Iterative learning control for the filling of wet clutches

Mechanical Systems and Signal Processing 24 (2010) 1924–1937

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Mechanical Systems and Signal Processing journal homepage: www.elsevier.com/locate/jnlabr/ymssp

Iterative learning control for the filling of wet clutches G. Pinte a,, B. Depraetere b, W. Symens a, J. Swevers b, P. Sas b a b

FMTC, Celestijnenlaan 300 D, B-3001 Leuven, Belgium Department of Mechanical Engineering, Celestijnenlaan 300 B, B-3001 Leuven, Belgium

a r t i c l e i n f o

abstract

Article history: Received 19 May 2010 Accepted 20 May 2010 Available online 26 May 2010

This paper discusses the development of an advanced iterative learning control (ILC) scheme for the filling of wet clutches. In the presented scheme, the appropriate actuator signal for a new clutch engagement is learned automatically based on the quality of previous engagements, such that time-consuming and cumbersome calibrations can be avoided. First, an ILC controller, which uses the position of the piston as control input, is developed and tested on a non-rotating clutch under well controlled conditions. Afterwards, a similar strategy is tested on a rotating set-up, where a pressure sensor is used as the input of the ILC controller. On a higher level, both the position and the pressure controller are extended with a second learning algorithm, that adapts the reference position/pressure to account for environmental changes which cannot be learned by the low-level ILC controller. It is shown that a strong reduction of the transmitted torque level as well as a significant shortening of the engagement time can be achieved with the developed strategy, compared to traditional time-invariant control strategies. & 2010 Elsevier Ltd. All rights reserved.

Keywords: Wet clutch Filling phase Clutch engagement Iterative learning control Position control Pressure control

1. Introduction A wet clutch is a mechanical device that transmits torque from its input axis to its output axis by means of friction. Wet clutches are often used in power transmissions of off-road vehicles and agricultural machines to selectively engage gear elements. These vehicles are operating under varying environmental conditions, e.g. different temperatures in winter and summer. Moreover, these vehicles are also used during several years such that the clutches are subject to a significant amount of wear and their dynamics will change over time. As a consequence of these varying conditions and system dynamics, the control signals for wet clutches leading to an optimal engagement change drastically during the transmission’s life cycle and the control action should therefore be adapted accordingly. In [1], the robust control of wet clutches is identified as a challenging industrial control problem. Much research has been carried out in this field in the past two decades and numerous patents have been generated [2–5]. In this paper, iterative learning control (ILC [6]) is presented as an alternative, efficient strategy for the control of wet clutches, which can find the appropriate control action despite the varying system dynamics and environmental conditions. Fig. 1(a) shows the design of a wet clutch. The input axis of the clutch is connected to a drum, which is a hollow cylinder with grooves on the inside. A first set of friction plates (clutch plates) with external toothing can slide in those grooves, while a second set of friction plates (clutch discs) with internal toothing can slide over a grooved bus connected to the output axis. An electro-hydraulic pressure-regulated proportional valve regulates the pressure inside the clutch with the objective to

 Corresponding author. Tel.: + 32 16 328035.

E-mail address: [email protected] (G. Pinte). 0888-3270/$ - see front matter & 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.ymssp.2010.05.016

G. Pinte et al. / Mechanical Systems and Signal Processing 24 (2010) 1924–1937

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Current

Feedforward in filling phase

0

0.5

1 1.5 Time [s]

2

Fig. 1. A wet clutch: (a) the mechanical design and (b) the typical feedforward current signal to the electro-hydraulic valve in the filling phase.

Fig. 2. The applied two-level control scheme with a low-level ILC controller and a high-level learning algorithm to update the reference of the low-level controller.

control the displacement of a piston which can press the two sets of friction plates together such that torque is transmitted. Initially, when the clutch is not engaged, the piston should be positioned as far as possible from the friction plates to avoid energy losses due to viscous friction of the oil between the plates. If the clutch is not hydraulically actuated, a return spring keeps the piston in this position. When the vehicle control unit gives the command to engage the clutch, the clutch is filled with oil in preparation of the effective engagement. The objective is to decrease the distance between the piston and the plates as fast as possible to zero, without the piston and the plates making brutal contact. This first phase in the engagement of a wet clutch is referred to as the filling phase. Afterwards, when the oil pressure is further increased, the friction plates are pressed together and torque is transmitted through the clutch. However, there is still a rotational speed-difference between the input and output shaft, resulting in energy dissipation in the clutch. A slip controller in this phase can be used to improve the quality of shifting [8]. Finally, when the oil pressure inside the clutch exceeds a certain level, the clutch will be fully engaged. The complete torque is transmitted through the clutch and the clutch is not slipping. In this paper, the control of the filling phase of wet clutches is studied. Nowadays, wet clutches in industrial transmissions are filled using a feedforward controller of the current to the electro-hydraulic valve, which regulates the oil pressure and hence the piston position in the clutch. Fig. 1(b) shows a typical parameterized, feedforward current signal, which is sent in the filling phase to the valve [2]. Although nowadays more advanced feedforward signals with more tunable parameters are sometimes applied [4], the above-mentioned parametrization perfectly illustrates the underlying idea behind the actual industrial control design. First, a current pulse is sent to the valve in order to generate a high pressure level in the clutch. This way, the piston will overcome the preloaded return spring and start to accelerate towards the friction plates. After this pulse, a lower constant current is sent out in order to decelerate the piston and position the piston near the friction plates. Finally a growing ramp current signal is sent to the valve such that the pressure in the clutch gradually increases and the clutch smoothly engages. The duration of the current pulse and the constant current level afterwards are critical to achieve a good filling and a smooth start of the engagement process [1]. On the one hand, a very long current pulse leads to an overfilling of the clutch such that the piston suddenly makes brutal contact with the friction plates resulting in undesired high peaks in the transmitted torque. On the other hand, a very short current pulse or a very low constant current level after the pulse leads to an underfilling of the clutch, resulting in a very slow engagement. To avoid over- and underfilling, in many industrial vehicles long calibration procedures are applied to find the optimal parameters of the feedforward current signal (i.e. the optimal combination of the pulse duration and constant current level) for a smooth clutch engagement. Furthermore, since the controlled system is time-varying, as described above, regular recalibrations of these parameters are inevitable. To avoid these cumbersome calibrations, some patents [5,2] describe adaptive algorithms to update the current pulse parameters at each filling of the clutch, based on the velocity and acceleration of the input and output shaft in the previous clutch engagement. This paper presents a two-level control system for the filling of wet clutches (Fig. 2), which does not update the discrete parameters of a predefined, feedforward current signal but determines a continuous current signal to the valve for a new

