other vehicles, due to the factthat it might be due to either front or rear additional loads due tothe various working instruments that need to be employed fordifferen tasks. Finally, note also that the variation of the operatingconditions is most often non measurable via on-board sensors, andthus asks for robust and easily tunable gear shift controllers. Thesefacts make the problem of ensuring an optimal and repeatable gearshift on an agricultural tractor a very challenging task.To design an effective transmission control system, first of allthe most significant variables which influence the gear shift qualitymust be identified, see e.g., 2,16. Further, the gear shift controlsystem has to optimally manage the trade-off among the followingconflicting requirements:(i) yield comfortable gear shifts;(ii) guarantee that no loss of power to the driving wheels occursduring gear shifts;(iii) cause a minimum wear and tear of mechanical componentsover the life of the vehicle transmission.0957-4158/$ - see front matter ? 2010 Elsevier Ltd. All rights reserved.doi:10.1016/j.mechatronics.2010.11.006Corresponding author. Tel.: +39 02 2399 3621; fax: +39 02 2399 3412.E-mail address: tanellielet.polimi.it (M. Tanelli).Mechatronics 21 (2011) 285297Contents lists available at ScienceDirectMechatronicsjournal homepage: /locate/mechatronicsMoreover, in the industrial context, once the control designphase is accomplished and the control system is implemented intofinal products, an end-of-line tuning phase is usually scheduled todeal with constructive tolerances and production spreads whichcause the final system to be different from the prototype one usedfor control validation and testing. Hence, this phase is tailored tooptimize the controller parameters so as to guarantee that theexpected gear shifting performance is achieved on all vehicles.Usually, this phase is carried out by human testers, who tune thecontroller parameters based on personal driving preferences andexperience. Thus, is it clear that end-of-line tuning is a crucialand difficult phase to deal with. As a matter of fact, since no objec-tive indexes to evaluate the gear shift performance and comfort ex-ist, a gear shift can be qualified as comfortable by one operator, butnot by another one: this means that the final tuning can lead tovery different gear shift behaviors on different vehicles of the sametype. Note that, as the vehicle handling qualities, of which the gearshift characteristics are a significant component, is often consid-ered as a trademark of the single manufacturer, the ability of deliv-ering vehicles with identical manoeuvre features can be a key toachieve customers satisfaction and to promote customers loyaltyto the brand. Moreover, another significant advantage of the pro-posed approach is that of reducing the industrial costs associatedwith end-of-line tuning by reducing the number of gear shiftsneeded to tune each vehicle and by making the process automatic,thus not requiring highly experienced operators to perform it.It is worth noting that the approach presented in this work,even though tailored to a specific application, has a validity whichgoes beyond the considered problem, as the aforementioneddesign steps constitute a working paradigm which can be appliedin many different production contexts. As a matter of fact, this pa-per is one of the first contributions which aims at formalizing theend-of-line tuning of industrial applications endowed with controlsystems, proposing a systematic approach to the considered prob-lem. In this respect, the results in 13,16 offer other applications ofthe proposed methodology and address the problem of quantifyingof the driving style and safety via measured data, and of designingand objectively tuning the motion inversion control of an agricul-tural tractor, respectively.Although being different problems with respect to that consid-ered herein, both these works share (all or part of) the systematicapproach presented in this work, which is constituted by the fol-lowing steps:? an evaluation of the characteristic features which define thequality of the considered system;? an experimental sensitivity analysis to single out the relationbetween the features to be optimized and the measurablevariables;? the definition of the cost functions;? the design of the control algorithm and of the procedures for itsend-of-line tuning grounded on the cost functions optimization.This methodology makes the results in the present paper ofgeneral interest for all those applications in which a control systemmust be designed and tuned while dealing with the dispersioncoming from production spreads and tolerances which make