IEEE/ASME TRANSACTIONS ON MECHATRONICS, VOL. 11, NO. 1, FEBRUARY 2006
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Gearshift Control for Automated Manual Transmissions Luigi Glielmo, Member, IEEE, Luigi Iannelli, Member, IEEE, Vladimiro Vacca, and Francesco Vasca, Member, IEEE
Abstract—A gearshift control strategy for modern automated manual transmissions (AMTs) with dry clutches is proposed. The controller is designed through a hierarchical approach by discriminating among five different AMT operating phases: engaged, slipping-opening, synchronization, go-to-slipping, and slippingclosing. The control schemes consist of decoupled and cascaded feedback loops based on measurements of engine speed, clutch speed, and throwout bearing position, and on estimation of the transmitted torque. Models of driveline, dry clutch, and controlled actuator are estimated on experimental data of a medium size gasoline car and used to check through simulations the effectiveness of the proposed controller. Index Terms—Automated manual transmissions (AMTs), automotive control, clutch engagement control, dry clutch, gearshift.
I. INTRODUCTION ARS with modern transmission systems exhibit high fuel economy, low exhaust emission, and excellent driveability. Recent reports on the future automotive market forecast that in 2010 the production of manual transmissions will have fallen below 50% while the modern automatic transmissions will have reached 25% of production [1], [2]. Among other responces, the automated manual transmissions (AMTs) represent a promising solution since they can be considered as an inexpensive add-on solution for classical (in European and Latin countries) manual transmission systems. Moreover, AMTs are also extensively used in racing cars and as a reconfiguration element in modern hybrid electric vehicles. One of the most critical operations in AMTs is represented by the gearshift and more specifically by the clutch engagement. In automotive drivelines, the goal of the clutch is to smoothly connect two rotating masses, the flywheel and the transmission shaft, that rotate at different speeds, in order to allow the transfer of the torque generated by the engine to the wheels through the driveline. The automation of the clutch engagement must satisfy different and conflicting objectives: It should obtain at least the same performance manually achievable by the driver (short gearshift time and comfort) and improve performance in terms of emission and facing wear. The engine and clutch speeds during the engagement and at the lockup play an important role both for comfort and friction losses [3], [4]. In order to achieve the objectives of the clutch engagement automation, several control approaches which deal with the vehicle
C
Manuscript received March 20, 2004; revised December 23, 2004. Recommended by Technical Editor H. Peng. The authors are with the Dipartimento di Ingegneria, Universit`a degli Studi del Sannio, 21-82100 Benevento, Italy (e-mail:
[email protected];
[email protected];
[email protected]). Digital Object Identifier 10.1109/TMECH.2005.863369
startup operating conditions have been proposed: quantitative feedback theory [5], model predictive control strategy [6], fuzzy control [7], decoupling control [4], and optimal control [8], further in [9], the authors propose a particular engagement technique. Problems and solutions related to the clutch engagement during the gearshift phase have been also considered in the literature. In [10], an analytical procedure for computing the desired engine speed during upshift and downshift is proposed. In [11], a model-based backstepping methodology is used to design the gearshift control in AMTs without the synchronizer. In [12], a neuro-fuzzy approach is used by considering the driver’s intention and variable loads. In spite of the extensive literature on AMT control, some problems still need further investigation: the role of speed feedback loops in the clutch engagement control, the definition of a controller architecture which can be exploited both during vehicle startup and gearshift, the robustness of the solution with respect to clutch aging, and uncertainties in the clutch characteristic. This paper tries to provide a contribution in this direction by proposing a new controller for gearshift and clutch engagement in AMTs. The paper is organized as follows. In Section II, models of driveline, dry clutch, and closed-loop electrohydraulic actuator are considered and tuned on experimental data. In Section III, five different operating phases of the AMT are considered: engaged, slipping-opening, synchronization, go-to-slipping, and slipping-closing. The controllers, designed through a hierarchical approach with decoupled and cascaded feedback loops based on measurements of clutch speed, engine speed, and throwout bearing position, are presented in Section IV. The controlled AMT is simulated in the Matlab environment where the Simulink scheme corresponding to the current AMT phase and the corresponding controller are selected by a Stateflow finite state machine. Simulation results showing the effectiveness of the proposed approach are presented in Section V. Conclusions that synthesize the results of the paper are reported in Section VI. II. MODELING A. Driveline A driveline model suitable for parameter identification and for the clutch engagement control design can be obtained assuming the clutch speed ωc is equal to the mainshaft speed ωm , and considering the mainshaft rigid (Fig. 1). Thus, when the engine flywheel and the clutch disk are in slipping operating conditions, the driveline model can be written as Je ω˙ e = Te − Tc (xc )
1083-4435/$20.00 © 2006 IEEE
(1)
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IEEE/ASME TRANSACTIONS ON MECHATRONICS, VOL. 11, NO. 1, FEBRUARY 2006
eration pedal positions and vehicle speeds. The clutch torque has been estimated by an offline inversion of (1): ˆ˙ e Tˆc = Te − Je ω
Fig. 1.