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Fig. 3. Test bench consisting of an electromotor which drives a flywheel via two mechanical transmissions: one transmission is controlled in this project, the other transmission is used to vary the load and to adjust the braking torque.

engagement based on measured sensor information at the current and previous engagements. The developed system only focuses on the control of the filling phase, afterwards the slip phase is controlled by a feedforward action. On the low level of the developed control system for the filling phase, a control algorithm is implemented to track a reference for a measured physical variable. In a first part of the paper, the piston position in the clutch is measured and regulated. This way, it is possible to make the piston follow a reference trajectory, where the piston initially moves quickly towards the friction plates, then stops near the friction plates and finally comes smoothly into contact with the friction plates. Based on this position-based algorithm, the oil pressure profile leading to a smooth engagement can be measured. This pressure profile is applied in the second part of the paper to determine the shape of the reference for a pressure-based learning algorithm, which regulates the filling phase based on a measurement of the oil pressure in the line between the valve and the clutch. Since the clutch filling is realized at successive clutch engagements, an ILC algorithm can be used at this low level to learn the current signal to the valve for the next engagement by using experience from the previous engagement. This way it is possible to obtain a good tracking accuracy of the piston position or the oil pressure despite a large model uncertainty of the controlled system between the current to the valve and the regulated variable due to nonlinearities, temperature changes, etc. On the high level of the developed control system, a parameterized reference signal for the regulated variable in the low-level controller is determined based on an adaptive algorithm. This high-level algorithm accounts for slowly changing system variations such as wear, which cannot be learned by the low-level controller. At regular intervals, after a fixed number of closings of the clutch, an assessment of the engagement quality at the previous closings is made by measuring one or more quality indices (e.g. the engagement time). Based on these measured quality indices, the reference trajectory for the low-level algorithm is adapted according to some adaptive rules. These adaptive rules have been derived for the high-level control of the position as well as pressure. The derived rules look similar to the above-mentioned rules described in some patents [5,2] to update the current pulse parameters. However, the rules to update the reference trajectory for the position or pressure are simpler than the existing rules to update the current parameters because they should only compensate for the slow systems variations. Furthermore, the derived rules are also more straightforward since the physical relation between the quality indices and the piston position/pressure is simpler than between these indices and the current to the valve, where the valve dynamics play an important role. The different controllers are tested on a dedicated test bench, where an electromotor (30 kW) drives a flywheel (1 kg m2) via a torque convertor and two mechanical transmissions (Fig. 3). The controllers developed in this project are tested on one of the five clutches of the first transmission, which is equipped with different sensors, measuring the speed of the ingoing and outgoing shaft, the position of the piston and the pressure of the oil to the clutch. The second transmission is used to vary the actual load observed by the first transmission and to apply an adjustable braking torque.

2. Control of piston position 2.1. Control strategy The motion of the piston in a wet clutch strongly determines the quality of the engagement of this clutch. In the first phase of the research, it was therefore decided to develop a controller, which regulates the position of this piston. In [9], a clutch position control system is implemented on the standard control unit of an automated manual transmission. This system significantly improves the starting off performance of the vehicle compared to conventional control approaches. To measure the piston position in the considered transmission in this project, a standard clutch was equipped with an inductive proximity sensor, which measures the displacement of a ring connected to the piston. Fig. 4 shows the installation of the ring on the controlled wet clutch. Due to the high level of the induced vibrations on a rotating set-up, the

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Fig. 4. The installation of a ring on a clutch to measure the piston’s position. The outgoing shaft is removed in order to show the different clutch components.

Fig. 5. The low-level part of the developed control system: a closed position loop with an additional ILC controller.