theunderlying plant (i.e., the final vehicle) different from that usedfor design purposes. The resulting research area requires tools bothof control theory and optimization, combined with the specificapplication-domain knowledge.The presented results are based on a joint research workbetween the Politecnico di Milano and the R&D Department ofthe SAME Deutz-Fahr Group (SAME, Lamborghini, Deutz-Fahr,Hrlimann, Adim Diesel and Deutz AG). The work has been focusedon a power-shift transmission designed for high-power (200 HP)agricultural tractors (see Fig. 1).The first effort has been devoted to define appropriate costfunctions which allow an objective evaluation of gear shift comfortand quality. Then, an accurate analysis of all relevant gear shiftdynamics has led to design a simple but effective transmissioncontrol strategy. Further, to obtain the best possible gear shift per-formance on every production vehicle, an automatic tuning phaseis proposed which guarantees satisfactory and repeatable gear shiftperformance.The structure of the paper is as follows. Section 2 provides adescription of the power-shift transmission system, both from anhydraulic and a mechanical viewpoint. Section 3 is focused on pre-senting the performance indexes which have been selected tojudge the gear shift quality. In Section 4, the proposed controlstrategy for power-shift gear shifts is described, both for the caseof single clutch and double clutch gearshifts, together with the re-sults of an experimental sensitivity analysis of the performance in-dexes with respect to the controller parameters. Finally, Section 5is devoted to describe the end-of-line self-tuning procedure and topresent related experimental results.2. System descriptionThe overall mechanical layout of the considered power-shifttransmission is depicted in Fig. 2. As can be seen, the power flowsfrom the engine (on the left of Fig. 2) towards the driving wheelsthrough two different gearboxes: the High-Mean-Low (HML)group, composed of three different gears and the 123 group, whichalso comprises three different gear ratios. The transmission is com-pleted with two other components, namely the motion inverterand the mode selector. The motion inverter (see 11,16) is an elec-tro-hydraulic system, constituted by two clutches, which allows toperform an automatic motion inversion, i.e., it takes the vehiclefrom a, say, forward speed to a reverse speed with the driver sim-ply acting on a lever. The mode selector allows to choose amongthree different working modes: creep, work and transport, whichcan be varied only when the tractor is at standstill. In what follows,we concentrate on the control of the gear shift, and consider thetwo gearboxes only, assuming that no motion inversion is occur-ring (note, in passing, that during a motion inversion the drivercannot command a gear shift), and that a fixed mode has beenengaged.As the two gearboxes are in series, nine transmission ratios be-tween the engine and the driving wheels are available (disregard-ing the final differential, whose ratio is fixed). Conceptually,although mechanically different, the two gearboxes can be treatedequally for control design purposes. Each gear is associated with aFig. 1. The tractor employed in this work.286M. Tanelli et al./Mechatronics 21 (2011) 285297wet clutch: to select a particular gear the corresponding clutchmust be completely engaged, so that the torque coming from theengine can be completely transferred via the clutch itself. Thewet clutches handled in this work are multi-plate wet: in orderto be engaged (and hence to select the associated gear) the surfacesof the plates must be in close contact and the normal force they ex-change must be large enough to develop a friction force whichguarantees that no relative slip occurs between them.Fig. 3 shows a schematic view of the physical relationship be-tween normal force and clutch oil pressure. For gear shift analysis,three different zones must be considered. Starting from zero (i.e.,from atmospheric pressure), an increase in the pressure bringsno changes in the normal force between the plates, which remainsnegligible.When the so-called kiss-point pressure is reached (see Fig. 3),this distance that separates the plates has been covered and thesurfaces come into contact. From here over, the normal force in-creases proportionally to the pressure. During this phase, thefriction force between the surfaces allows to transfer a certainamount of incoming torque through the clutch but, as there is anon-zero relative slip between the plates, the gear ratio isindefinite.Once the engage pressure is reached (refer again to Fig. 3), thenormal force is large