Driveline scheme.
[Jc + Jeq (ig , id )]ω˙ c = Tc (xc ) −
ωc 1 − ωw ktw ∆θcw + βtw (2) ig id ig id
ˆ˙ e is obtained through the so-called dirty derivative, where ω i.e., a filtered incremental ratio on the measured engine speed. The model parameters have been identified by using the least square method and the corresponding results have been found as follows: Jc + Jeq = 0.004 kg·m2 , Jw = 133 kg·m2 , βtw = 295 N·m/(rad/s), and ktw = 6200 N·m/rad. Note that in the sum Jc + Jeq , the dependence of Jeq on the gear ratio is negligible. It can be also verified that, as typical for the type of driveline and car under investigation, the first resonance in the frequency response of the model appears at a few hertz. B. Dry Clutch
Jw ω˙ w
= ktw ∆θcw + βtw
ωc − ωw ig id
− TL (ωw )
(3)
∆θ˙cw =
(7)
ωc − ωw ig id
(4)
where J’s are inertias; ω’s speeds; T ’s torques; xc the throwout bearing position; and the subscripts e, c, t, and w indicate engine, clutch, transmission, and wheels, respectively. Moreover, ig is the gear ratio, id is the differential ratio, Jeq (ig , id ) = Jm + (1/i2g )(Js1 + Js2 + (Jt /i2d )), Js1 and Js2 are the inertias of the two disks connected to the synchronizer, Jm is the mainshaft inertia, TL is the load torque, θ’s are angles, k’s are elastic stiffness coefficients, and β’s are friction coefficients. When the clutch is engaged, the engine speed ωe and the clutch disk speed ωc are equal. The corresponding engaged model can be obtained by adding (1) and (2) with the assumption ωe ≡ ωc . For more details see [13], where a more complex model that also takes into account the flexibility of the mainshaft has been derived. A further reduction of the model can be obtained by also considering the driveshaft to be rigid. By assuming ωc ≡ ωm ≡ ig id ωw and by reporting the vehicle inertia to the mainshaft, one obtains the following model: Je ω˙ e = Te − Tc (xc ) Jv (ig , id )ω˙ c = Tc (xc ) − TL
ωc ig id
(5) (6)
where Jv (ig id ) = Jc + Jeq (ig id ) + (Jw /i2g i2d ). The corresponding engaged model can be obtained by adding (5) and (6) with ωe ≡ ωc . The model (1)–(4) provides a good compromise between description of the driveline dynamics and model complexity. The parameters of (1)–(4) have been tuned from experimental data carried out on a FIAT STILO 2.4 gasoline car with Je = 0.2 kg·m2 , id = 3.94, and the set of gear ratios ig = [3.08, 2.23, 1.52, 1.16, 0.91] from the first gear to the fifth gear, respectively. The signals ωe , ωc , ωw , and Te have been acquired with a sampling frequency of 100 Hz during tests in which a series of upshifts were carried out with different accel-
From a physical point of view, the dry clutch consists of two disks (the clutch disk connected to the mainshaft and the flywheel disk connected to the engine) covered with a high friction material and a mechanism which presses the disks against each other (clutch closed or engaged) or keeps them apart (clutch open or disengaged). During an engagement phase, the clutch disk is moved towards the flywheel disk until the friction due to their contact allows the torque transmission. The throwout bearing position xc determines the pressure between the flywheel disk and the clutch disk and, therefore, the transmitted torque during the slipping phases. The nonlinear characteristic Tc (xc ) that relates the throwout bearing position xc to the torque transmitted by the clutch is not easy to model. The clutch wear drastically influences such a characteristic and thus the torque transmission. Moreover, the clutch characteristic is also influenced by the dependence of the friction coefficient on both temperature [14] and slip speed. In particular, the negative variations of the friction coefficient with slip speed can induce torsional self-excited vibrations of the driveline [15], [16]. The nominal nonlinear characteristic Tc (xc ) has been identified from the experimental tests described above. By representing the estimated values of the clutch torque obtained through (7) as a function of the corresponding values of the signal xc , the set of points reported in Fig. 2 (top diagram) is obtained. The absolute value of the clutch torque has been modeled by using the interpolation curve reported in bottom diagram of Fig. 2 (curve b), and its variations (curves a and c) which model different clutch wear and have been used to test the controller robustness. Note that the wear changes the bearing position, say x ¯c , at which the two disks come in contact and the transmitted torque becomes different from zero. C. Clutch Actuator In AMTs, the electrohydraulic actuator is mainly composed of a hydraulic piston connected to a system of springs that keep the clutch closed when the piston does not apply any force (see Fig. 3). The piston is controlled by a three-port electrovalve that regulates the oil flow through the hydraulic circuit and then determines the force on the mechanical actuator. In standard commercial applications, the electrohydraulic actuator is used
GLIELMO et al.: GEARSHIFT CONTROL FOR AUTOMATED MANUAL TRANSMISSIONS
