Robust Roll and Yaw control systems using fuzzy model of the vehicle dynamics N. Daraoui, O. Pag` es and A. El Hajjaji Laboratory Modelling, Information & Systems, University of Picardie Jules Verne 7 rue Moulin Neuf, 80000 Amiens, France e-mail: {nawal.daraoui, opages, hajjaji}@u-picardie.fr Abstract—This paper introduces a methodology for robust control of vehicle dynamics. The vehicle lateral behavior with roll dynamics is described by Takagi-Sugeno (TS) model. A fuzzy observer is first developed to estimate the vehicle sideslip angle as well as the roll parameters using the yaw rate measurement, while taking into account the road bank angle and the unmeasurable premise variables of the TS model. The objective of this study is the design of an observer-based controller to improve the stability and vehicle safety with perturbations related to the nonlinearities of the contact forces, the variations of the adhesion coefficients, the road bank angle. The proposed observer based controller is represented in the linear matrix inequality (LMI) form. The simulation results show the effectiveness of the proposed control method when different cornering maneuvers are applied to the vehicle. Key-words Takagi-Sugeno fuzzy model, lateral dynamics, roll dynamics, LTRd, vehicle skid control, unmeasurable premise functions, sideslip angle estimation, LMI. I. I NTRODUCTION The active control systems perform an important role in improving the vehicle safety and comfort. Although, sev- eral active safety systems exist (ABS, ASR, TCS, DYC . . . ) and some of them have already been commercialized and becoming as standard equipment in many vehicles, the increasing demands in safety and comfort terms encourage the manufacturers and the researchers to develop even more efficient security systems. In this context, considerable efforts continue to be made to improve the safety and comfort of passengers in dangerous driving situations [1],[10],[17],[23]. Thus, in order to take the nonlinearities tire contact forces, the TS fuzzy representation is often used. However, most of these works do not consider roll dynamics and unmeasurable premise variables. In this paper, the observer based control problem for a three freedom degrees model including sideslip, yaw and roll dynamics is considered. The vehicle dynamics nonlinear model is approximated by a Takagi-Sugeno (TS) fuzzy model. Then, a robust observer-based fuzzy controller with unmeasurable premise is designed to ensure the vehicle stability and to prevent the rollover. The paper is organized as follows: in section 2, we present the considered nonlinear vehicle dynamics model and its represen- tation by a T-S fuzzy model. Section 3 presents active control objectives and design methodology of robust observer based controller with unmeasurable premise variables. In section 4, simulation results are given to highlight the effectiveness of the design procedure of the observer. Section 5 concludes this paper. II. MATHEMATICAL VEHICLE MODEL AND    A. Sideslip Yaw and roll dynamics The model used in this work describes the vehicle yaw and roll dynamics, which is obtained by considering the bicycle model with a roll degree of freedom (Fig. 1). The vehicle three Fig. 1. Vehicle model dimensional model with the road bank angle consideration and nonlinear tire characteristics of the four wheels can be described by the following differential equations: (Σ:) ⎧  ⎨  ⎩   ( ˙  + ˙  ) = −ℎ  ¨  +2(  +  ) −   ¨  =2(    −   )  ¨  = ℎ + ℎ() −    −   ˙  + ℎ U.S. Government work not protected by U.S. copyright WCCI 2012 IEEE World Congress on Computational Intelligence June, 10-15, 2012 - Brisbane, Australia FUZZ IEEE