Limit cycles analysis in hybrid anti-lock braking systems

Abstract

We investigate the stability and robustness properties of Anti-lock Braking Systems based on actuators with on/off dynamics. Namely, we propose a hybrid ABS controller which gives rise to an asymptotically stable limit cycle on the wheel slip. The proposed approach allows to derive exact information on the maximum allowable uncertainty in the measured variables which guarantee the cycle stability. Moreover, a structural stability analysis is performed with respect to different road conditions and to the actuator rate limit

Vehicle state estimation for anti-lock control with nonlinear observer

“…Development of anti-lock control systems has attracted considerable attention of many researchers. Wheel slip controllers (Petersen, Johansen, Kalkkuhl, & Lüdemann, 2001;Vries, Fehn, & Rixen, 2010) and anti-lock strategies based on logic switching (Tanelli, Osorio, di Bernardo, Savaresi, & Astolfi, 2007;PasillasLépine, 2006) are the most widely used control methods in the anti-lock brake systems.…”

Towards the Exhaustive Verification of Real-Time Aspects in Controller Implementation

“…ABS controllers are indeed a safety critical application, as they have to take care of managing panic-brakes which cannot be handled by common drivers. The design of an appropriate controller for these systems has been presented in [12], where it has been shown that the closed loop system has the desired stability properties. System and Actuator Model.…”

“…System and Actuator Model. The braking dynamics have been modeled based on a quarter car model, [12]. The considered actuator is an HAB, which, according to its physical characteristics, is only capable of providing three control actions: Increase the brake pressure; Hold the brake pressure and Decrease the brake pressure.…”

“…Note that u = −k corresponds to the Decrease control action, u = 0 to the Hold control action and u = k to the Increase control action. As shown in [12], a controller which guarantees closed-loop stability of the braking system is that shown in Figure 2. By analyzing Figure 2 one can see that we employ the braking torque T b and the wheel slip λ as switching variables and that the switching conditions change according to the current discrete controller state q = {0, 1, 2, 3}.…”

On linear‐parameter‐varying (LPV) slip‐controller design for two‐wheeled vehicles

“…ABS systems have been commercially available on cars for more than 20 years [1]. In the past few years, with the introduction of the electronic stability control (ESC), electro-mechanical (EM) brakes and drive-by-wire systems, the literature on wheel-slip control for cars has seen many important contributions [2][3][4][5][6][7][8]. Notably, the goal has cannot guarantee satisfying performance; instead, linear-parameter-varying (LPV) techniques can be successfully used to automatically schedule the controller with respect to different operating conditions, in order to design a feedback control law.…”