Clamping Force Control for an Electric Parking Brake System: Switched System Approach

Abstract

This paper addresses the modeling, controller design, and stability analysis of an electric parking brake system in which a screw-nut self-locking mechanism is used. The system is modeled as a state-dependent switched system according to the operating mode. A nonlinear proportional (P) clamping force controller using the measured force is proposed to enhance the performance specifications. We show the uniform stability of the state-dependent switched system with the nonlinear P controller using a common Lyapunov theorem and LaSalle's invariance principle. We derive the conditions to assure stable self-locking operation of the system. We also show the existence of the largest invariant set depending on the target braking force. This analysis offers a guideline as to how a nonlinear controller can be designed in view of the self-locking stability and control performance. Through simulation and experimental results, we confirm that the solution is locally uniformly ultimately bounded. Through the experimental results, we show that the nonlinear P controller outperforms a simple on/off controller in terms of the average and deviation of the braking force error. Furthermore, it is experimentally verified that the system is also able to function as a pseudo-antilock braking system. Index Terms-Electric parking brake (EPB), Lyapunov stability, self-locking, state-dependent switched system.

Slide Mode Control for Integrated Electric Parking Brake System

“…The proposed SMC control law is validated by simulation performed in Matlab/Simulink. Figure 6 shows the target motor angle tracking performance between the Bang-bang control [4], nonlinear Proportion control [3,7], and sliding mode control with the desired motor angle 492 rad. From Figure 6(a), it is obvious that before 0.6 sec, there is nearly no difference among these three controllers.…”

“…Based on (15) and researches in [1,[3][4][5][6][7]12], we know that the clamping force has a direct relationship with the motor angle.…”

“…Electronic parking brake (EPB) system is one kind of brake-by-wire systems, which generates the parking force by motor torque instead of the manual force. Hence, the EPB system can increase the vehicle cabin space, facilitate the parking process, and have potential function [3]. There are mainly two kinds of EPB: the first one generates the force by pulling down traditional parking cable, as seen in [3][4][5][6][7][8][9].…”

“…Hence, the EPB system can increase the vehicle cabin space, facilitate the parking process, and have potential function [3]. There are mainly two kinds of EPB: the first one generates the force by pulling down traditional parking cable, as seen in [3][4][5][6][7][8][9]. The second one is called integrated EPB (IEPB), which has the similar structure with the electromechanical brake [10][11][12] and hence it can offer numerous possibilities [13].…”

“…For EPB with traditional cables, Lee et al studied the bang-bang [4], nonlinear P controllers [3,6,7] to control the clamping force and the controller stability is also analyzed in [3,7]. The traditional EPB system models were built in [3][4][5][6][7]; however, motor friction and screw-nut system inertia were neglected. Actually, during the motor idle stage, the motor friction and the nut inertia have direct effects on the modeling precision.…”