enough to annihilate any relative slip be-tween the plates of the clutch and a precise gear ratio can bedefined.Fig. 4 shows a schematic view of the hydraulic scheme, whichallows to understand how the pressure in a clutch can be con-trolled. There are six ONOFF directional valves which connecteach clutch to the master hydraulic pressure, regulated by a pro-portional solenoid valve. Such hydraulic architecture yields the fol-lowing clutch pressure behavior: when a directional valve isswitched ON the pressure in the clutch is equal to the master pres-sure. Being this a one-way valve, note that the pressure can onlyincrease, even if the master pressure decreases. Conversely, whenthe directional valve is switched OFF the pressure in the clutch iszero. As such, the available control variables are the following:(1) the master hydraulic pressure. Note that, as no pressure sen-sors are available, the real control variable is the currentdriving the proportional valve. Such a variable can be linkedto the output pressure via a static map. In what follows, wewill regard the pressure as control variable, keeping in mindthat the aforementioned conversion from current to pres-sure has to be performed;(2) the onoff status of each directional valve.To execute a gear shift with a power-shift transmission, theoutgoing clutch must be brought to zero pressure, whereas theincoming clutch must be brought to maximum pressure. Note thata non-power-shift gear shift would disengage the outgoing clutchand then engage the incoming one. In so doing, there is a timeinterval in which the vehicle is in a neutral state, and no enginetorque can reach the driving wheels. In agricultural vehicles theneutral state must be avoided, as the large load forces would causethe vehicle to stop. Thus, it is of utmost importance to ensure acontinuous torque transfer to the driving wheels during the gearshift, which is the main characteristic of a power-shift gear shift.To conclude the system description, Table 1 shows the nineavailable gears together with the associated engaged clutches. Ascan be seen, usually a gear shift requires to change only one clutch(i.e., the one belonging to the HML gearbox). We refer to such gearshifts as single clutch gear shifts. However, when the 34 and 67gear shifts are considered, two clutches must be changed (oneHML gearbox 123 gearboxMotion InverterMode selector Fig. 2. Schematic view of the power-shift transmission.Kiss-pointEngagePressure bar Normal force NFig. 3. Oil pressure in the clutch as a function of the normal force.H M L1 2 3Fig. 4. Simplified hydraulic scheme of the considered transmission.Table 1Available gears and respective engaged clutches.GearLMH1231?2?3?4?5?6?7?8?9?M. Tanelli et al./Mechatronics 21 (2011) 285297287belonging to the HML and one to the 123 gearbox), making the de-sign of the gear shift controller more complex, as will be shownsubsequently. We refer to such gear shifts as double clutch gearshifts.3. Gear shift quality assessmentAs discussed in Section 1, defining an objective gear shift qualityassessment yields the following advantages:? it provides a unique and objective indication of gear shift per-formance, helpful to compare different vehicles and/or differentcontrol algorithms.? it makes the end-of-line tuning phase easier and cheaper byrelying on the automatic optimization of appropriate perfor-mance indexes.The crucial issue to deal with in defining the most suitable costfunctions is that of determining meaningful relationships betweenmeasured signals and gear shift comfort and quality. Several stud-ies have been carried out in the Automotive context, showing goodresults in evaluating comfort via acceleration measurements, seee.g., 9,14. For the type of vehicle considered in this work, it is easyto understand that this kind of signal is not suitable, as soil irreg-ularities cause measurement noise which shadows the actual gearshift contributions to vehicle accelerations. Moreover, accelerome-ters are not standard sensors to have on-board of agricultural trac-tors. Thus, we concentrated on investigating the relationshipsbetween gear shift quality and vehicle speed, whose measurementis commonly available via wheel encoders. As discussed in 16,this signal can be exploited to provide satisfactory comfortevaluation.To understand the rationale behind the quality index design,Fig. 5 shows the time histories of the vehicle speed in three differ-ent gear shifts, whose performance was judged by an expert driver:the first one (Fig. 5a) has been classified as good, whereas the lasttwo (Fig. 5b and c) as medium and bad, respectively. The speedbehavior in the three considered gear shifts is