piston’s position can only be measured accurately on a non-rotating set-up. Consequently, the position-based control system could only be tested in this situation. The main challenge in the actuation of wet clutches is the control of the piston’s motion at the beginning of the slip phase when a hard non-linear transition occurs between two reasonably linear dynamic ranges. Initially, when the clutch is still completely open, the piston is not in contact with the friction plates and passes through a first linear working range. In this filling phase the dynamic behavior of the electro-hydraulic valve [10,11] plays an important role. When the piston comes into contact with the friction plates, the slip phase starts, which is characterized by a completely different linear dynamic behavior. A detailed model of this changing dynamic behavior of a wet clutch is presented by Morselli et al. [12]. Based on the piecewise linear character of the clutch, the control is split into two parts. In a first part, the objective is to bring the piston as close as possible to the friction plates. Hence, a position reference trajectory with an end position close to the friction plates and a low end velocity is defined that has to be learned by the low-level ILC controller. The exact determination of this reference trajectory is handled by a high-level control algorithm, which is explained in detail in Section 2.6. In a second phase, the final engagement of the clutch is realized using an additional feedforward action (i.e. a growing current signal in feedforward). Good tracking of the reference leads to a small feedforward action and consequently to a smooth and fast clutch engagement. This demonstrates that the engagement quality will be defined by the performance of the developed ILC, which will be discussed in detail in the remainder of this section. Iterative learning control (ILC) is a well-known technique to increase the tracking accuracy of a system repeating a given operation [6,7,13,14]. The idea is to adjust the control signal by using experience from one trial in an appropriate way such that the performance in the next trial is improved. In doing so, a high control performance can be achieved with a low transient tracking error despite large model uncertainty. These features make ILC a suitable control strategy for the low-level filling phase control of wet clutches, which have to be engaged regularly in the same way. Due to the repetitive character of the different engagements, a prescribed position reference in the filling phase can be tracked accurately by an ILC controller in spite of the changing environmental conditions such as a varying temperature. As shown in Fig. 5, the ILC scheme, used for the reference tracking in the filling phase, is added to a closed position loop. This way, the current signal at time interval k to the controlled plant P, i.e. the system between the valve current and the piston’s position, is the sum of a signal uFB(k) from the feedback controller C and a signal uILC(k) from the ILC controller. The ILC signal is calculated in

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between two successive engagements using the linear filters Q and L, according to the following update formula: uILC,i þ 1 ðkÞ ¼ Q ðDÞuILC,i ðkÞ þLðDÞðCðDÞei ðkÞÞ,

ð1Þ

where D is the delay operator, uILC,i(k) is the ILC signal at time interval k of the ith engagement and ei(k) is the difference between the reference r(k) and the measured position yi(k) at time interval k of the ith engagement. The relation between the error e at successive engagements is given by the following equation: ei þ 1 ðkÞ ¼ ðQ ðDÞLðDÞTðDÞÞei ðkÞ,

ð2Þ

with T ¼ PC=ð1 þ PCÞ the complementary sensitivity of the feedback controller. This leads to the following condition for monotonic convergence of an ILC controller in the frequency domain [6,7]: jQ ðoÞLðoÞTðoÞj o 1:

ð3Þ

The remaining error after convergence e1 can be written as e1 ðoÞ ¼

1Q ðoÞ SðoÞr, 1Q ðoÞ þ LðoÞTðoÞ

ð4Þ

with SðoÞ ¼ 1=ð1þ PðoÞCðoÞÞ the sensitivity of the feedback controller. This formula clearly shows that the final error reduction is caused on the one hand by the feedback controller ðSðoÞÞ and on the other hand by the ILC controller ðð1Q ðoÞÞ=ð1Q ðoÞ þ LðoÞTðoÞÞÞ. 2.2. System identification Although ILC can deal with large model uncertainties, a plant model is necessary for the design of converging ILC filters Q and L, as indicated by Eq. (3). Therefore, an identification is performed of the system between the current to the valve and the position of the piston, while the piston is located in the range between the completely open clutch position and the friction plates. The resulting frequency response function is shown in Fig. 6(a). The identified frequency response function shows a second-order low-pass characteristic with a break frequency of 0.3 Hz and an additional pair of zeros (around 8 Hz) and pair of poles (around 10 Hz). The exact frequencies of these zeros and poles are temperature-dependent. Moreover, the plant is also characterized by a small time-delay of approximately 8 ms. Due to the nonlinear relation between the oil flow and plunger displacement in the valve on the one hand and due to the friction between the piston and the drum on the other hand, the controlled system behaves nonlinearly. The evaluation of the level of nonlinearities is based on an odd-odd multisine excitation [15]. Odd and even nonlinearities cause higher harmonics at a combination of an odd and even number of excited frequencies respectively. Therefore, the response at the detection lines (the unexcited frequency lines) is a measure for the odd and even nonlinear distortions. Fig. 6(b), which shows the spectrum of the piston position during a multisine excitation, gives an indication of the level of the odd and even nonlinearities. The noise level is also indicated on this figure. It is clear that the level of nonlinearities is significantly higher

Plant current−position

Nonlinearity current−position 0

20 −10

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40

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Fig. 6. Identification of the plant model between the current to the valve and the position of the piston: (a) the identified frequency response function and (b) the frequency spectrum of the piston position when the electro-hydraulic valve is excited with an odd–odd multisine excitation, showing the linear and odd nonlinear contributions (bold line), even nonlinear contributions (grey line), odd nonlinear contributions (dashed line) and the noise-spectrum (thin line).

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than the noise-level and only in the lower frequency range (below 7 Hz) considerably lower than the level of the linear contributions.

