Exploring yaw and roll dynamics of ground vehicles using TS fuzzy approach and a novel method for stability analysis based on Lyapunov exponents

Abstract

Vehicle yaw stabilization and rollover prevention are two key factors in safety of vehicles. Designing a controller that can address both of the above safety concerns is of interest. In addition, it is essential that the performance of such a controller is evaluated properly. This can be done using a proper stability analysis. The above research problem is challenging for two reasons. First, maintaining both of the objectives, yaw stabilization and rollover mitigation, is contradictory at some instances, specifically when the vehicle is close to the verge of wheel lift-off. Second, the complexity of the dynamics of vehicle systems, which mostly arises from tire dynamics, makes the problems of controller design and stability analysis more challenging.

In this Ph.D. thesis, a novel method for stability analysis of dynamical systems using the concept of Lyapunov exponents is proposed. The proposed method for stability analysis does not have the limitations of the current methods, and more specifically, can identify boundaries of the whole stability regions of attractors in a dynamical system. Furthermore, this method is computationally efficient and can be applied to general forms of nonlinear systems. The proposed stability analysis scheme is applied to the closed loop systems of ground vehicles with T-S fuzzy controllers for the purpose of evaluating and comparing the performance of the systems. The T-S fuzzy controllers integrate yaw stabilization and rollover avoidance. The ground vehicles that are studied in this research consist of torsionally flexible and torsionally rigid vehicles, which have differences in their dynamics because of the torsional compliance in their frames. The torsional compliance plays an important role in the dynamics, specifically for long vehicles, leading to different rollover indexes in the front and rear axles of the vehicles. The T-S fuzzy controllers are capable of prioritizing the contradictory objectives, and capturing all the essential complexities of dynamics of the systems.