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Traction motor systems for electric vehicles provides fast torque response that may let the driver input result in excessive propelling or regenerative braking torque, which can reduce tire-road adherence. The same situation can also occur due to excessive wheel slip that tends to spin or skid the wheels, resulting in safety issues or energy losses. However, to measure the slip ratios for vehicle control, vehicle speed measurement instruments are needed, which are too expensive to implement on commercial electric vehicles. This paper presents a slip ratio observer based on a Kalman-like observer for a state-affine system, which does not use the tire-road friction model and does not require knowledge of vehicle parameters. We also propose a wheel slip controller, based on fuzzy sliding mode control (FSMC), which uses a slip ratio estimate given by the observer. The FSMC is capable of manipulating the slip ratio to at a desired value, for which the traction or braking force is maximum. The slip ratio observer and FSMC have been tested extensively with numerical simulations, and the results confirm their validity.