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where Mv is the spool mass, yv is the spool position, Fm is the force caused by the solenoid current I, bv is the friction coefficient, Kv is the effective spring constant, and Fk o is the mechanical spring force due to the preload of the spring. The oil force Foil is the Bernoulli’s force defined as [18] Foil = ϕCv wyv ∆p cos(ϑ(yv ))
(9)
where ϕ is the discharging coefficient, Cv is the velocity coefficient, w is the control port width, ϑ(yv ) is the jet angle described by a polynomial function of the spool position (ϑ(yv ) = C3 yv3 + C2 yv2 + C1 yv + C0 ), and the variation of pressure in the three-port electrovalve is defined as pL − pA for L-A opened (yv > 0) → Clutch open ∆p = pA − pT for A-T opened (yv ≤ 0) → Clutch close Fig. 2. Set of points (xc , Tˆc ) obtained from experimental data (top diagram) and clutch characteristics (bottom diagram) for positive slip speed with different wear. Curve a: new clutch. Curve b: medium wear. Curve c: high wear.
where pL is the line pressure, pT is the tank pressure, and pA is the oil pressure in the actuator chamber. The variation of the oil pressure pA can be described by p˙A =
E [Q(yv , ∆p) − Ap x˙ c ] Ap xc + Vt
(10)
where E is the fluid bulk modulus, Ap is the piston cross sectional area, xc is the actuator position (or, equivalently, the throwout bearing position), Vt is the minimum actuator chamber volume (corresponding to xc = 0), Q(yv , ∆p) is the oil flow in the servocylinder computed as shown by the equation at the bottom of the page, where d is the underlap to the port, Clk is the leakage coefficient, and ρ is the oil density. The last equation of the hydraulic actuator model describes the motion of the servocylinder piston as xc = −bp x ¨c − Fspring (xc ) + Ap pA (Mp + Mc )¨ Fig. 3.
Hydraulic actuator scheme corresponding to the clutch engaged.
with a feedback control on the throwout bearing position. Usually a further inner control loop on the current is implemented. By identifying the parameters of the detailed actuator model proposed in [17], we now show that, for the goal of this paper, the actuator with a position feedback loop can be satisfactorily approximated by a first-order linear system. The actuator model consists of a set of equations describing the dynamics of the electrovalve spool, the servocylinder piston, and the pressure variation in the mechanical actuator chamber. The motion of the valve spool is described by a force balance equation Mv y¨v = Fm (I, yv ) − Foil (∆p, yv ) − bv y˙ v − Kv yv − Fk o (8)
(11)
where Mp and Mc are respectively the piston and the clutch mass, bp is the friction coefficient, and Fspring is the nonlinear spring force of the diaphragm spring modeled through a static characteristic. For further details on the model, see [17]. Some considerations on the model are needed. First of all, several parameters (e.g., bulk modulus and other oil parameters) depend on temperature and operating conditions. Furthermore, some hydraulic dynamics due to the pipeline and the actuator chamber are difficult to model. So the model does not catch all dynamics and second-order phenomena of the actual system, yet it is sufficiently detailed for showing that, when the actuator is controlled by using a feedback loop on the position, the overall control system is quite robust with respect to parameter variations and uncertainties as well as unmodeled dynamics.
2|∆p| (y + d)ϕw sign(∆p) − Clk (∆p), for yv > d v
ρ
2|∆p| Q = (yv + d)ϕw 2|∆p| ρ sign(∆p) + (yv − d)ϕw ρ sign(∆p),
(y − d)ϕw 2|∆p| sign(∆p), for yv < −d v ρ
for − d < yv < d
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IEEE/ASME TRANSACTIONS ON MECHATRONICS, VOL. 11, NO. 1, FEBRUARY 2006
TABLE I ACTUATOR PARAMETERS, KNOWN (K) OR IDENTIFIED (I)
formance of the overall engagement control strategy may be relevant. However, the actuator is typically equipped with a local feedback control on the bearing position which provides robustness to the closed-loop system. In order to show that, a position feedback control loop with a classical regulator (PI) has been added to the identified open-loop model. Some simulations have been carried out by considering the nominal model and the perturbed one. In the bottom diagram of Fig. 4, the outputs (bearing position) of the controlled system are reported in the nominal (solid line) and perturbed (dashed line) cases: The two curves are almost equal, thus showing the robustness provided by the position feedback control. Therefore, for the purposes of evaluating the performance of an AMT control strategy, an equivalent model of the controlled actuator not dependent on the actuator parameters can be enough. An identification procedure has been then carried out in order to approximate the complete closed-loop actuator model with a simpler one. The input of the model to be identified is now the reference bearing position and the output is the actual bearing position. So as justified by the simulation results (dotted line) reported in Fig. 4, a first-order linear system has been found to be a good approximation for the closed-loop actuator model. This equivalent model has been used in the gearshift simulations.