2.3. Controller design For the control of the filling phase, the objective is to apply an ILC controller to improve the performance of the feedback controlled system (Fig. 5). Therefore, first, a feedback controller is designed and tested. This feedback controller consists of a PID-compensator with an additional lead compensator to increase the bandwidth of the feedback system. Based on Fig. 6(a), and if scaled properly, a bandwidth of at least 4 Hz should be achievable with this controller as the amplitude plot is crossing at that point the 0 dB line. However, in the practical tests the gain of the controller has to be reduced significantly compared to the theoretical situation to guarantee stability over the whole working range of the considered transmission (at low and high temperatures) due to the nonlinear character of the controlled plant. As a consequence, a bandwidth of only 3 Hz (Fig. 7(b)) can be realized with the feedback controller on the practical set-up and the response of the controlled system is too slow to realize the filling of the clutch in the desired time interval of less than 0.5 s (as will be illustrated below). This limited performance demonstrates the need for an ILC controller. In Fig. 7(a) the complementary sensitivity of the feedback controlled system is shown, which is important in the ILC design. Different strategies can be used to design the ILC filters Q and L: strategies based on plant inversion, optimization-based strategies,y[6,14]. In this paper, a frequency-domain approach [16–18] is applied to develop a relatively simple, monotonically converging ILC algorithm, which reduces the final tracking error e1 after a high number of clutch engagements as much as possible. Eqs. (3) and (4) are the crucial formulas and form the basis for this frequency-domain approach. To obtain a zero error after convergence, it is clear from Eq. (4) that Q should be chosen equal to 1. For Q= 1, the criterion for monotonic convergence, as presented in Eq. (3), can only be fulfilled if the phase of LT stays between  901 and 901. Therefore, in the frequency range, where the phase of T remains between  901 and 901, L is designed as a proportional gain. In the higher frequency range above 4 Hz, where the phase of T exceeds the phase bounds, the amplitude of L is decreased by the introduction of an eighth-order noncausal zero-phase low-pass filter with a break frequency of 4 Hz. To fulfill the convergence criterion at these frequencies, where the phase of LT lies outside the band between 901 and 901, Q cannot be chosen equal to 1 but should be slightly reduced (Q= 0.9). As a consequence, a certain remaining error cannot be eliminated. The achievable reduction with the selected ILC filters is shown in Fig. 7(b): it is clear that the performance of the feedback controller can be strongly enhanced in the lower frequency range below 5 Hz by the addition of the ILC controller. Although it is possible to further increase this bandwidth of the ILC algorithm by compensating the dynamics of T in the learning filter L, the implementation of this learning filter L as a simple proportional gain combined with a zero-phase low-pass filter already leads to satisfactory results as will be illustrated below. Fig. 7(c) proves that the criterion for monotonic convergence is fulfilled for the selected filters.

2.4. Reference position trajectory As mentioned above, the goal of the ILC controller is to quickly bring the piston from the completely open position to a position close to the friction plates. Moreover, this end position should be attained with a low velocity. A cosine trajectory, which describes this motion without discontinuities of the velocity at the beginning and the end, is used as the reference input for the ILC algorithm. This reference trajectory is plotted in Fig. 8(a) (grey line). Due to the time delay in the controlled system and the noncausal filtering of the learning filter L, the reference trajectory only starts to rise 0.05 s after

−30 100 101 Frequency [Hz]

200 100 0 −100 −200 −1 10

100 101 Frequency [Hz]

1 0 Q − L * System

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Sensitivity 10

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0.6 0.4 0.2

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100 101 Frequency [Hz]

0 0

2

4

6

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10 12 14 16 18 20

Frequency [Hz]

Fig. 7. The design of the feedback and ILC controller of the piston position: the complementary sensitivity of the feedback controller, (b) the achievable reduction (error with control/error without control) of the feedback controller (solid line) and the combined feedback/ILC controller (bold line) and (c) the monotonic convergence criterion with jQ LTj (solid line) and the convergence limit 1 (bold line).

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Non−adaptive ILC of piston position

Non−adaptive ILC of piston position

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Non−adaptive ILC of piston position 3

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10 15 20 Nr. of closing

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Fig. 8. Validation of the non-adaptive position ILC controller: (a) the reference trajectory (grey line) and the piston position after 1 (dashed thin line), after 2 (dashed thick line), after 5 (solid thin line) and after 10 (solid thick line) engagements, (b) the current to the valve after 1 (dashed thin line), after 2 (dashed thick line), after 5 (solid thin line) and after 10 (solid thick line) engagements and (c) the rms-value of the error between the piston position and the reference signal as a function of the number of past engagements.

the command for a new engagement is given. This way, the ILC algorithm can anticipate for the increase of the reference trajectory. 2.5. Results Because the piston’s position cannot be measured precisely on a rotating set-up, the developed controllers are only validated on a non-rotating wet clutch. Fig. 8 shows the results for the ILC of the piston position: Fig. 8(a) compares the piston position and the reference trajectory at different engagements, Fig. 8(b) plots the current1 at different engagements and Fig. 8(c) shows the rms-value of the error between the piston position and the reference signal as a function of the number of past engagements. Since at the first engagement the ILC controller has no information from previous engagements, only the feedback controller is active. The response of this controller is clearly too slow to follow the desired reference trajectory (Fig. 8(a)). At the following engagements, the ILC controller observes the remaining error, updates the control signal accordingly (Fig. 8(b)) and, as a consequence, the tracking response gradually improves. After 5 engagements, the ILC control action has converged (Fig. 8(c)) and the piston follows the prescribed reference trajectory accurately. After the ILC action, a feedforward controller becomes active (at t = 0.36 s), which generates a minimal current to the valve and in this way completely opens the valve and closes the clutch. The closer the piston is located to the friction plates at the end of the ILC action, the smaller the feedforward action will be. As a consequence, the engagement will also become smoother and faster. 2.6. High-level learning of the reference position Although the tracking accuracy of the ILC algorithm still significantly improves, the engagement quality does not improve any more after the second engagement (Fig. 8(a)): the large feedforward action, which is inevitable because the end position of the ILC reference trajectory is located too far from the friction plates, mainly determines the engagement quality. For this reason and also to take into account the wear of the friction plates, the reference trajectory of the ILC system is adapted online by a high-level learning algorithm (Fig. 2). Every 5 engagements, when the output of the ILC algorithm has converged to its final value for the current reference, this high-level controller changes the end point of the reference trajectory rmax based on the one hand on the performance of the ILC algorithm at the previous engagement and on the other hand on an estimate of the position of the friction plates. First, an estimate is made of the position where the piston comes into contact with the friction plates. This position, often referred to as the kiss point, is estimated based on ,i the piston’s position at full engagement of the clutch (y full): ¼ y,i 0:3 mm: y,i kiss full

