The mixed fuzzy controller for anti-braking systems with quasi-nonholonomic constraints

Abstract

The quasi-constrained dynamics is composed of motions not only onto the constraint space but also onto the unconstraint or the "freedom" space, which may occur when the system escapes or slips away from its constraint manifold during high-speed motion. Traditionally, slippage phenomenon, which has been an issue in the automobile industry, is usually ignored because of its high frequency and strong nonlinear features. Conventional Frobenius theorem is focused on the holonomic dynamics, which are integrable on the freedom space. On the other hand, a complementary Frobenius theorem (CFT) is proposed to release conventional constraints from "hard" to "soft' models. In this paper, we derive a geometric formulation instead of its algebraic counterpart for acatastatically nonholonomic systems in the viewpoint of topology. Besides, we propose a mixed fuzzy controller (MFC) for the nonholonomic system with escaping motions, which includes a traditional controller for the hard subsystem and a non-tradtional controller with fuzzy rules for another soft subsystem on the constraint manifold. The closedloop stability of'the nonholonomic system with an MFC scheme will be proved under admissible condtions. Finally, th proposed algorithm is applied to a wheeled vehicle with an anti-lock braking system (ABS) under the assumption of Coulomb's viscous friction. Computer simulation is used to jus* the results.

Non-Traditional Controllers: Composite ABS/TCS for Wheeled Vehicle

“…The vehicle dynamics in its broadest sense encompasses all forms of vehicles [3,4,7,8]. The performance of vehicle dynamics depends on sensory information from accelerating, braking, cornering and riding.…”

“…The empirical understanding is derived from trial and error by which one learns which factors influence vehicle performance and lead to failure. On the other hand, the escaping dynamics of the wheeled vehicle is a significant branch of analytical mechanics, which plays a significant role in the development of nonholonomic systems [1,3,5,6]. It implies fast, however, infinitesimal displacement existed in the normal space of the constraint manifold.…”

“…Bloch, McClamroch et al [1,2,5,6] have derived equations of motion by reducing degrees of freedom from constraints. Huang and Wang [2,3] proposed the concept of complementary distribution under the assumption of complementary Frobenius Theorem (CFT). Different approaches developed for the modeling of ABS/TCS have been discussed in the past few years.…”

“…Different approaches developed for the modeling of ABS/TCS have been discussed in the past few years. [3,4,7,8]. Sensor-based approaches [7,8] as well as theoretical approaches [3,4] are both considered as significant methods in the development of the ABS/TCS environment.…”

“…[3,4,7,8]. Sensor-based approaches [7,8] as well as theoretical approaches [3,4] are both considered as significant methods in the development of the ABS/TCS environment. This paper is organized as follows.…”