An Uniformly Stable Observer for Tire Friction Estimation During Braking Process

Abstract

Abstract: There are patents that consider some interesting characteristics as are [1] and [2] related with the pneumatic and in [3] the electrical elements for the rapid braking, in this paper, an uniformly stable observer for tire/road friction model estimation during braking process is proposed. In this observer the angular speed of the tire is taken as the output and it is used to estimate the internal friction state, the linear speed of the tire and the relative velocity of the vehicle [4]. It is proven that the state error of the observer applied to the nonlinear model is uniformly stable. The observer proposed is based on the solution of a Linear Matrix Inequality (LMI) equation [5]. A simulation shows the effectiveness of the suggested observer. Keywords: Braking process, observer, longitudinal dynamics. INTRODUCTION The tire/road friction phenomenon plays an important role in vehicle safety and handling. Researchers are often trying to improve the safety, driving comfort and traffic circulation. They also are trying to reduce the environmental pollution associated with vehicles. In this days, many con-trollers are available to improve safety and vehicle handling including anti-lock brake systems (ABS), traction control systems (TSC), adaptive intelligent cruise control, active yaw control systems and active suspension systems. How-ever these control systems only perform to their potential if they have access to the accurate information about the vehicle behavior in real time. Some authors have proposed the equations to model the dynamic behavior of the braking in a car. Two equations are related with the simplified motions of a wheel in a car are defined in [6-8], and other two equation are the Lumped LuGre friction model defined in [7-11]. In [12], they provide an excellent material for both service brake an parking brake. In [13], a device for selectively controlling and varying a frictional force level at an interface between two bodies was proposed. In [1], a pneumatic tire containing a combination plasticizer was proposed. In [2], a pneumatic tire with component containing asphaltene was proposed. In [4], improved methods and systems for controlling hydraulically or electrically actuated anti-lock brake systems (ABS) was proposed. In [3], the electrical engineering to processes for rapid braking was proposed.