as follows: the speedalways starts from a constant value and increases (up-shifts havebeen performed in all cases) until it reaches a higher final value,which depends only on the final gear ratio as the engine speed iskept fixed and constant during the gear shift. What really makesthe gear shifts different is the smoothness with which the speed in-creases. Note, in fact, that while in the good gear shift in Fig. 5a thespeed increases with a smooth ramp, in the medium quality gearshift the speed increase is only piecewise linear (see dotted ovalbox in Fig. 5b) and shows a significant initial undershoot. Finally,the bad gear shift is characterized by a quite irregular speed behav-ior and large oscillations (see dotted oval box in Fig. 5c).Based on these considerations, the performance index has beendefined asJ Varvmt ?vreft?;1wherevm(t) is the measured wheel speed andvref(t) is a referencesignal to be designed, which describes the speed behavior in anoptimal gear shift. The measured vehicle speedvm(t) is computed asvmt 14X4i1xitri;2wherexi(t), i = 1, . , 4 are the wheel rotational speeds measuredvia the wheel encoders and ri, i = 1, . , 4 are the wheel radii.The reference signalvref(t) has been designed as composed ofthree different parts (see Fig. 6). The first is defined by the constantspeed value at the beginning of the manoeuvre, i.e.,vref1vmtreq;3where treqis the time instant at which the gear shift is requested bythe driver. The reference speed in the last part of the manoeuvre isalso constant and computed asvrefendxengtreqrsInc:;4wherexeng(treq) is the engine speed at the beginning of the gearshift (recall that the engine speed is fixed and constant during thegear shift), r is the average wheel radius andsincis the transmissionratio of the incoming gear (also known when the gear shift is issuedby the driver).The reference speed evolution in time between these limitingspeed levels, which definesvref2, is chosen as linear, yieldingvref2t vref1vrefend?vref1t2? t1t ? t1;5where the time instant t1is defined ast1:jvmt1 ?vref1j P 0? fjvmt ?vref1j t1g:6Namely, t1is the last time instant at which the measured speed islower than the initial reference speedvref1, while the time instantt2is defined ast2:jvmt1 ?vrefendj 0;8t tDO,HMLbut the two incoming clutchesmay not engage simultaneously. With the proposed controlapproach, the fact that the engagement phase occurs in a correctway is evaluated by means of the cost functions, therefore withouta direct tuning of the engagement instant.The obtained results are reported in Fig. 11, which shows thevalues of J1and J2, respectively, as functions of Overlap and Delay-HML. For the sake of conciseness, the analysis for the KP pressurevalue is not shown, as the obtained results are similar to those dis-cussed for the single clutch gear shift.By inspecting Fig. 11, some remarks can be made.? First of all note that each controller parameter, i.e., Overlap andDelayHML, has a predominant effect over one single index.Namely, Overlap mostly affects the J1index, whereas DelayHMLthe J2one. This fact allows to decouple the optimization phase,and to consider two successive single variable optimization-1000-50005001000150002468101214P kiss-point pressureJ1 index1-22-3010020030040000.511.522.53Overlap msJ1 index1-22-3mbarFig. 8. Sensitivity analysis on single shifts controller parameters.0123456785.566.577.588.5Time sSpeed km/hNot optimizedOptimizedFig. 9. Time histories of the measured vehicle speed in a single clutch shift: results with non-optimized (dashed line) and with optimized (solid line) controller parameters.ttFig. 10. Double clutch gearshift control: master pressure profile (solid line) andoutgoing clutches disengagement (dashed lines).M. Tanelli et al./Mechatronics 21 (2011) 285297291problems, which can more easily managed in view of the auto-matic end-of-line tuning phase. Specifically, as will be describedin more detail in Section 5, the optimal value for Overlap will befound by minimizing J1, while DelayHML will be tuned accord-ing to J2. Specifically, to assess the correctness of the sequentialminimization of the performance indexes, one has to observethat the function J2(?, DelayHML) has the same shape for all val-ues of Overlap. Therefore, once a value of Overlap has been fixedby optimizing J1, then the optimization of J2done by varying thevalue of DelayHML will lead to a final value for J2which isapproximately always the same (note also that the cost functionalways decreases as the value of DelayHML increases indepen-dently of the value of Overlap). Of course, the final value of J2will not be rigorously the same irrespectively of the value ofOverlap with which it