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a , Carlo 20133 analysis double spreads control it. mented vehicle. with fact, agricultural speed of moving trailers clutches connected to an hydraulic circuit, whose pressure can be regulated by a proportional solenoid valve. Considering the large number of gears available and the fact that to achieve an optimal gear 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 the scientific literature, some works dealing with power-shift or dual To design an effective transmission control system, first of all the most significant variables which influence the gear shift quality must be identified, see e.g., 2,16. Further, the gear shift control system has to optimally manage the trade-off among the following conflicting requirements: (i) yield comfortable gear shifts; (ii) guarantee that no loss of power to the driving wheels occurs during gear shifts; (iii) cause a minimum wear and tear of mechanical components over the life of the vehicle transmission. Corresponding author. Tel.: +39 02 2399 3621; fax: +39 02 2399 3412. Mechatronics 21 (2011) 285297 Contents lists available E-mail address: tanellielet.polimi.it (M. Tanelli). sure the maximum flexibility of use at each speed and to exploit the maximum engine power available in all working conditions, nowadays agricultural vehicles are often equipped with a so-called power-shift transmission. This kind of transmission has a large number of gears available (typically from 9 to 30) and it allows to perform a gearshift with no (or at least with a minimum) loss of power from the engine to the driving wheels. Usually, a power-shift transmission is characterized by the presence of two or more (depending from the number of gears and the overall mechanical architecture of the gearbox) wet the comfort of the driver on all working grounds, which vary from asphalt roads to rough off-road terrains. Also the load distribution in tractors is much different than for other vehicles, due to the fact that it might be due to either front or rear additional loads due to the various working instruments that need to be employed for differen tasks. Finally, note also that the variation of the operating conditions is most often non measurable via on-board sensors, and thus asks for robust and easily tunable gear shift controllers. These facts make the problem of ensuring an optimal and repeatable gear shift on an agricultural tractor a very challenging task. 1. Introduction and motivation Agricultural vehicles have to cope which are more complex and demanding by other ground vehicles, 10. In essentially designed to work at low traction forces. Moreover, their ease makes them suitable also for heavy 0957-4158/$ - see front matter C211 2010 Elsevier Ltd. All doi:10.1016/j.mechatronics.2010.11.006 working conditions than those experienced vehicles are while providing large on uneven soil transportation. To en- clutch transmissions control for ground vehicles are available, see e.g., 38,15, but very little has been done on specific solutions for agricultural tractors. This is mainly due to the fact that agricul- tural vehicles have very specific performance specifications due to the very broad range of working conditions and variability of the vehicle 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 and Automotive systems End-of-line tuning C211 2010 Elsevier Ltd. All rights reserved. Transmission control for power-shift agricultural and end-of-line automatic tuning Mara Tanelli a, , Giulio Panzani a , Sergio M. Savaresi a Dipartimento di Elettronica e Informazione, Politecnico di Milano, Piazza L. da Vinci, 32, b SAME Deutz-Fahr Group, Viale F. Cassani, 15, 24047 Treviglio (Bergamo), Italy article info Article history: Received 24 May 2010 Accepted 14 November 2010 Available online 8 December 2010 Keywords: Power-shift transmission Agricultural tractors abstract This paper addresses the power-shift agricultural tractor. of both single clutch and providing good shifting performance components tolerances and tuning of the transmission and automatically optimize Mechatron journal homepage: www.elsevi rights reserved. tractors: Design Pirola b Milano, Italy and design of the transmission control system for a high-power Specifically, all the criticalities involved with the correct management clutch gear shifts are investigated, and a control system capable of in all operating conditions is proposed. Further, to comply with in the production line, an automatic procedure for the end-of-line system is proposed to objectively classify the quality of the gear shift The suitability of the proposed approach is thoroughly tested on an instru- at ScienceDirect ics is proposed which guarantees satisfactory and repeatable gear shift pleted with two other components, namely the motion inverter and the mode selector. The motion inverter (see 11,16) is an elec- tro-hydraulic system, constituted by two clutches, which allows to perform an automatic motion inversion, i.e., it takes the vehicle from a, say, forward speed to a reverse speed with the driver sim- ply acting on a lever. The mode selector allows to choose among three different working modes: creep, work and transport, which can be varied only when the tractor is at standstill. In what follows, we concentrate on the control of the gear shift, and consider the two gearboxes only, assuming that no motion inversion is occur- ring (note, in passing, that during a motion inversion the driver cannot command a gear shift), and that a fixed mode has been engaged. 