ð5Þ

,i ,i Since y full only changes slowly over time due to wear, ykiss will remain almost equal at successive clutch engagements  ,i  ðykiss  ykiss Þ. After this estimation of ykiss, the maximum achieved position of the piston in the ILC phase at the previous i þ 1:i þ 5 is then trial, denoted as yimax, is determined. The end position of the reference for the following 5 engagements rmax i  updated proportionally based on the deviation of ykiss and ymax according to the following formula:

i þ 1:i þ 5 i4:i rmax ¼ rmax þKðykiss yimax Þ,

1

It should be mentioned that low currents to the valve lead to high oil pressures to the clutch and vice versa.

ð6Þ

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Fig. 9. Principle of the high-level learning algorithm to update the position reference trajectory for the low-level ILC algorithm.

Adaptive ILC of piston position

Adaptive ILC of piston position

2.5 2

Pressure [bar]

Position of piston [mm]

3

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20 18 16 14 12 10 8 6 4 2 0

0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 time (sec)

Fig. 10. Validation of the adaptive position ILC controller: (a) the reference trajectory at engagement 1–5 (black thick line), at engagement 6–10 (dark grey thick line), at engagement 11–15 (light grey thick line), and the piston position after 1 (black solid thin line), after 5 (black dashed thick line), after 10 (dark grey dashed thick line) and after 15 (light grey dashed thick line) engagements and (b) the pressure in the line to the clutch after 15 engagements.

with K the selected proportional gain of the learning algorithm. Fig. 9 illustrates the theoretical working principle of this high-level learning controller. The high level controller places the end point of the reference trajectory closer to the friction plates, when the tracking accuracy of the ILC controller improves. Furthermore, when the friction plates are worn down, the reference end position will be increased. The results achieved with the two-level control system are shown in Fig. 10(a). It is clear that after 5 and 10 engagements the high level controller places the end point of the reference trajectory closer to the friction plates. This leads to a decrease of the feedforward action and consequently to an improvement of the clutch engagement quality. In spite of the small distance between the reference end position and the friction plates there is no undesired contact between the piston and the friction plates (overfilling) during the ILC action due to the good tracking accuracy of the ILC algorithm. Moreover, since the end position of the piston lies close to the friction plates, the piston comes rapidly into contact with the friction plates after the ILC phase which guarantees that there is no underfilling of the clutch. Fig. 10(b) shows the pressure of the oil in the line between the valve and the clutch after convergence of the high-level learning algorithm (at the 15th engagement). This pressure profile leads to a quick and smooth engagement of the wet clutch. In the next section, where a control system will be developed that regulates the oil pressure instead of the piston position, the shape of the reference pressure signal will be determined based on this measured pressure profile.

3. Control of oil pressure 3.1. Control strategy Since it is too expensive to equip all industrial wet clutches with a sensor to detect the piston’s displacement, in a second part of the project, a pressure transducer is used as the error sensor in a similar ILC control configuration as presented in the previous section. The perfect place for a pressure sensor would be in the clutch, where it can measure the pressure immediately behind the piston and detect the centrifugal forces on the oil due to the shaft rotation. However, it is too expensive in industrial applications to transmit the signal from the rotating sensor to the non-rotating control board. Therefore, the pressure sensor is placed in the valve block and measures the pressure in the line to the clutch.

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A similar strategy as for the control of the piston position (Fig. 2) is used for the control of the oil pressure to the clutch in the filling phase. First, an ILC controller is placed around a feedback loop to improve the tracking of a prescribed reference pressure profile. Afterwards, a high-level controller learns the appropriate reference pressure based on the quality of the previous engagements of the clutch. After the filling phase, a feedforward current is sent to the valve for the effective engagement of the clutch. 3.2. Identification First of all, an identification is performed of the system between the current to the valve and the generated oil pressure to the clutch, while the piston is located in the range between the completely open clutch position and the friction plates. The resulting frequency response function is shown in Fig. 11(a) (thick line). The identified frequency response function clearly shows a first-order low-pass characteristic with a break frequency of 0.3 Hz and an additional time-delay of approximately 8 ms. The level of the nonlinearities was also checked for this system with an odd-odd multisine excitation. Fig. 11(b), which shows the spectrum of the oil pressure during a multisine excitation, gives an indication of the level of the odd and even nonlinearities and the noise level. It is clear that for this system the level of nonlinearities is significantly higher than the noiselevel and is comparable to the level of non-linearities in the system between current and piston position. Fig. 11(a) also illustrates the different dynamic behavior in the filling phase and the slipping phase. The bandwidth of the controlled system between the current to the valve and the pressure to the clutch is much higher in the slipping phase than in the filling phase. Since the control over a hard nonlinear transition between two linear working ranges is very complicated, as stated above, the control action is split into two parts: the pressure controller is only applied in the filling phase, while the final engagement is realized by a feedforward control action. 3.3. Controller design Based on the identified model, first a feedback controller and afterwards an ILC controller are designed. The feedback controller is a PID-compensator. Due to the nonlinear character of the controlled plant the gain of the controller is restricted, compared to the theoretically possible value based on the linear frequency response model. This limited gain is necessary to guarantee stability of the feedback controller over the whole working range of the considered transmission, but involves on the other hand also a slower system response. The resulting sensitivity of the practical controller is plotted in Fig. 12(b), where it is clear that a bandwidth of less than 1 Hz can be realized with the feedback controller on the practical set-up. Since this developed pressure feedback controller is too slow to realize the filling of the clutch in the desired time interval (as will be illustrated below), an ILC controller is also necessary in this control configuration to attain the required performance. A similar frequency-domain ILC design approach is used, which was also applied for the design of the position controller in the previous section. Fig. 12(a) plots the complementary sensitivity of the feedback system, which will be used in the ILC design: due to the very low amplitude ð o1 even at low frequencies) of the loop gain of the applied feedback controller and the

