System Modeling and Control of a Clutch Actuator System for Dual Clutch Transmissions

Transcription

1 Syste Modeling and Control of a Clutch Actuator Syste for Dual Clutch Transissions Jinsung Ki *) Seibu B. Choi ) Heerak Lee ) Jiwoo Kang ) Mandae Hur ) ) Departent of Mechanical Engineering, KAIST, 9 Daehak-ro, Yuseong-gu, Daejeon 35-7, Korea *) Valeo Pyeong Hwa, 36-7, Jangdong, Dalseo-Gu, Daegu, 74-9, Korea Abstract : In this paper, a clutch actuator syste for DCTs is developed by integrating a brushless DC otor with echanical subsystes. The syste odeling is perfored with experiental validations. However, since the developed odel is based on the linear syste, it ay include odeling uncertainties and external disturbances. To overcoe this difficulty, a cascade control structure is proposed. Therefore, the position controller is coposed of two parts. One is a proportional derivative controller in the outer-loop, and the other is a disturbance observer (DOB) based on the noinal syste odel in the inner-loop. Key words : Clutch Actuator, Position Actuator, Transission, Position Control, Modeling. Noenclature J: oent of inertia of rotor, kg /s g : viscous coefficient, θ : angular position, rad ω : angular velocity, rad/s ξ dynaic syste k: otor torque constant, N/A r: radius, u: control input, A x: linear stroke of the actuator carrier, y: syste output F: force, N K: control gain T : torque, N P: plant Q: Q-filter (low-pass filter) c: carrier Subscripts * Jinsung Ki, E-ail: jsk@kaist.ac.kr l : load : BLDC otor n : noinal odel p: pinion gear ca: ca : fork d: desired trajectory of a BLDC otor. INTRODUCTION As the progress of advanced echatronic technology, there have been servo-controlled autootive subsystes for any parts. In this context, a clutch syste within transissions is also autoated by using electronic or hydraulic actuators. In particular, dual clutch transissions (DCTs) can iprove the perforance of driver s convenience and fuel efficiency at the sae tie. Consequently, the DCT has received considerable attention in autootive industry -7). Since DCT have two power flow paths without a torque converter, control probles are quite challenging. Moreover, the use of dry-clutches akes a control ore difficult in spite of high efficiency. Since the clutch engageent torque is proportional to the stroke of

2 8 6 Test Results Experient Model 4 Motor Speed (rad/s) Tie(s) the actuator, the position control quality of the clutch servo syste deterines the overall perforance of DCTs. If there is a isatch between the coand fro the transission control unit and the actual position signal, the resulting clutch torque will be inaccurate. Thus, the position control of the clutch actuator should be as accurate as possible. Fro this background, this paper considers the clutch positioning syste for DCTs that plays the role in actuating the clutch disk by an electric otor. The dynaic syste is odeled with the experiental validation. With this odel, the control developent uses a disturbance observer-based control to eliinate the effect of unodeled dynaics. Siulation results show the effectiveness of this approach.. SYSTEM MODELING. Syste Description Overall clutch actuator syste consists of the BLDC otor and the echanical subsyste shown in Fig.. The otor torque generated by electrical energy is converted into the linear force through a rack-and-pinion gear. This force oves the carrier toward the direction in the clutch disk along with the actuator ounting frae. The linear otion of the carrier x in Fig. is controlled such c that the required clutch torque is generated. Fro this forulation, the clutch torque is considered as a variable load applied in the electrical otor. Note that the ca is equipped with the spring in order to obtain the assistance force to react to the fork load shown in Fig.. Due to the high stiffness of the diaphrag spring, such additional coponents should be required. Without the assistance echaniss, the required otor power needs to be increased significantly.. Dynaic Model Since the electrical otor is driven by a current controlled aplifier, it can be described by the following odel: & () J ω + g ω + T = k u l The load torque T l includes the clutch force F during the clutch engageent phase and the ca assistance force F. Therefore, the load torque odel is represented as ca ( ) ( ) T = r F x r F x () l p c p ca c Where, r is the rack and pinion gear radius and p x is the c linear stroke of the carrier of echanical subsystes through the rack and pinion gear,.e.g. v = rω, x& = v. c p c c

