Duprey, B. and Taheri, S., "A Fuzzy Based Stability Index Using a Right Sigmoid Membership Function," SAE Int. J. Commer. Veh. 2(2):131-145, 2010, doi:10.4271/2009-01-2871.
The increasing use and implementation of yaw and roll stability control in heavy trucks has contributed to an increased level of safety for truck drivers and other motorists. It has been shown that the combination of the stability control systems with a predictive model-based stability index can dramatically improve the truck stability and hence road safety. In this respect the authors introduced a new Total Safety Margin (TSM) using a fuzzy logic-based stability index. That methodology utilized a smoothed step and provided acceptable results; however, continuing development has shown that a right sigmoid membership function distribution would provide more complete coverage of the fuzzy space. Compared to the more common triangular membership function which is discontinuous when the membership grade equals one, sigmoid functions facilitate obtaining smooth, continuously differentiable surfaces of a fuzzy model. This is advantageous since continuous surfaces presumably yield smooth control. This was simulated using a 3 degree-of-freedom, single track vehicle model in Matlab and validated using TruckSim 7, the simulation platform of choice. This allowed the new membership functions for Lateral Acceleration, Lateral Velocity, Yaw Rate, and Roll Angle to contribute to the updated Total Safety Margin (TSM).