Simulated and Experimental Study of Antilock Braking System Using Grey Sliding Mode Control Yesim Oniz, Erdal Kayacan and Okyay Kaynak Abstract— Antilock Braking System (ABS) exhibits strongly nonlinear and uncertain characteristics. To overcome these difficulties, robust control methods should be employed. In this paper, a grey sliding mode controller is proposed to track the reference wheel slip. The concept of grey system theory, which has a certain prediction capability, offers an alterna- tive approach to conventional control methods. The proposed controller anticipates the upcoming values of wheel slip, and takes the necessary action to keep wheel slip at the desired value. The control algorithm is applied to a quarter vehicle model, and it is verified through simulations indicating fast convergence and good performance of the designed controller. Simulated results are validated on real time applications using a laboratory experimental setup. I. INTRODUCTION ABS is an electronically controlled system that helps the driver to maintain control of the vehicle during emergency braking while preventing the wheels to lock up. Furthermore, by keeping brake pressure just below the point of causing a wheel to lock, ABS ensures that maximum braking power is used to stop the vehicle, and minimum possible stopping distance is achieved. During accelerating or braking, the generated friction forces are proportional to the normal load of the vehicle. The coefficient of this proportion is called road adhesion coefficient and it is denoted by μ. Studies show that μ is a nonlinear function of wheel slip, λ [1]. The typical μ- λ curve is obtained from the data of numerous experiments. Most of the ABS controllers are expected to keep the vehicle slip at a particular level, where the corresponding friction force (i.e. road adhesion coefficient) reaches its maximum value. Zanten states in [2] that the wheel slip should be kept between 0.08 and 0.3 to achieve optimal performance. Furthermore, some research papers show that the reference wheel slip does not have to be a constant value. In [3], the reference wheel slip is considered as a nonlinear function of some physical variables including the velocity of the vehicle. Although many attempts have been made over the decades, an accurate mathematical model of ABS has not been ob- tained yet. One of the shortcomings is that the controller must operate at an unstable equilibrium point in order to get the Y. Oniz is with Department of Electrical and Electronics Engineering, Bogazici University, 34342, Bebek, Istanbul, Turkey yesim.oniz@boun.edu.tr E. Kayacan is with the Department of Electrical and Electron- ics Engineering, Bogazici University, 34342, Bebek, Istanbul, Turkey erdal.kayacan@ieee.org O. Kaynak is with the Department of Electrical and Electron- ics Engineering, Bogazici University, 34342, Bebek, Istanbul, Turkey okyay.kaynak@boun.edu.tr optimal performance. A small perturbation of the controller input may result in a drastic change in the output. Further- more in today’s technology, there are no affordable sensors which can accurately identify the road surface, and make this data available to ABS controller. Regarding the fact that the system parameters highly depend on the road conditions and vary over a wide range, the performance of ABS may not always be satisfactory. Moreover, sensor signals exhibit usually highly uncertain and noisy characteristics [4]. Because of the highly nonlinear and uncertain structure of ABS, many difficulties arise in the design of a wheel slip regulating controller. Sliding mode control is a preferable option, as it guarantees the robustness of the system for changing working conditions. The stability requirements for switching surface are described in [5]. In [6] and [7], it is assumed that the optimal value of wheel slip, which will result in maximum braking torque, is known. Drakunov [8] employs sliding mode to achieve the maximum value of friction force without the priori knowledge of optimum slip value. Kachroo and Tomizuka proposed a Sliding Mode Controller (SMC) in [9] that can maintain the wheel slip at any desired value. Unsal [10] proposed a sliding mode observer to track the reference wheel slip, and a PI-like controller is used to reduce the chattering problem. This paper proposes a SMC and a Grey Sliding Mode Controller (GSMC) for tracking a reference wheel slip. Due to highly nonlinear and uncertain characteristics of ABS, a grey predictor is employed to anticipate the future outputs of the system using current data available. Grey predictor estimates the forthcoming value of wheel slip, and SMC takes the necessary action to maintain wheel slip at the desired value. To investigate the performance of the proposed controller, the reference wheel slip is considered both a constant value and a nonlinear function of the vehicle velocity. In the next section, a laboratory setup of an ABS is described and its dynamic equations are derived. SMC and grey predictor are developed in Section 3 and in Section 4, respectively. Simulation and experimental real time results are provided and compared in Section 5. Section 6 makes some concluding remarks. II. SYSTEM DESCRIPTION The laboratory setup of ABS consists of two rolling wheels. The lower wheel imitates of relative road motion. The upper wheel mounted to the balance lever animates the wheel of the vehicle. While two rotary encoders are installed on both of the wheels to measure the angular velocities, an additional one is used to identify the angular position of the 90 1-4244-0991-8/07/$25.00/©2007 IEEE Authorized licensed use limited to: ULAKBIM UASL - BOGAZICI UNIVERSITESI. Downloaded on February 19, 2009 at 07:46 from IEEE Xplore. Restrictions apply.