is evaluated and which is determinedby the minimization of J1, but the small differences in the finalvalue for J2are not practically relevant as they yield no signifi-cant changes in the final gear shift performance.? Note further that the results in Fig. 11b seem to suggest that alarge value of DelayHML would bring good quality gear shifts.Nonetheless, it is worth pointing out that, as DelayHMLincreases, the clutches are left slipping for an increasing amountof time. Thus, this parameter should be kept at the lowest pos-sible value so as to prevent an excessive wear of the clutches.Section 5 will better discuss how to effectively deal with thisissue.? Finally, it is worth comparing the results obtained in the singleand double clutch gear shift controllers as far as the value ofOverlap is concerned. Specifically, at the end of the previous sec-tion we pointed out that in the single clutch gear shift at leastin low load conditions a non-zero Overlap would induce onlythe detrimental effect of yielding a longer manoeuvre, withoutintroducing any potential increment in the performance. Inthe double clutch gear shifts, instead, a trade-off arises, due tothe fact that one needs to manage the two gearboxes differ-ently. Therefore, while on the one hand allowing a non-zeroOverlap time interval has indeed the detrimental effect of yield-ing a longer (hence worse) gear shift, on the other hand it offersthe advantage of taking the pressure level up to a value which isappropriate for the correct disengagement of the two gearboxesthat work at different pressure levels. Finally, note that, as men-tioned in Section 4.1, if a single clutch gear shift performancemust be handled in the face of additional large loads, then anon-zero Overlap might be of help to optimally deal with theincreased inertia of the vehicle, thereby leading to an adapta-tion of the Overlap time duration as a function of the load con-dition. Up to now, however, the tuning of this parameter hasbeen optimized for the end-of-line test conditions, whichinvolve gear shifts carried out at nominal load on asphalt road,and thus led to set it to zero for the single clutch case.To assess the controller effectiveness, Fig. 12 shows the timehistories of the measured vehicle speed in a double clutch shiftwith non-optimized and optimized controller parameters.The corresponding values of the J1and J2indexes are J1= 24 andJ2= 102.98 for the non-optimized manoeuvre and J1= 1.31 andJ2= 35.38 for the optimized one, respectively. The optimized valuesfor the gear shift shown in Fig. 12 are KP = 5.2 bar, Overlap = 390 msand DelayHML = 210 ms.4.3. Analysis of the acceleration phaseThe last issue to be considered for gear shift control, which isshared both by single and double clutch gear shifts, is the possibleovershoot and oscillatory behavior present at the end of themanoeuvre, when the clutch of the incoming gear needs to be fullyengaged and the vehicle must be brought to reach the final, steady-state, speed value.Before discussing this issue and presenting the proposed solu-tion to limit the overshoot, it is worth pointing out that in theFig. 11. J1and J2index values as functions of the controller parameters.234567891011Time sSpeed km/hNon optimizedOptimizedFig. 12. Time histories of the measured vehicle speed in a double clutch shift: results with non-optimized (dashed line) and with optimized (solid line) controller parameters.292M. Tanelli et al./Mechatronics 21 (2011) 285297considered tractor the engine speed is regulated via a dedicatedengine control unit, the internal controller of which is not directlyaccessible. The only interaction with the engine controller can berealized via the specification of the engine speed reference signalwhich should be tracked during the gear shift. The nominal choiceis to have a constant reference engine speed equal to the onemeasured immediately before the gear shift request.Within this setting, if we consider an up-shift, and we letxeng,xoeng,xwandsbe the engine speed, the engine reference speed, thewheel speed and the transmission ratio of the incoming gear,respectively, the evolution in time of these variables during thegear shift can be schematically represented as in Fig. 13.Specifically, immediately before the gear shift the tractor pro-ceeds at substantially constant engine (dotted line in Fig. 13) andvehicle speed (the solid line in Fig. 13 is the scaled wheel speedxw/s, which can be directly compared with the engine speed).Once the gear shift is requested (in correspondence of the leftmostsolid vertical line in Fig. 13), the disengagement of all the clutchesassociated with the incoming gear occurs, and there is a slippingphase