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Fig. 11. Identification of the plant model between the current to the valve and the oil pressure to the clutch: (a) the identified frequency response function in the filling phase (thick line) and in the slipping phase (thin line) and (b) the frequency spectrum of the oil pressure in the filling phase when the electro-hydraulic valve is excited with an odd–odd multisine excitation, showing the linear and odd nonlinear contributions (thick black line), even nonlinear contributions (grey line), odd nonlinear contributions (dashed black line) and the noise-spectrum (thin black line).

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G. Pinte et al. / Mechanical Systems and Signal Processing 24 (2010) 1924–1937

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Fig. 12. The design of the feedback and ILC controller of the oil pressure: (a) the complementary sensitivity of the feedback controller, (b) the achievable reduction (error with control/error without control) of the feedback controller (solid line) and of the combined feedback/ILC controller (bold line) and (c) the monotonic convergence criterion with jQ LTj (solid line) and the convergence limit 1 (bold line).

8 7

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Fig. 13. The reference pressure profile (thick line) fitted through the measured pressure after convergence of the position ILC algorithm (thin line).

presence of an integrator in this controller, the complementary sensitivity exhibits an integrating behavior at low frequencies. As mentioned in the section on position control, the phase of LT should stay between 901 and 901. Since the phase of T remains between  901 and 901 up to approximately 4 Hz, L is designed as a proportional gain in this frequency range. In the higher frequency range above 4 Hz, where the phase of T exceeds the phase bounds, the amplitude of L is decreased by the introduction of an eighth-order noncausal zero-phase low-pass filter with a break frequency of 4 Hz. Q is chosen equal to 0.9 in order to fulfill the convergence criterion (Fig. 12(c)). The achievable reduction with the selected ILC filters is shown in Fig. 12(b): it is clear that due to the introduction of the ILC controller the bandwidth of the control system can be increased up to 4 Hz. The value of jQ LTj, which is shown in Fig. 12(c), also gives an indication of the convergence rate at each frequency: the lower the value of jQ LTj at a certain frequency, the faster the convergence rate at this frequency [6,7]. Since jQ LTj is considerably higher for the pressure controller than for the position controller (Fig. 12(c)), the convergence rate will be significantly slower in this case. An introduction of a plant model in the L-filter could solve this issue and would also result in a higher bandwidth of the ILC controller. However, to limit the controller’s complexity, the learning filter is implemented in the following experiments as a proportional gain combined with a zero-phase low-pass filter.

3.4. Reference pressure profile The shape of a suitable reference profile for the pressure controller is determined based on the measured pressure in the case of position control of the piston. Since after convergence of the position ILC algorithm the generated oil pressure leads to a quick and smooth clutch engagement, a curve is fitted through this measured pressure and is used as the reference input of the ILC controller (Fig. 13). At the start of the reference profile, a small pressure level should already

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be generated to guarantee that the line to the clutch is completely filled with oil. An empty line would introduce an additional delay in the controlled system and lead to a slower response. From this initial pressure level, the generated pressure should first quickly rise to a maximum level (to accelerate the piston) and afterwards decrease to a constant level (to decelerate and stabilize the piston). The peak pressure of the reference profile mainly determines the rise time of the piston from the completely open position in the clutch to a position close to the friction plates. A low peak pressure results in a long rise time and consequently an underfilling of the clutch, while a high peak pressure leads to an overshoot of the final position and consequently an overfilling of the clutch. A trade-off has to be made between both effects in order to obtain a sufficiently fast motion of the piston to its end position without a large overshoot. The end pressure of the reference profile determines the end position of the piston, which should be chosen as close as possible to the friction plates.

