The hysteresis in mechanical subsystems is a well-known effect. It causes a delay of system reaction and reduces the control accuracy. For brake system, the static hysteresis is usually considered in loading-unloading cycle. Usually for simulation studies, hysteresis is expressed as a time delay or as linear functions. The paper introduces investigations of hysteresis-characterized processes in the brake system and relevant dynamic model of this effect for further application to ABS and ESC control algorithms.

The paper is organized as follows: the first part analyzes the literature sources and previous research works on the experimental data of hysteresis-characterized processes under different operational conditions. The hysteresis process is analyzed for the cases: (i) "input pressure vs. brake piston displacement", and (ii) "input pressure vs. realized brake moment in the friction pair". The experimental results demonstrated that the hysteresis taking place in the brake mechanism has a nonlinear asymmetric form.

The second part of the article introduces a mathematical model based on the Bouc-Wen method and its computer realization in Matlab to describe an asymmetrical hysteresis. The method is verified through the experimental results. The analysis of hysteresis influence on vehicle dynamics has been provided for the case of the ABS straight-line braking by considering two variants of the ABS controller: PID control and sliding mode control.

The nonlinear behaviour of hysteresis requires a more complex control law to achieve precise tracking of reference signals. This issue is marked out as future work.

Shyrokau, Barys, Wang, Danwei - Nanyang Technological University; Augsburg, Klaus, Ivanov, Valentin* - Ilmenau University of Technology