III. AMT OPERATING PHASES
Fig. 4. Clutch bearing positions in open loop (top diagram) and closed loop (bottom diagram) in the nominal case and the perturbed case. In the bottom diagram, the position obtained with an equivalent first-order system (dotted line) is also reported.
The parameters of the model have been identified by using the available experimental data on a controlled actuator: the solenoid current I and the throwout bearing position xc . A backstepping approach has been used to identify the servocylinder parameters, whereas a least square approach has been used to identify the electrovalve parameters. The results of the identification procedure are reported in Table I. The actuator behaviour is nonnegligibly dependent on its model parameters. To verify this, the identified model has been simulated in open loop with an increased (+20%) value of the bulk modulus. In the top diagram of Fig. 4, the experimental clutch bearing position is reported (solid line) compared with the clutch bearing position corresponding to the same input signal but with the perturbed parameter (dashed line). Thus, the influence of the actuator parameter’s variations on the per-
In order to determine a possible classification of the AMT operating phases, let us consider the engine speed and clutch speed signals during the gearshift reported in Fig. 5. Five different phases can be identified: engaged, slipping-opening, synchronization, go-to-slipping, and slipping-closing (see Fig. 6). During ordinary operating conditions the AMT is in the engaged phase, the clutch is locked up, and the engine torque is directly transmitted to the driveline. A gearshift request from the driver corresponds to the start of the clutch opening phase: The throwout bearing position is decreased and the clutch disk starts slipping with respect to the flywheel disk, although the two masses rotate at approximatively the same speed (see Fig. 5). When the clutch is fully opened, a new gear can be engaged and the synchronization phase starts. The clutch disk speed moves quickly toward the speed value corresponding to the vehicle speed reported to the mainshaft through the new gear ratio (during the synchronization phase the vehicle speed can be assumed to be constant because of the short duration of the phase with respect to the vehicle dynamics). During the synchronization phase the engine speed also starts reducing (see Fig. 5). Once the new gear is fully engaged, the flywheel disk and the clutch disk must be connected again and the go-to-slipping phase starts. In that phase, the bearing position increases and should move as quickly as possible toward the value x ¯c for which the clutch ¯c the AMT disk and the flywheel come into contact. For xc > x is in the slipping-closing operating phase; the speed regulation in this phase is very important for the overall performance of the AMT. When the clutch and the flywheel reach the same speed, they are locked up and a new engaged operating phase of the AMT starts.
GLIELMO et al.: GEARSHIFT CONTROL FOR AUTOMATED MANUAL TRANSMISSIONS
Fig. 5.
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Engine speed and clutch speed signals during a gearshift; the five operating phases are highlighted.
system switches between two different configurations: one in which ωe and ωc are different velocities and one in which they coincide. Such a switch excites the system dynamics and it is not difficult to realize that a rough measure of the extent of excitation is given by the discontinuity ω˙ c (t¯+ ) − ω˙ c (t¯− ). To compute this discontinuity, let us assume, for simplicity’s sake that the engine torque is continuous at t¯. Now, we add (1) and (2) and use the fact that ωe ≡ ωc after lockup to obtain ω˙ c (t¯+ ) =
1 [Te (t¯+ ) − Ω(t¯+ )] Je + J˜c
(13)
where Fig. 6.
ωc 1 − ωw Ω= ktw ∆θcw + βtw . ig id ig id
Finite-state diagram of the AMT operating phases.
By assuming the state and the engine torque to be continuous at lockup one obtains
IV. GEARSHIFT CONTROL A. Controller Objectives During a gearshift, the clutch engagement should be carried out as quickly as possible and with strict constraints on driving comfort and engine operating conditions. The fundamental constraint on the clutch engagement is the so-called no-kill conditions, i.e., one must avoid the engine stall. This condition can be modeled by imposing that ωe (t) ≥ ωemin
∀t.