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, Moreover, in the industrial context, once the control design phase is accomplished and the control system is implemented into final products, an end-of-line tuning phase is usually scheduled to deal with constructive tolerances and production spreads which cause the final system to be different from the prototype one used for control validation and testing. Hence, this phase is tailored to optimize the controller parameters so as to guarantee that the expected gear shifting performance is achieved on all vehicles. Usually, this phase is carried out by human testers, who tune the controller parameters based on personal driving preferences and experience. Thus, is it clear that end-of-line tuning is a crucial and 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, but not by another one: this means that the final tuning can lead to very different gear shift behaviors on different vehicles of the same type. Note that, as the vehicle handling qualities, of which the gear shift 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 to achieve customers satisfaction and to promote customers loyalty to the brand. Moreover, another significant advantage of the pro- posed approach is that of reducing the industrial costs associated with end-of-line tuning by reducing the number of gear shifts needed 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 which goes beyond the considered problem, as the aforementioned design steps constitute a working paradigm which can be applied in many different production contexts. As a matter of fact, this pa- per is one of the first contributions which aims at formalizing the end-of-line tuning of industrial applications endowed with control systems, proposing a systematic approach to the considered prob- lem. In this respect, the results in 13,16 offer other applications of the proposed methodology and address the problem of quantifying of the driving style and safety via measured data, and of designing and 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 systematic approach presented in this work, which is constituted by the fol- lowing steps: C15 an evaluation of the characteristic features which define the quality of the considered system; C15 an experimental sensitivity analysis to single out the relation between the features to be optimized and the measurable variables; C15 the definition of the cost functions; C15 the design of the control algorithm and of the procedures for its end-of-line tuning grounded on the cost functions optimization. This methodology makes the results in the present paper of general interest for all those applications in which a control system must be designed and tuned while dealing with the dispersion coming from production spreads and tolerances which make the underlying plant (i.e., the final vehicle) different from that used for design purposes. The resulting research area requires tools both of control theory and optimization, combined with the specific application-domain knowledge. The presented results are based on a joint research work between the Politecnico di Milano and the R (2) the onoff status of each directional valve. To execute a gear shift with a power-shift transmission, the outgoing clutch must be brought to zero pressure, whereas the power-shift transmission. H M L 1 2 3 Fig. 4. Simplified hydraulic scheme of the considered transmission. can 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 gear shifts as single clutch gear shifts. However, when the 34 and 67 gear shifts are considered, two clutches must be changed (one Table 1 Available gears and respective engaged clutches. Gear L M H 1 2 3 1 C2 C2 2C2 C2 3C2C2 4 C2 C2 5C2 C2 6C2 C2 7 C2 C2 8C2 C2 9C2 C2 v ref 1 v m t req ; 3 where t req is the time instant at which the gear shift is requested by the driver. The reference speed in the last part of the manoeuvre is also constant and computed as v ref end x eng t req rs Inc: ; 4 where x eng (t req ) is the engine speed at the beginning of the gear shift (recall that the engine speed is fixed and constant during the gear shift), r is the average wheel radius and s inc is the transmission ratio of the incoming gear (also known when the gear shift is issued by the driver). The reference speed evolution in time between these limiting speed levels, which defines v ref 2 , is chosen as linear, yielding v ref 2 tv ref 1 v ref end C0 v ref 1 t 2 C0 t 1 t C0 t 1 ; 5 where the time instant t 1 is defined as t 1 : jv m t 1 C0v ref 1 jP0 C8C9 fjv m tC0v ref 1 j t 1 g: 6 Namely, t 1 is the last time instant at which the measured speed is lower than the initial reference speed v ref 1 , while the time instant t 2 is defined as t 2 : jv m t 1 C0v ref end j 0; 8t t DO,HML but the two incoming clutches may not engage simultaneously. With the proposed control approach, the fact that the engagement phase occurs in a correct way is evaluated by means of the cost functions, therefore without a direct tuning of the engagement instant. The obtained results are reported in Fig. 11, which shows the values of J 1 and J 2 , respectively, as functions of Overlap and Delay- HML. For the sake of conciseness, the analysis for the KP pressure value 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. C15 First of all note that each controller parameter, i.e., Overlap and DelayHML, has a predominant effect over one single index. Namely, Overlap mostly affects the J 1 index, whereas DelayHML the J 2 one. This fact allows to decouple the optimization phase, and to consider two successive single variable optimization 200 300 400 shifts controller parameters. 4 5 6 7 8 Not optimized Optimized non-optimized (dashed line) and with optimized (solid line) controller parameters. Fig. 11. J 1 and J 2 index values as functions of the controller parameters. 