MODEL REFERENCED ADAPTIVE CONTROL TO COMPENSATE SLIP-STICK TRANSITION DURING CLUTCH ENGAGEMENT

1. INTRODUCTION
Clutches are key components in various conventional or newly developed high-efficiency transmissions such as dual clutch transmissions (Niu et al., 2004; Goetz et al., 2005) and electric variable transmissions of hybrid electric vehicles (Liao et al., 2005; Ryu et al., 2009). Because of the stick and slip motion between the friction couplers, the process of clutch engagement has three phases, i.e., open, slipping, and sticking. Transitions between different phases introduce nonlinearity and discontinuity to the vehicle driveline dynamics. Literature (Bin 2007) has shown that vehicle jerk during slip-stick transition is more intensive than in one engagement phase. Optimal control (Zhang et al., 2002; Sun and Zhang, 2004) and constant speed control (Lei et al., 2000; Sun and Qin, 2003) have been investigated to obtain a smooth and low wear engagement. However, this research did not address the slip-stick transition, and the clutch engagement is still intractable. Basically, the frictional torque in the slipping phase is proportional to the normal pressure on the clutch plates, whereas the friction torque in the locked phase can assume any value up to an upper limit determined by the clutch pressure (Duan and Singh, 2006). In other words, the frictional torque in the slipping phase is controllable by pressure actuators, while that in the sticking phase is not. Therefore, the frictional torque during slip-stick transition may change sharply and lead to intensive vehicle jerk. *Corresponding author. e-mail: li.h.chen@
MODEL REFERENCED ADAPTIVE CONTROL TO COMPENSATE SLIP-STICK TRANSITION DURING CLUTCH ENGAGEMENT
L. CHEN1)*, G. XI2) and C. L. YIN1)
1)
National Key Lab of Automotive Electronics and Control, Shanghai Jiao Tong University, Shanghai 200240, China 2) United Automotive Electronics System Co., Rongqiao Road 555, Shanghai 201206, China (Received 20 July 2009; Revised 27 April 2011)
913
914
L. CHEN, G. XI and C. L. YIN
the clutch as follows Mc = abs(µ · pc · A · R)·Sign(ωe−ωc) (2)
Figure 1. Dynamic model for clutch engagement.
intense jerk. The designed MRAC is applied to the clutch of a powertrain system on a bus. The startup case is typically a big challenge for clutch engagement (Lei et al., 2000). This paper provides comparisons between MRAC and the conventional control algorithm with both simulation and experiment results under the startup case.
ABSTRACT−Clutches are widely used in various vehicle powertrains. The engagement process of a friction clutch has three phases, i.e., open, slipping, and sticking. Transitions between different phases introduce a discontinuity to the powertrain dynamics, which has been neglected in previous research. A model referenced adaptive controller (MRAC), based on Popov hyper-stability criterion, is designed to compensate the discontinuity. MRAC adjusts the frictional torque along with the errors of the state variables compared with those of a referenced model. The designed MRAC is applied to a clutch in a bus. Simulation and experimental results under fast and slow startup cases show that MRAC can simultaneously reduce vehicle jerk and frictional dissipation when compared with the conventional controller. KEY WORDS : Popov hyper-stability, Model reference, Adaptive control, Clutch engagement, Slip-stick transition
International Journal of Automotive Technology, Vol. 12, No. 6, pp. 913−920 (2011) DOI 10.1007/s1211 KSAE 1229−9138/2011/061−14
To reduce the jerk, there must be control of the frictional torque in the slipping phase tracking that approaches the sticking phase. However, the frictional torque in the sticking phase is time-varying along with the powertrain dynamics and uncertain external torques. Therefore, it is useless to apply a conventional control algorithm, which demands a predefined torque target (Dong and Wu, 2008) to smooth the slip-stick transition. In this paper, a model referenced adaptive control (MRAC) is proposed to deal with the varying torque tracking problem. MRAC is a well-established method that has demonstrated its capabilities in many publications (Shyu et al., 2008; Crnosija et al., 2002; Ban and Crnosija, 2003; Yacoubi et al., 2006). In MRAC systems, the desired performance of the plant is expressed via a reference model, which gives the desired response to a command signal. Hence, a considerable flexibility is granted to the designer to alter the goals by modifying the reference model. Thus, it is expected that MRAC can overcome the shortcomings of other control algorithms with a predefined constant goal. Under the architecture of MRAC, a real-time referenced model, which is considered as the target of the dynamics in the slipping phase, is built to describe the desired sticking dynamics. The stability of MRAC is guaranteed by the Popov hyper-stability criterion (Xu, 2007). In the slipping phase, state errors with respect to the referenced model occur. The adaptive controller adjusts the frictional torque based on the state errors. When the state errors become larger, the frictional torque is increased, and vice versa, until the errors gradually approach zero. In this way, the slip-stick transition can be made smoothly without an