during which the system is characterized by two degreesof freedom, as the engine and the tractor can proceed at differentspeeds and they interact via the torque transmitted by the incom-ing clutches, which are slipping.Once the clutches are fully engaged (in correspondence of thesecond solid vertical line in Fig. 13), the engine and the wheelshave the same speed (denoted byxEin Fig. 13), and the systemhas only one degree of freedom. As can be seen from Fig. 13, duringthe slipping phase the engine speed decreases even though the ref-erence engine speedxoeng(horizontal solid line in Fig. 13) is keptconstant at the value at which the gear shift began. This is due tothe fact that the torque at the clutch in this phase is generatedalong the direction of motion of the transmission output shaft, sothat it accelerates the vehicle while it opposes to the rotationof the incoming shaft, thus decelerating the engine. During thetraction phase which follows the clutches engagement, the enginecontroller, in view of the engine speed error, tries to compensatefor it by increasing the engine torque. Due to large vehicle inertia,this acceleration phase has a long settling time, and the enginecontroller dynamics (most probably endowed with an integralaction) is such that the transient is characterized by an overshootand subsequent oscillations, which cause discomfort to the driver.To counteract this phenomenon, which is more critical in thedouble clutch up-shifts, the idea is to appropriately modify the en-gine reference speed (of course, an alternative may be to directlyact on the engine controller; in our case, this is not possible asthe engine control algorithm cannot be accessed or modified).To this end, consider the modified engine speed referenceshown in Fig. 14: as can be seen in the slipping phase the enginereference speed is decreased along a ramp up to the point at whichthe incoming clutches are fully engaged, while, during the tractionphase, the reference is increased along a second ramp which takesthe engine speed back to the final value which coincides with thatat the beginning of the gear shift.The motivation for this choice is as follows: in the slippingphase the engine is forced to decelerate in view of the torque gen-eration mechanics. Hence, in order to limit the magnitude of thetracking error and the resulting detrimental effect of the relatedintegral action of the controller, it is convenient to let the referencespeed decrease accordingly. This has also the additional beneficialeffect of shortening the slipping phase, as the engine does not try33.544.555.566.577.581250130013501400145015001550160016501700Time sEngine speed rpmtraction phaseslipping phaseengEw/oengFig. 14. Schematic view of the time histories of engine speed, wheel speed in a gear shift with modified engine speed reference.33.544.555.566.577.581250130013501400145015001550160016501700Time sEngine speed rpmtraction phaseslipping phaseoengEw/engFig. 13. Schematic view of the time histories of engine and wheel speed in a gear shift with constant engine speed reference.M. Tanelli et al./Mechatronics 21 (2011) 285297293to accelerate opposing to the clutch engagement, thus limiting theclutch wear and tear.Then, once the clutch engagement is detected the engine mustbe accelerated as quickly as possible while avoiding the overshoot.To achieve this, a ramp set-point has proved appropriate, and anappropriate (fixed) value of the slope has been tuned for each gearshift. The same tuning has been performed to define the ramp dur-ing the slipping phase, with the only difference that the point atwhich the clutch is engaged is not known a priori, and thus needsto be estimated. Specifically, the clutch is defined to be engagedwhen the engine speedxengequals the scaled wheel speedxw/s.To correctly compare the two speed values, however, one mustconsider that, even during constant motion, these are not perfectlyequal due to the geometry of the transmission.Based on a large set of gear shifts data, the residuals of theequation:xeng?xw=s 012have been studied, so that it was possible to verify that they arenormally distributed and that the confidence interval at 99% wasgiven by a spread of 30 rpm. Thus, the clutch is considered to befully engaged when the relationjxeng?xw=sj 6 30 rpm13holds over a time window ofDt = 250 ms. This last condition isneeded to average out the measurement noise and avoid outliers.To appreciate the effectiveness of the proposed approach Fig. 15compares the time histories of the engine speed, of the engine tor-que and of wheel speed measured in a double clutch gear shift withconstant (dashed line) and modified (solid line) engine