Morteza Azizi - Department of Electrical Engineering, Faculty of Engineering, Shahid Chamran University, Ahvaz, Iran
Seyyed sajjad Moosapour - Department of Electrical Engineering, Faculty of Engineering, Shahid Chamran University, Ahvaz, Iran
S.saeedollah Mortazavi - Department of Electrical Engineering, Faculty of Engineering, Shahid Chamran University, Ahvaz, Iran

This article focuses on designing antilock braking system (ABS) controller to adjust the slip to the optimum value, using fractional order calculus and sliding mode control based on the Lyapunov stability and confirming itsperformance and robustness under system uncertainties. The ABS should consideration external disturbances likealterations in the friction force among the tire and road because of variations in the steering, road conditions, loadingsand etc. In this paper, two new controllers are designed for ABS. First, a new fractional order proportional-integralderivative ( PI D  ) sliding surface is proposed and the corresponding controller called fractional order sliding mode controller (FOSMC) is derived. Then at the second design, for develop the convergence rate with a robustness featureand also to possess more degrees of freedom, a fractional terminal sliding mode controller (FOTSMC) is offered. Thefinite time stability of the close loop system is guaranteed for both designs. Simulation results and compared with traditional sliding mode controller (SMC) display the effectiveness of the offered FOSMC and FOTSMC in terms of fast tracking with high robustness when compared with traditional sliding mode controller (SMC).

Antilock Braking System; Fractional calculus; Sliding mode control; Fractional order sliding mode controller; Terminal sliding mode controller