3.5. Results The developed pressure control system is validated on the rotating test bench, shown in Fig. 3. The objective is to realize a comfortable neutral to drive shift of the transmission, characterized by a quick and smooth engagement of the controlled wet clutch. In this paragraph only the low-level ILC algorithm for the filling phase, which is active during the first 0.4 s of the engagement, is evaluated. In the next paragraph, a two-level algorithm is tested, where a high-level controller adapts the pressure reference profile for the ILC algorithm. Fig. 14 plots the results for the low-level ILC algorithm. Fig. 14(a) compares the generated oil pressure in the line to the clutch with the reference pressure profile at different engagements. Initially, at the first engagement, only the feedback controller is active and the regulated pressure cannot follow the prescribed reference trajectory due to its low bandwidth. At the following engagements the regulated pressure moves gradually towards the reference signal. This is confirmed in Fig. 14(c), which shows the rms-value of the error between the generated pressure and the reference pressure during the first 0.4 s of the engagement as a function of the number of past engagements. Due to the learning behavior of the ILC algorithm, this error decreases during the first 10 engagements. Afterwards, the ILC algorithm has converged and no further reduction of the ILC is realized. Fig. 14(b), which plots the current at different engagements, shows that the current output to the valve is iteratively updated. From this figure, it is also clear that after the filling phase ðt 40:4 sÞ a feedforward current is sent to the valve. First, a steep ramp current is generated to assure a quick engagement of the clutch. Afterwards, when the clutch starts to engage, which is detected by observing a decrease of input speed and an increase of output speed, an almost constant current level is generated for the further engagement. Since the tests are carried out on a rotating test bench, additional sensor signals are available to assess the quality of the engagements: Fig. 15(a) shows the transmitted torque, Fig. 15(b) shows the input speed of the clutch and Fig. 15(c) shows the output speed of the clutch at successive engagements. It is clear that due to the ILC action the initial torque peaks, resulting from brutal engagements due to an underfilling of the clutch, can be gradually decreased (Fig. 15(a)). Another advantage of the ILC controller is that the torque vibrations, which should absolutely be avoided to obtain a smooth engagement, disappear after a few trials of the ILC algorithm. Moreover, the clutch engages faster after the end of the filling phase due to the introduction of the ILC controller (Fig. 15(c)): while in the case of feedback control (engagement 1) the output shaft starts to rotate only 0.7 s after the command is given for an engagement, this shaft rotates already 0.5 s after this command in the case of ILC control (engagement 15). This shows that the proposed ILC strategy for the filling phase can significantly enhance the engagement quality of a wet clutch.

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Fig. 14. Validation of the non-adaptive pressure ILC controller: (a) the reference pressure profile (thick black line) and the oil pressure in the line after 1 (thin solid black line), after 2 (thin dashed black line), after 5 (thick solid grey line) and after 15 (thick dashed grey line) engagements, (b) the current to the valve after 1 (thin solid black line), after 2 (thin dashed black line), after 5 (thick solid grey line) and after 15 (thick dashed grey line) engagements and (c) the rms-value of the error between the oil pressure in the line and the reference pressure profile as a function of the number of past engagements.

G. Pinte et al. / Mechanical Systems and Signal Processing 24 (2010) 1924–1937

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Fig. 15. Monitoring of the engagement quality with the non-adaptive pressure ILC controller: (a) the transmitted torque after 1 (thin solid black line), after 2 (thin dashed black line), after 5 (thick dark grey line) and after 15 (thick light grey line) engagements, (b) the rotational speed of the input shaft after 1 (thin solid black line), after 2 (thin dashed black line), after 5 (thick dark grey line) and after 15 (thick light grey line) engagements and (c) the rotational speed of the output shaft after 1 (thin solid black line), after 2 (thin dashed black line), after 5 (thick solid grey line) and after 15 (thick light grey line) engagements.

3.6. High-level learning of the reference pressure Up till now, the reference profile was chosen based on the position control of the clutch. In real applications, this reference profile will have to be defined for each type of clutch, which is a time-consuming procedure. Moreover, the appropriate reference profile will change during the lifetime of the clutch due to e.g. wear of the friction plates. Therefore, similarly to the position controller, a high-level controller is added to the basic ILC scheme, which adapts the reference profile of the pressure ILC algorithm (Fig. 2). Because of the slower convergence rate of the pressure ILC algorithm, the high level controller in this case only updates the reference profile every 8 engagements. Since the position of the friction plates cannot be measured on an industrial transmission, the adaptation of the reference profile is now performed according to a two-step learning algorithm based on the rotational velocity of the outgoing shaft, which gives a good indication of the engagement quality. In the first step, the peak reference pressure is determined. Afterwards, in the second step, the appropriate end pressure is learned while the peak pressure remains constant. The learning process proceeds according to the following rules, which are illustrated in Fig. 16: 1. As long as the output shaft does not start to rotate during the filling phase, the peak pressure of the reference profile is increased with 0.5 bar i þ 1:i þ 8 ¼ pi7:i Tstart 4 Tfill ) pmax max þ0:75 bar,

ð7Þ

with Tstart and Tfill the time between the engagement command and, respectively, the start of rotation of the output shaft and the end of the ILC algorithm, and pimax the peak pressure of the reference at the ith engagement. If the output shaft starts to rotate during the filling phase, the clutch is overfilled and consequently the peak pressure of the reference profile is slightly decreased: i þ 1:i þ 8 ¼ pi7:i Tstart o Tfill ) pmax max 0:75 bar:

ð8Þ

After this decrease of the peak pressure, the tracking of the reference will lead to a short rise time of the piston towards the friction plates without an overfilling of the clutch. Therefore, the reference peak pressure is kept constant afterwards and the learning algorithm proceeds to the second step. 2. If the output shaft starts to rotate too long/short after the end of the filling phase, the end position of the piston in the filling phase is too far/close from/to friction plates. Therefore, the end pressure of the reference profile is increased

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Fig. 16. Principle of the high-level learning algorithm to update the pressure reference trajectory for the low-level ILC algorithm.