3 Cobining equations () and () yields &. (3) Jω + gω + rf = ku+ rf p p ca Note that F includes soe nonlinearities due to the ca inherent design of the ca assistance force. Since the clutch torque is affected by a diaphrag spring and daper springs built in the disk, F is also nonlinear. Although these loads are nonlinear as entioned before, they could be approxiated by a linear odel in the operating range for a controller developent. Thus, the ca assistance force and the fork load on the actuator are linearly paraeterized as Fca = kcaxc = kcarθ. (4) p F = F + k xc = F + krθ (5) p Where, F is the preload of the clutch disk, and k ca and k are the equivalent stiffness of the ca and the fork, respectively. Replacing the corresponding ters with (4) and (5) yields the following linear odel J & ω + gω + rf p + d= ku + rf. (6) p ca where, d denotes unknown disturbances including linearization error, nonlinear friction effect, and external disturbances..3 Syste Identification To validate the odel developed in the previous subsection, syste identification is perfored by experients. The input and the output are chosen as the current u and the otor speedω respectively. This proble is taken into consideration as the following optiization proble: where in J, k, g N ( ξ ) odel,k ξ. (7) eas,k N k = ξ and odel,k eas,k ξ denote outputs of the noinal odel and the actual plant, respectively. And, k is the sequence of experients, N is the total easureents. The input is chosen as a pseudo rando binary signal having sufficiently large aplitude to overcoe static friction nonlinearity and then a sinusoidal signal is applied to verify the identified result. The otor paraeters are first considered to solve this optiization proble. Therefore, the paraeters identified fro this procedure are J g and k least square ethod is applicable to deterine these unknown paraeters. The identification result is shown in Fig. 3. The identified odel could fit the noinal odel well. 3. CONTROLLER DESIGN Based upon the developed odel, a controller is designed such that the otor position follows the desired one precisely. First, siple proportional-derivative (PD) controller will be developed as a reference controller. Then, a disturbance observer (DOB) based controller will be proposed to copensate the nonlinearities. A

4 PD control DOB based control Desired Controlled Desired Controlled.5.5 Position [rad].5 Position [rad] Tie [s] Tie [s] 3. PD Controller The first controller considered is a PD type controller whose structure is given by ( θ θ ) ( ω ω ) u =Kp d Kd d (8) θ is available fro where, the position easureent the BLDC otor drive and the rotational velocity signal ω can be obtained fro the nuerical differentiation of two consecutive position easureents. 3. Disturbance Observer Based Controller The Second control ethod is based on the disturbance observer (DOB). The ain role of the DOB is to estiate unknown disturbance in the fraework of a linear syste. The estiated disturbance by the DOB can be fed back into the control loop to copensate the variation of the 8) 9) odeling uncertainties The concept is depicted in Fig. 4. The equivalent disturbance estiate can be calculated by the difference between the control input u and the inverse of the noinal plant odel Pn ( s) Then it is filtered out by a low-pass filter Q(s) over specified frequency range. The DOB perforance depends on the selection of Q(s). The bandwidth of Q(s) is related with the natural frequency of a given syste. For an ipleentation purpose, Q(s) has to be selected such that Pn ( sqs ) ( ) becoes proper. In our case, the noinal plant odel Pn ( s) is coposed of the otor paraeters as follows. k Pn ( s) = (9) Js+ g Under the assuption that the DOB works well in the inner-loop, the actual plant, which is uncertain, can be viewed as a noinal odel in (9). Therefore, the outer-loop controller is siply designed for a noinal odel without uncertainties to achieve the desired control objective. This control architecture is shown in Fig. 5 where the inner-loop controller is represented by a dash-dot box. In Fig. 5, the output y is written as PP PPn ( Q n ) y = ur + d P + P P Q P + P P Q () ( ) ( ) n n n n where, u is the output of the outer-loop controller F(s). r When the low-pass filter is set by Q(s)=, the above equation becoes y= Pu which shows that the n r disturbance d disappears It iplies that disturbance rejection is only valid in a certain frequency range. The outer-loop controller is constructed as the following for where, In (), ur = updo + u () FF ( θ θ ) ( ω ω ) u : =K K u : =F k rθ k rθ pdo po d do d FF kf p ca p u is the PD controller for the noinal plant, and pdo