speed refer-ence. As can be seen, with constant engine speed reference the en-gine controller makes the engine torque saturate to its maximumvalue, and this causes of course a delay in the settling time and sig-nificant oscillations at the end of he transient. This clearly reflectson the vehicle speed, the transient of which significantly benefitsfrom the engine reference modification, yielding a much morecomfortable gear shift. The positive effect can be objectively quan-tified by means of the quality index J3(see Eq. (10): the gear shiftwith constant engine speed reference yielded J3= 720.4, while thatwith the modified reference scored J3= 73.4.05101512501300135014001450150015501600Time sEngine speed rpmwith modified engine reference speedwith constant engine reference speedEngine reference speed(a) 051015102030405060708090100Time sEngine torque % maximum torquewith modified engine reference speedwith constant engine reference speed(b) 0510152324252627282930Time sSpeed km/hwith modified engine reference speedwith constant engine reference speed(c) Fig. 15. Time histories of engine speed (a), engine torque (b) and wheel speed (c) in a double clutch gear shift: results obtained with constant (dashed line) and modified(solid line) engine speed reference.294M. Tanelli et al./Mechatronics 21 (2011) 2852975. End-of-line automatic gear shift tuningWe now present the automatic end-of-line tuning algorithm de-signed to optimize the gear shift controller parameter values whichis needed to ensure satisfactory and repeatable performance ondifferent production vehicles. The parameters that have to be cor-rectly tuned are:(1) the KP pressure for each clutch;(2) the Overlap and DelayHML time intervals duration for doubleclutch shifts.Note that the profile chosen for modifying the engine referencespeed is not object of end-of-line tuning, as the fact that a closed-loop controller is present to regulate the engine speed, combinedwith the chosen reference signal adaptation strategy, yielded a ro-bust solution not needing additional tuning.As the kiss-point pressure has a clear physical meaning, a modelbased procedure will be followed to identify its value.For the double shift parameters, instead, an optimizationprocedure is proposed, based on the quality indexes described inSection 3.5.1. Kiss-point pressure identificationWe have previously discussed that, if a clutch is completely en-gaged, the overlap of another clutch is seen by the engine as anadditional load torque. As the engine is itself controlled so as tokeep its speed constant (at a set-point imposed by the driver),when this additional load torque acts on it more power is neededto keep the engine speed constant. From this basic idea, the algo-rithm to identify the kiss-point is as follows. While a clutch is en-gaged, the clutch pressure whose kiss-point value is to beidentified is slowly increased. The engine power (available asoutput by the engine control unit) is monitored: when its value in-creases meaning that the overlapping clutch is actually transfer-ring torque the corresponding pressure value is identified as thekiss-point one.As the sensitivity analysis showed (see Fig. 8), a precision of atleast 500 mbar is needed in the KP pressure identification to guar-antee optimal gear shift performance.Fig. 16 reports the KP pressure identification results obtained byapplying the above identification procedure for four times on threedifferent vehicles (each colored1bar refers to a single vehicle and itis divided into four smaller bars that represent different executionsof the automatic procedure proposed). The maximum standarddeviation of the identified KP values is of 90 mbar, which, com-pared to the measured KP values, shows that the proposed algo-rithm is strongly repeatable. It is also worth underlining that theprocedure can be carried out in a fully automatic way, as it doesnot require the vehicle to move. In fact the tuning involves onlythe HML and 123 clutches, and the procedure can be executedwhile opening the final clutch between the transmission and driv-ing wheels, thus without transferring torque to the ground andwith the vehicle at standstill.5.2. Automatic tuning of the double clutch gear shift controllerparametersUnlike the kiss-point pressure, the two parameters involved in adouble clutch gear shift do not have a precise physical meaning.Therefore, their optimal values will be found by experimental opti-mization of the introduced cost functions. Namely, the Overlaptime interval will be tuned so as to minimize the cost function J1.Notice, in fact, that for double clutch gear shifts this parametercannot be easily set to a fixed value for all