(14)
(12)
A further important condition to be satisfied during the engagement is the so-called no-lurch condition. A nonsmooth engagement process determines a mechanical oscillation of the power train, which should be avoided in order to preserve the passengers comfort. To gain some insight into the phenomenon, we first point out that at the time of engagement, e.g., t¯, the
ω˙ c (t¯+ ) =
=
1 [Te (t¯− ) − Tc (t¯− )] Je + J˜c 1 + [Tc (t¯− ) − Ω(t¯− )] Je + J˜c J˜c Je ω˙ e (t¯− ) + ω˙ c (t¯− ) ˜ Je + Jc Je + J˜c
(15)
which leads to ω˙ c (t¯+ ) − ω˙ c (t¯− ) =
Je ω˙ sl (t¯− ). Je + J˜c
(16)
Thus, the engagement smoothness is somehow related to the slip acceleration at lockup and, hence, we will consider this quantity as a quantitative performance criterion.
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Fig. 7.
IEEE/ASME TRANSACTIONS ON MECHATRONICS, VOL. 11, NO. 1, FEBRUARY 2006
General closed-loop scheme during the slipping-closing phase. Except for the gearshift controller, the scheme is also the same for the other phases.
Another control objective consists of maintaining as low as possible the energy dissipated during the engagement, which can be written as t¯ Ed = ωsl (t)Tc (t) dt. (17) 0
In our approach, the control objectives are met by ensuring that the engine speed ωe and the clutch speed ωc (or the slipping speed ωsl ) track desired reference signals. In what follows, the controllers of the different AMT phases are described, starting from the critical slipping-closing phase, which is also the most important phase during the vehicle launch, i.e., starting from a standstill. The input signals for the controllers are measurements of the engine speed and clutch speed, and the estimation of the transmitted torque during the slipping phases. At a lower hierarchical level, which is only ideally modeled in this paper, measurements of the throwout bearing position and estimation of the engine torque are also needed.
Fig. 8. phase.
Block diagram of the gearshift controller during the slipping-closing
TABLE II GEAR-RATIO-DEPENDENT PARAMETERS OF THE PI CONTROLLERS
B. Slipping-Closing Controller In this phase, a new gear has already been engaged, the throwout bearing position has reached x ¯c , and the clutch has started transmitting torque to the driveline. The general architecture of the controlled system is reported in Fig. 7. The driveline model to be considered is (1)–(4). The controller output signals are the reference engine torque Teref and the reference throwout bearing position xref c , and are generated from the gearshift controller on the basis of the reference speeds ωeref and ωcref . The signal Teref is actuated by the engine control unit, which is here assumed to be ideal, i.e., Te = Teref . The reference signal xref c is actuated by the closed-loop electrohydraulic actuator approximated by the first-order system presented in the previous section. Finally, xc is converted to the transmitted torque Tc through the clutch characteristic. A block diagram of the gearshift controller is shown in Fig. 8. The controller C1 realizes a feedforward action obtained by computing the left-hand side of (1) after replacing the actual engine speed with the corresponding reference signal. The feedback loop on the clutch speed provides the reference clutch torque Tcref . The loop on the engine speed, together with the corresponding feedforward compensation, provides the desired difference between the engine torque and the clutch torque. By adding to this signal the transmitted torque [estimated by using (7)], the reference engine torque Teref is obtained. This scheme can be viewed as a decoupling controller (see [4]) and thus the two controllers C2 and C3 are PI designed by applying
to the model (1)–(4) classical single-input single-output linear controller design techniques. Furthermore, the controllers’ parameters are designed (and then scheduled at run-time) for each gear so as to obtain the same closed-loop decoupled transfer matrix and, hence, the same performance. By assuming for C2 and C3 the transfer function form KP + KI /s, the resulting parameters are KI = 1.9 and KI = 25, respectively, for C2 and C3 , and proportional gains, are reported in Table II. An inner feedback loop on the clutch torque is introduced in order to compensate for the uncertainties on the static torque characteristic (see Fig. 2). The nonlinearities in the clutch model Tc (xc ) make it difficult to design the controller C4 through an analytical procedure. Here, C4 has been chosen as a PI controller whose parameters have been manually tuned (KP 4 = 0.01 and KI 4 = 0.5). Robustness of the closed-loop system with respect to different C4 parameters have been checked in simulations showing that such parameters are not critical for the closedloop performance. C. Engaged Controller In this phase, the clutch is fully engaged and the transmitted torque is directly supplied by the engine to the mainshaft. The