292 M. Tanelli et al./Mechatronics 21 (2011) 285297 problems, which can more easily managed in view of the auto- matic end-of-line tuning phase. Specifically, as will be described in more detail in Section 5, the optimal value for Overlap will be found by minimizing J 1 , while DelayHML will be tuned accord- ing to J 2 . Specifically, to assess the correctness of the sequential minimization of the performance indexes, one has to observe that the function J 2 (C1, DelayHML) has the same shape for all val- ues of Overlap. Therefore, once a value of Overlap has been fixed by optimizing J 1 , then the optimization of J 2 done by varying the value of DelayHML will lead to a final value for J 2 which is approximately always the same (note also that the cost function always decreases as the value of DelayHML increases indepen- dently of the value of Overlap). Of course, the final value of J 2 will not be rigorously the same irrespectively of the value of Overlap with which it is evaluated and which is determined by the minimization of J 1 , but the small differences in the final value for J 2 are not practically relevant as they yield no signifi- cant changes in the final gear shift performance. C15 Note further that the results in Fig. 11b seem to suggest that a large value of DelayHML would bring good quality gear shifts. Nonetheless, it is worth pointing out that, as DelayHML increases, the clutches are left slipping for an increasing amount of 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 this issue. C15 Finally, it is worth comparing the results obtained in the single and double clutch gear shift controllers as far as the value of Overlap is concerned. Specifically, at the end of the previous sec- tion we pointed out that in the single clutch gear shift at least in low load conditions a non-zero Overlap would induce only the detrimental effect of yielding a longer manoeuvre, without introducing any potential increment in the performance. In the double clutch gear shifts, instead, a trade-off arises, due to the fact that one needs to manage the two gearboxes differ- 2 3 4 8 9 10 11 Time s Speed km/h Fig. 12. Time histories of the measured vehicle speed in a double clutch shift: results with ently. Therefore, while on the one hand allowing a non-zero Overlap time interval has indeed the detrimental effect of yield- ing a longer (hence worse) gear shift, on the other hand it offers the advantage of taking the pressure level up to a value which is appropriate for the correct disengagement of the two gearboxes that work at different pressure levels. Finally, note that, as men- tioned in Section 4.1, if a single clutch gear shift performance must be handled in the face of additional large loads, then a non-zero Overlap might be of help to optimally deal with the increased 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 has been optimized for the end-of-line test conditions, which involve 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 time histories of the measured vehicle speed in a double clutch shift with non-optimized and optimized controller parameters. The corresponding values of the J 1 and J 2 indexes are J 1 = 24 and J 2 = 102.98 for the non-optimized manoeuvre and J 1 = 1.31 and J 2 = 35.38 for the optimized one, respectively. The optimized values for the gear shift shownin Fig. 12 are KP = 5.2 bar, Overlap = 390 ms and DelayHML = 210 ms. 4.3. Analysis of the acceleration phase The last issue to be considered for gear shift control, which is shared both by single and double clutch gear shifts, is the possible overshoot and oscillatory behavior present at the end of the manoeuvre, when the clutch of the incoming gear needs to be fully engaged 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 the 5 6 7 Non optimized Optimized non-optimized (dashed line) and with optimized (solid line) controller parameters. considered tractor the engine speed is regulated via a dedicated engine control unit, the internal controller of which is not directly accessible. The only interaction with the engine controller can be realized via the specification of the engine speed reference signal which should be tracked during the gear shift. The nominal choice is to have a constant reference engine speed equal to the one measured immediately before the gear shift request. Within this setting, if we consider an up-shift, and we let x eng , x o eng , x w and s be the engine speed, the engine reference speed, the wheel speed and the transmission ratio of the incoming gear, respectively, the evolution in time of these variables during the gear 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) and vehicle speed (the solid line in Fig. 13 is the scaled wheel speed x w /s, which can be directly compared with the engine speed). Once the gear shift is requested (in correspondence of the leftmost solid vertical line in Fig. 13), the disengagement of all the clutches associated with the incoming gear occurs, and there is a slipping phase during which the system is characterized by two degrees of freedom, as the engine and the tractor can proceed at different speeds and they interact via the torque transmitted by the incom- ing clutches, which are slipping. Once the clutches are fully engaged (in correspondence of the second solid vertical line in Fig. 13), the engine and the wheels have the same speed (denoted by x E in Fig. 13), and the system has only one degree of freedom. As can be seen from Fig. 13, during the slipping phase the engine speed decreases even though the ref- erence engine speed x o eng (horizontal solid line in Fig. 13) is kept constant at the value at which the gear shift began. This is due to the fact that the torque at the clutch in this phase is generated along the direction of motion of the transmission output shaft, so that it accelerates the vehicle while it opposes to the rotation of the incoming shaft, thus decelerating the engine. During the traction phase which follows the clutches engagement, the engine controller, in view of the engine speed error, tries to compensate for it by increasing the engine torque. Due to large vehicle inertia, this acceleration phase has a long settling time, and the engine controller dynamics (most probably endowed with an integral action) is such that the transient is characterized by an overshoot and subsequent oscillations, which cause discomfort to the driver. To counteract this phenomenon, which is more critical in the double clutch up-shifts, the idea is to appropriately modify the en- gine reference speed (of course, an alternative may be to directly act on the engine controller; in our case, this is not possible as the engine control algorithm can