vehicles (as for singleclutch ones) as it changes significantly from a vehicle to another.As for DelayHML, recalling the discussion at the end of Section 4,its tuning phase is performed by minimizing the following costfunction:JHMLJ2;DelayHML c1J2 c2DelayHML14where c1and c2are constant scaling factors. The cost function JHMLtakes into account both J2and the value of DelayHML itself in orderto prevent excessive wear of the clutch surfaces. Specifically, theconstant parameters c1and c2in (14) are selected so that the twoterms on the right-hand size of (14) have the same size. The neces-sity of an equal weighting of the two components is motivated bythe following fact: as mentioned in Section 4.2 the optimal valueof J2occurs for large values of DelayHML, which are not appropriatein general, as they induce wear and tear of the HML clutches thatare left slipping for long times. Thus, one needs to weight DelayHMLso that its final value is not too large. On the other hand, however,DelayHML must not be too low either so not to lose the advantage ofdifferent disengagement times for the two gearboxes involved in adouble clutch gear shift.As all indexes can be computed in real time, the tuning proce-dure is as follows:1. define a maximum number of gear shifts NMaxand a lower-bound JiMinon the performance index JiHLM123050001000015000ClutchPressure mbarVehicle 1Vehicle 2Vehicle 3Fig. 16. Kiss-point pressure identification results obtained on three different vehicles.1For interpretation of color in Figs. 118, the reader is referred to the web versionof this article.M. Tanelli et al./Mechatronics 21 (2011) 2852972952. while N 6 NMaxi. perform a gear shift and compute the performance index Jiii. if Ji6 JiMinin the last three gear shifts go to Step 3iii. else update the value of the parameter pkto be optimized viaa gradient-based optimization algorithm, i.e.,pk1 pk?arJipk;wherearJi(pk) is the step size which depends on the experimen-tally computed gradient of the cost function (ais a positive real-val-ued parameter used to scale the gradient);3. save and store the current value of pkNote that, to terminate the auto-tuning procedure, it is requiredthat the termination condition on the cost function value is met inthree successive manoeuvres, so as to account for possible varia-tions in the working condition which can affect the single gearshift. Furthermore, the tuning cycle is repeated while the numberof performed gear shifts is lower than the upper-bound NMax= 35.This additional condition has been added to the tuning logic forsafety reasons, so as to ensure that the automatic procedure termi-nates even in case of faults or unexpected system behavior. In allthe experimental campaign conducted up to now this limit hasnever been hit and the procedure has always terminated in viewof condition 2.ii.This procedure is applied for DelayHML and subsequently forthe Overlap time duration. The self-tuning procedure has been re-peated four times on the same vehicle (whose controller parame-ters have been manually de-tuned after each run) in order toverify that the proposed algorithm allows to obtain repeatable gearshift performances at the end of the tuning phase.Fig. 17 reports the time histories of the two performanceindexes J1and J2and of the two parameters DelayHML and theOverlap time duration obtained in a run of the automaticprocedure. As can be seen, the procedure starts with the tuningof DelayHML, while Overlap is kept at zero. Then Overlap istuned, while keeping DelayHML at its optimized value. Note thatwhile Overlap is being tuned based on the cost function J1,the value of the performance index J2remains substantially con-stant, therefore confirming the possibility of relying on a singleperformance index at a time to perform the tuning of the twoparameters.It is worth noting that the choice of tuning tune first DelayHMLand then Overlap is due to physical considerations. In fact, if wetuned first Overlap with the same rationale used to tune DelayHML,i.e., with DelayHML equal to zero, we would start the optimizationof J2from large values of the cost function (see Fig. 11b), and thiscorresponds to large bumps in the vehicle speed coming from anon correct disengagement of the clutches, yielding very demand-ing working conditions for the transmission. On the other hand, ifone would tune Overlap with large values of DelayHML, then theclutches would be left slipping for long times, and this again wouldsignificantly stress the clutches and the whole transmission. Assuch, the safest approach is to tune first DelayHML and thenOverlap.Finally, Fig. 18 shows the results obtained in
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