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driveline model is obtained from (1)–(4) by adding (1) and (2) with the assumption ωe ≡ ωc . Since the clutch is completely closed, i.e., not controlled, the only control signal is the reference engine torque, which is regulated by the engine control unit. D. Slipping-Opening Controller When a new gearshift is requested, it is necessary to open the clutch and, thus, a new slipping phase starts. The driveline model is (1)–(4). The controller output signals are Teref and xref c . The reference torque is obtained with the engine speed control loop of the scheme reported in Fig. 8. The signal ωeref is constant for comfort reasons (see Fig. 5). The throwout bearing reference position xref c is selected in open loop as a decreasing ramp. This phase is concluded when the engine flywheel disk and the clutch disk are completely separated. E. Synchronization Controller During this phase, the clutch disk is completely separated from the flywheel disk and, therefore, Tc = 0. Since during this phase the vehicle speed can be assumed constant, e.g., ω ¯ w , the driveline model can be obtained from (5) and (6) with Tc = 0 and the load torque replaced by the synchronization torque Ts . The controller output signals are the reference engine torque and the reference synchronization torque. Such control signals can be obtained with two independent single-input single-output feedback loops designed by using classical control methods on the linear model described above. The reference clutch speed is assumed to vary linearly from the speed at which the synchronization phase starts and the speed corresponding to the wheel ¯ w /(ig id ), speed transformed by the new gear ratio, i.e., ω ¯c = ω within a desired time interval. F. Go-to-Slipping Controller The main aim of this phase is to reach the bearing position x ¯c at which the friction between the flywheel and the clutch disk, and hence the torque transmission, starts. The driveline ¯c , the clutch torque model is (1)–(4). Since in this phase xc < x is zero (see Fig. 2). The control signals are Teref and xref c . The reference engine torque is obtained with the same controller used in the slipping-opening phase. The throwout bearing reference position xref c is set (without clutch speed feedback) to the ¯c can be obtained by exploiting constant value x ¯c . The value x the clutch torque estimator and averaging the throwout bearing positions at which torque started to be transmitted in the most recent gearshifts. V. SIMULATION RESULTS The simulation results have been obtained by implementing the driveline model and the controllers of the different AMT phases in the Matlab environment. The parts of the model that change with the AMT phases are implemented with different Simulink schemes; the model corresponding to the active phase is selected by a Stateflow finite state machine similar to that shown in Fig. 6. For instance, the commutation from the slipping-closing phase to the engaged phase is obtained with
Fig. 9. Engine, clutch, and vehicle speeds for a sequence of upshifts with medium wear of the clutch.
TABLE III PERFORMANCE FOR A SEQUENCE OF UPSHIFTS
a state-dependent condition, i.e., ωe = ωc , whereas an external event (the driver gearshift request) determines the commutation from the engaged phase to the slipping-opening phase. ¯c ) determines the comAnother state-dependent event (xc = x mutation from the go-to-slipping phase to the slipping-closing phase. The commutation among the different controllers is done by setting their initial conditions so that bumpless transfer is ensured. Figs. 9 and 10 show the simulation results of the controlled AMT for a sequence of consecutive upshifts. The behaviors of the engine speed and clutch speed, and those of the throwout bearing position and engine torque, are presented. In particular, Table III shows some performance indexes of the simulation test: dissipated energy, gearshift time duration, and slip acceleration at lockup are all within acceptable limits and testify the validity of the proposed control strategy. Dealing with driving comfort in particular, by assuming that the lockup phenomenon has a finite time duration, the left-hand side of (16) can also be interpreted as an incremental ratio and, therefore, as an approximation of the jerk caused by the lockup of the clutch. We wish to remark that the controller structure for the slipping-closing phase can also be used both during gearshift and when the clutch must be locked up from standstill. Fig. 11 shows that the control strategy also ensures a smooth clutch engagement during the vehicle startup, which is one of the most critical situations for AMTs. It is apparent that the bearing position and the engine torque have similar shapes. This is due to the fact that in the main part of the slipping-closing phase the clutch
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Fig. 10. Zoom of the upshift from gear 2 to gear 3 with medium wear of the clutch. (a) Engine speed (solid line), clutch speed (dashed line), desired engine speed (dashed-dotted), and desired clutch speed (dotted line). (b) Throwout bearing position. (c) Engine torque.
Fig. 11. Zoom of the startup phase with medium wear of the clutch. (a) Engine speed (solid line), clutch speed (dashed line), desired engine speed (dashed-dotted), and desired clutch speed (dotted line). (b) Throwout bearing position. (c) Engine torque.
is operating in an approximately linear region of the transmitted torque characteristic reported in Fig. 2 and the engine speed is varying slowly, from (1) Te ≈ Tc (xc ). The proposed controller is also effective for downshifts as shown in Fig. 12.
The simulation results reported in Fig. 13 show the robustness of the proposed control strategy in the presence of uncertainties or variations of the clutch static characteristics Tc (xc ). During the slipping-opening phase, corresponding to the first part
GLIELMO et al.: GEARSHIFT CONTROL FOR AUTOMATED MANUAL TRANSMISSIONS
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Fig. 12. Downshift from gear 5 to gear 4 in the presence of a clutch with medium wear (curve b in Fig. 2). (a) Engine speed (solid line), clutch speed (dashed line), desired engine speed (dashed-dotted), and desired clutch speed (dotted line). (b) Throwout bearing position. (c) Engine torque.