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Fig. 17. Validation of the adaptive pressure ILC controller: (a) the reference pressure profile (thick black line) for engagement 1–8 (solid black line), 9–16 (dashed black line), 17–24 and 33–40 (solid dark grey line), 25–32 (dashed dark grey line) and 41–48 (dashed light grey line) and (b) the transmitted torque at successive engagements (the black vertical lines indicate the moments when the reference pressure profile is adapted).

proportionally to the difference between the actual and the desired start of rotation of the output shaft: i þ 1:i þ 8  ¼ pi7:i pend end þ KðTstart Tstart Þ,

ð9Þ

with T start the desired start time of the output rotation. This way, the end pressure is always adapted to the actual environmental conditions. This procedure can be repeated regularly on industrial transmissions after a certain number of working hours, to redefine the peak reference pressure. The results of this adaptive algorithm are plotted in Fig. 17. Fig. 17(a) shows the different reference profiles which are used. Initially (engagement 1–32) the reference peak pressure is too low and has to be increased gradually in order to avoid an underfilling of the clutch. At a certain moment however (engagement 33), the peak pressure becomes too high, leading to an overfilling of the clutch. At that moment, the reference peak pressure is reduced and kept constant afterwards. Finally, the reference end pressure is adapted in order to decrease the response time of the output shaft after the end of the filling phase (engagement 34–48). Fig. 17(b) shows how the torque peaks are decreased at the successive engagements. Initially these peaks decrease due to the ILC operation, similar to the previous section. Afterwards, the torque peaks decrease further due to the adaptation of the reference signal, which demonstrates the effectiveness of the adaptive pressure ILC algorithm. 4. Conclusion This paper demonstrates the effectiveness of ILC algorithms to automatically find the appropriate control action for the filling phase of wet clutches. This way, an ILC-controller can be a good alternative for the time-consuming (re)calibration procedures which are performed nowadays in off-road vehicles to determine the optimal control action. A position-based

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as well as a more industrially relevant pressure-based control system have been presented. Both control systems consist of a combination of a feedback control algorithm and an ILC algorithm. The ILC significantly enhances the performance of the feedback system, by using the knowledge of the quality of previous engagements to calculate the control signal for the next engagement. Finally, also an adaptive ILC algorithm is presented, which automatically defines the most suitable reference signal for the ILC algorithm, leading to a significant improvement of the engagement quality. Future work consists of a study of the other phases in the engagement of a clutch after the filling phase. Up till now, these phases are controlled by the generation of a feedforward control action. The objective is to explore the possibilities of model-based (e.g. ILC) as well as non-model-based (e.g. Reinforcement Learning) learning techniques for control after the filling phase. References [1] Z. Sun, K. Hebbale, Challenges and opportunities in automotive transmission control, in: Proceedings of the 2005 American Control Conference, Portland, OR, USA, 2005 June 8–10, Portland, 2005, pp. 3284–3289. [2] K.V. Hebbale, C.-K. Kao, D.E. McCulloch, Adaptive electronic control of power-on upshifting in an automatic transmission, US Patent No. 5,282,401, 1994. [3] M. Henning, Method for determining the filling pressure for a clutch, US Patent No. 20080076631, 2008. [4] J.R. Hillman, D.P. Simon, Method for determining the fill time of a transmission clutch, US Patent No. 6,216,074, 2001. [5] T.R. Berger, T.A. Yu, S.B. Pollack, Neutral to drive shift time control, US Patent No. 5,307,727, 1994. [6] D.A. Bristow, M. Tharayil, A.G. Alleyne, A survey of iterative learning control, IEEE Control Systems Magazine 26 (3) (1995) 96–114. [7] D.A. Bristow, M. Tharayil, A.G. Alleyne, Iterative learning control and repetitive control for engineering practice, International Journal of Control 73 (2000) 930–954. [8] B. Paijmans, Interpolating gain-scheduling control for mechatronic systems with parameter-dependent dynamics, Ph.D. Thesis, KU Leuven, Department of Mechanical Engineering, Division of Production Engineering, Machine Design and Automation, 2007. [9] J. Horn, J. Bamberger, P. Michau, S. Pindl, Flatness-based clutch control for automated manual transmissions, Control Engineering Practice 11 (2003) 1353–1359. [10] G. Lucente, M. Montanari, C. Rossi, Modelling of an automated manual transmission system, Mechatronics 17 (2007) 73–91. [11] M. Montanari, F. Ronchi, C. Rossi, A. Tilli, A. Tonielli, Control and performance evaluation of a clutch servo system with hydraulic actuation, Control Engineering Practice 12 (2004) 1369–1379. [12] R. Morselli, R. Zanasi, R. Cirsone, E. Sereni, E. Bedogni, E. Sedoni, Dynamic modeling and control of electro-hydraulic wet clutches, in: Proceedings of the IEEE Conference on Intelligent Transportation Systems, vol. 1, 2003, pp. 660–665. [13] K. Moore, Iterative learning control—an expository overview, Applied and Computational Control, Signals, and Circuits 1 (1998) 151–213. [14] M. Norrlof, S. Gunnarsson, Experimental comparison of some classical iterative learning control algorithms, IEEE Transactions on Robotics and Automation 18 (4) (2002) 636–641. [15] R. Pintelon, J. Schoukens, System Identification: A Frequency Domain Approach, IEEE Press, New York, 2001. [16] G. Pinte, Active control of repetitive impact noise, Ph.D. Thesis, KU Leuven, Department of Mechanical Engineering, Division of Production Engineering, Machine Design and Automation, 2007. [17] G. Pinte, B. Stallaert, P. Sas, W. Desmet, J. Swevers, A novel design strategy for iterative learning and repetitive controllers of systems with a high modal density: theoretical background, Mechanical Systems and Signal Processing 24 (2) (2010) 432–443. [18] B. Stallaert, G. Pinte, P. Sas, W. Desmet, J. Swevers, A novel design strategy for iterative learning and repetitive controllers of systems with a high modal density: application to active noise control, Mechanical Systems and Signal Processing 24 (2) (2010) 444–454.