5 u is the feed-forward input which is obtained fro the FF experients. 4. SIMULATION RESULTS This section show the siulation results for the evaluation of the developed controller discussed in the previous section. Fig. 6 shows the siulation result of the PD control. The PD controller does not work properly in a transient period. The transient response in Fig. 6 has soe oscillation. In clutch operations, the ultiate goal of control is to ensure a fast but sooth engageent as fast as possible. Overshoot in a clutch positioning akes the engageent operation uncofortable. But, such a behavior cannot be eliinated in spite of repeated gain tuning process. Moreover, the steady-state error does not converge to zero. This behavior is due to the preload fro the ca assistance force that is nonlinear. Fro this result, it is concluded that the PD control cannot guarantee the robustness under the presence of uncertainties. On the other hand, the DOB based approach proposed in Section 3. can overcoe this proble. Fig. 7 shows that the transient perforance is iproved significantly copared with the result of the PD control case. The steady-state error also converges to zero. The DOB as an inner-loop controller can successively eliinate odeling uncertainties and external disturbances. It can be concluded that the DOB based controller is superier than the PD controller. 4. CONCLUSION A clutch positioning control syste is developed. The BLDC otor is connected with the carrier ass through a echanical linkage. The carrier position is controlled to ensure the clutch engageent by a disturbance observer based controller. The syste odel is validated experientally. Coparable study for the proposed DOB based controller with siple PD controller is perfored by siulations. The result shows the effectiveness of the proposed DOB based control ethod. References ) M. Kulkarni, T. Shi, Y. Zhang, Shift dynaics and control of dual-clutch transissions, Mechanis and Machine Theory, Vol. 4, pp. 68 8, 7. ) B. Matthes, Dual Clutch Transissions Lessons Learned and Future Potential, SAE Tech. Report. No. 5--, 5. 3) J. C. Wheals, J. McMicking, S. Shepherd, B. Bonnet, N. Jackson and O. Hall, Proven High Efficiency Actuation and Clutch Technologies for eamt and edct, SAE Tech. Report. No , 9. 4) M. Goetz, M. C. Levesley, D. A. Crolla, Dynaic Modeling of a Twin Clutch Transission for Controller Design, Materials Science Foru, Vol , pp 53-6, 3. 5) Y. Zhang, X. Chen, X. Zhang, H. Jiang, and W. Tobler, Dynaic Modeling and Siulation of a Dual-Clutch Autoated Lay-Shaft Transission, ASME J. of Mechanical Design, Vol. 7, pp ) S. J. Park, W. S. Ryu, J. G. Song, H. S. Ki and S. H. Hwang, Developent of DCT Vehicle Perforance Siulator to Evaluate Shift Force and Torque Interruption, International Journal of Autootive Technology, Vol. 7, No., pp. 666, 6. 7) Jaeho Youn, Sangoon Lee, Hyunsoo Ki, Analysis of Shift Perforance for a Wet Type Dual Clutch Transission, 5 KSAE Annual Conference pp , 5 (in Korean). 8) T. Ueno, T. Kaneko, and Y. Hori, Robust servosyste design with two degrees of freedo and its application to novel otion control of robot anipulators, IEEE Trans. on Indus. Electrn., vol. 4, no. 5, pp , oct ) B. K. Ki and W. K. Chung, Advanced disturbance observer design for echanical positioning systes, IEEE Trans. on Indus. Electron., vol. 5, no. 6, pp. 7 6, dec. 3.