Fig. 13. Upshift from 2 gear to 3 gear in the presence of a clutch with high wear (curve c in Fig. 2). (a) Engine speed (solid line), clutch speed (dashed line), desired engine speed (dashed-dotted), and desired clutch speed (dotted line). (b) Throwout bearing position. (c) Engine torque.
of Fig. 13, the engine speed has an overshoot due to the fact that for this simulation x ¯c is larger than in the previous case (see curves b and c in Fig. 2). By comparing Figs. 10 and 13 during the slipping-closing phase, analogous considerations justify the fact that the controller imposes larger values of xc in the latter simulation in order to obtain similar performance.
VI. CONCLUSION The analysis of the existing literature on AMT control strategies shows that a generally recognized good solution to the problem of the gearshift control in AMT with dry clutch is still missing. In this paper, a solution based on cascaded and decoupled speed and torque control loops is proposed. Dynamic
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models of the driveline, the static characteristic of the torque transmitted by the dry clutch during the slipping phases, and an equivalent model of the controlled electrohydraulic actuator have, been tuned on experimental data and used for the controllers design. The control strategy exploits the hybrid nature of the AMT by discriminating among five different operating phases and by designing dedicated controllers for each phase. Simulation results show the effectiveness of the proposed solution during startups, upshifts, and downshifts. Performance is evaluated in terms of duration of gearshift, comfort, dissipated energy, and robustness with respect to uncertainties of the clutch characteristic. The low computational load needed to implement the proposed controller allows its realization on commercial electronic control units. REFERENCES [1] Knibb-Gormezano and Partners. (2000) Trasmissions in Europe 2000– 2010: A decade of significant change. [Online]. Available: http://www. kgpauto.com/Initiatives/Transmissions%20Press%20Release.pdf [2] Just-Auto.com Editorial Team (2001, Jan.) The global transmission market. [Online]. Available: http://www.just-auto.com/features detail.asp? art=417&c=1 [3] Y. Lei, M. Niu, and A. Ge, “A research on starting control strategy of vehicle with AMT,” in Proc. FISITA World Automotive Congress, Seoul, Korea, 2000. [4] F. Garofalo, L. Glielmo, L. Iannelli, and F. Vasca, “Smooth engagement for automotive dry clutch,” in Proc. 40th IEEE Conf. Decision and Control, Orlando, FL, 2001, pp. 529–534. [5] J. Slicker and R. N. K. Loh, “Design of robust vehicle launch control system,” IEEE Trans. Contr. Syst. Technol., vol. 4, no. 4, pp. 326–335, Jul. 1996. [6] A. Bemporad, F. Borrelli, L. Glielmo, and F. Vasca, “Hybrid control of dry clutch engagement,” in Proc. European Control Conf., Porto, Portugal, 2001. [7] H. Tanaka and H. Wada, “Fuzzy control of clutch engagement for automated manual transmission,” Veh. Syst. Dyn., vol. 24, pp. 365–376, 1995. [8] L. Glielmo and F. Vasca, “Optimal control of dry clutch engagement,” SAE Trans., J. Passenger Cars: Mech. Syst., vol. 6, no. 2000-01-0837, 2000. [9] A. Szadkowski and R. B. Morford, “Clutch engagement simulation: Engagement without throttle,” SAE Tech. Paper Series, no. 920766, 1992. [10] F. Amisano, G. Serra, and M. Velardocchia, “Engine control strategy to optimize a shift transient during clutch engagement,” SAE Tech. Paper Series, no. 2001-01-0877, pp. 115–120, 2001. [11] J. Fredriksson and B. Egardt, “Nonlinear control applied to gearshifting in automated manual transmission,” in Proc. 39th IEEE Conf. Decision and Control, Sydney, Australia, 2000, pp. 444–449. [12] K. Hayashi, Y. Shimizu, S. Nakamura, Y. Dote, A. Takayama, and A. Hirako, “Neuro fuzzy optimal transmission control for automobile with variable loads,” in Proc. IEEE Industrial Electronics, Control, and Instrumentation Conf., Maui, HI, 1993, vol. 1, pp. 430–434. [13] L. Glielmo, L. Iannelli, V. Vacca, and F. Vasca, “Speed control for automated manual transmission with dry clutch,” in Proc. 43th IEEE Conf. Decision and Control, Atlantis, Bahamas, 2004, pp. 1709–1714. [14] F. Amisano, R. Flora, and M. Velardocchia, “A linear thermal model for an automotive clutch,” SAE Tech. Paper Series, no. 2000-01-0834, 2000. [15] D. Centea, H. Rahnejat, and M. T. Menday, “The influence of the interface coefficient of friction upon the propensity to judder in automotive clutches,” Proc. Inst. Mech. Eng., vol. 213, pt. D, pp. 245–268, 1999. [16] E. M. A. Rabeih and D. A. Crolla, “Intelligent control of clutch judder and shunt phenomena in vehicle drivelines,” Int. J. Veh. Des., vol. 17, no. 3, pp. 318–332, 1996. [17] M. Montanari, F. Ronchi, C. Rossi, A. Tilli, and A. Tonielli, “Control and performance evaluation of a clutch servo system with hydraulic actuation,” Control Eng. Practice, vol. 12, pp. 1369–1379, 2004. [18] H. Meritt, Hydraulic Control Systems. New York: Wiley, 1967.
