Journal of Systems Engineering and Electronics ›› 2019, Vol. 30 ›› Issue (5): 995-1006.doi: 10.21629/JSEE.2019.05.16

• Control Theory and Application • Previous Articles     Next Articles

Constrained sliding mode control of nonlinear fractional order input affine systems

Vedadi Moghaddam TAHMINEH(), Yadavar Nikravesh SEYYED KAMALEDDIN(), Azam Khosravi MOHAMMAD*()   

  • Received:2018-07-18 Online:2019-10-08 Published:2019-10-09
  • Contact: Azam Khosravi MOHAMMAD;;
  • About author:TAHMINEH Vedadi Moghaddam was born in 1985. She received her B.S. degree in 2007 from Imam Khomeini International University, Qazvin, Iran. She received her M.S. degree in 2011, in the field fractional order controller, from Electrical Engineering Department of Imam Khomeini International University, Qazvin, Iran. Currently, she is working towards her Ph.D. degree at Amirkabir University of Technology, Tehran, Iran. Her current research interests include robust control, adaptive control and nonlinear fractional order systems. Email:|SEYYED KAMALEDDIN Yadavar Nikravesh was born in 1944. He received his B.S. degree in 1967 from Electrical Engineering Department of Tehran Polytechnic University, Tehran, Iran. He received his M.S. degree in 1971, in the field of major option in control, from Electrical Engineering Department of University of Missouri, Rolla, U.S.A. He received his Ph.D. degree in 1973, in the field of major option in control, from Electrical Engineering, University of Missouri, Columbia, U.S.A. He taught over the past 40 years as a professor at the Amirkabir University of Technology, Tehran, Iran. His current research interests include optimal control theory, electrical circuit analysis, industrial control systems and nonlinear control theory. Email:|MOHAMMAD Azam Khosravi was born in 1976. He received his M.Sc.and his Ph.D. degrees from K.N. Toosi University of Technology, Tehran, Iran, in 2000 and 2013, respectively, all in electrical engineering. He is currently an assistant professor with Amirkabir University of Technology. His research interests include nonlinear control theory, parallel robotics, cable driven robots and robust control. Email:


Asymptotic stability of nonlinear fractional order affine systems with bounded inputs is dealt. The main contribution is to design a new bounded fractional order chattering free sliding mode controller in which the system states converge to the sliding surface at a determined finite time. To eliminate the chattering in the sliding mode and make the input controller bounded, hyperbolic tangent is used for designing the proposed fractional order sliding surface. Finally, the stability of the closed loop system using this bounded sliding mode controller is guaranteed by Lyapunov theory. A comparison with the integer order case is then presented and fractional order nonlinear polynomial systems are also studied as the special case. Finally, simulation results are provided to show the effectiveness of the designed controller.

Key words: constrained sliding mode control, nonlinear fractional order systems, input affine systems