Luigi Glielmo (S’87–M’90) was born in 1960. He received the Laurea degree in electronic engineering and the Ph.D. degree in automatic control from the Universit`a di Napoli Federico II, Naples Italy. Currently, he is a Professor of Automatic Control in the School of Engineering of the Universit`a degli Studi del Sannio, Benevento, Italy, where he is also Head of the Dipartimento di Ingegneria. In 1989 and 1990, he was a Visiting Scholar at the School of Aeronautics and Astronautics, Purdue University, and a Visiting Scientist at the NET Team, Max-PlanckInstitut f¨ur Plasmaphysik, Germany, in 1990. In 2002, he was Visiting Professor at the Johannes Kepler Universit¨at, Linz, Austria. His research interests include singular perturbation methods, analysis and control of uncertain systems, dynamic positioning of ships, plasma control in (Tokamak) fusion reactors, Kalman filtering, nonlinear system analysis, automotive control, manufacturing systems simulation, modeling, and control of wine production. He has coauthored more than 70 papers published in international archival journals and proceedings of international conferences, and edited Robust Control via Variable Structure and Lyapunov Techniques (Springer-Verlag, 1996). Dr. Glielmo has participated in scientific committees of various international conferences and organized an international workshop. He proposed the establishment of and chaired for four years the IEEE Control Systems Society Technical Committee on Automotive Controls. He is a member of ASME, SIAM, and SAE and is an Associate Editor of the IEEE TRANSACTIONS ON AUTOMATIC CONTROL. Luigi Iannelli (S’01–M’03) was born in 1975 in Benevento, Italy. He received the Laurea degree in computer engineering from the Universit`a degli Studi del Sannio, Benevento, Italy, in 1999, and the Ph.D. degree in information engineering from the Universit`a di Napoli Federico II, Naples, Italy, in 2003. During 2002 and 2003, he was a Guest Researcher in the Department of Signals, Sensors, and Systems, Royal Institute of Technology (KTH), Stockholm, Sweden. In 2003, he was a Research Assistant in the Dipartimento di Informatica e Sistemistica, Universit`a di Napoli Federico II. He is currently an Assistant Professor of Automatic Control in the Dipartimento di Ingegneria, Universit`a degli Studi del Sannio. His current research interests include analysis and control of switched and hybrid systems, automotive control, and applications of control theory to electronic systems. Dr. Iannelli is member of the IEEE Control Systems Society, IEEE Circuits and Systems Society, and SIAM. Vladimiro Vacca was born in 1975 in Naples, Italy. He received the Laurea degree in computer engineering with orientation toward industrial automation from the Universit`a di Napoli Federico II, Naples, Italy, in 2002. He is currently working toward the Ph.D. degree in control engineering, sponsored by Carlo Gavazzi Space, in the Dipartimento di Ingegneria, Universit`a degli Studi del Sannio, Benevento, Italy. From July 2002 to June 2003, he was involved in modeling and clutch control for automated manual transmissions during a collaboration with the ELASIS research center. His current research interests include automotive control, satellite formation flying, wireless monitoring systems, and real-time control in avionics. He is currently working on the ESA project (Fluid Science Laboratory). Francesco Vasca (S’94–M’95) was born in Naples, Italy, in 1967. He received the Laurea degree in electronic engineering and the Ph.D. degree in automatic control from the Universit`a di Napoli Federico II, Naples, Italy, in 1991 and 1995, respectively. Since 2000, he has been an Associate Professor of Automatic Control in the Dipartimento di Ingegneria, Universit`a degli Studi del Sannio, Benevento, Italy. His research interests include automated manual transmissions, energy management of hybrid vehicles, battery state of charge estimation, nonlinear dynamics and control techniques for power converters, averaging of nonsmooth systems through dithering, and formation control of multiagent systems.
