Fractional order predictive sliding-mode control for a class of nonlinear input-delay systems: singular and non-singular approach

ABSTRACT

Nonlinear models of physical systems usually suffer from input delay and external disturbances. Moreover, when a delayed state is in the input signal gain, it can be non-singular or singular. So, designing a robust controller in a nonlinear system with input and state delay, suitable for non-singular and singular input signal gain, is imperative. The main contribution of our study is to design a new state feedback fractional order predictive sliding mode control (FOPSMC) procedure which not only guarantees the stability of a nonlinear system with known constant input and state delay but also controls the output signal to the desired value. Firstly, a predictor is designed for the system to achieve an input-delay-free one. Then, a state feedback FOPSMC is proposed based on a fractional order sliding signal for a nonlinear system with non-singular control gain. Also, a state feedback FOPSMC and a fractional order sliding mode observer (FOSMO) for the virtual disturbance are designed for singular control gain situation. It is proved analytically, through the Lyapunov stability criteria, that both control procedures can stabilise the system and can control the output signal to the desired value, effectively. Finally, the simulation results verify the effectiveness of the analytical achievements.

KEYWORDS:

• Nonlinear input-delay system
• fractional calculus
• predictive sliding mode control
• Robustness
• non-singular and singular control gain

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Notes on contributors

Ladan Khoshnevisan

Ladan Khoshnevisan received her B.S. degree from the University of Science and Technology, Tehran, Iran in 2008, and her M.Sc. and Ph.D. degrees from Tarbiat Modares University and University of Tehran, Tehran, Iran in 2010 and 2017, respectively, all in electrical engineering. She was an International Visiting Ph.D. Student at the Applied Math Department, Faculty of Mathematics, University of Waterloo, Waterloo, Canada. Her research interests include robust and adaptive control systems, congestion and flow control in computer networks, bifurcation and system analysis, fault detection and isolation, fault tolerant control and fractional order systems.

Xinzhi Liu

Xinzhi Liu received the B.Sc. degree in mathematics from Shandong Normal University, Jinan, China in 1982, and the M.Sc. and Ph.D. degrees from the University of Texas at Arlington, TX, USA in 1987 and 1988, respectively. He was a Post-Doctoral Fellow with the University of Alberta, Edmonton, AB, Canada, from 1988 to 1990. He joined the Department of Applied Mathematics, University of Waterloo, Waterloo, ON, Canada, as an Assistant Professor in 1990, where he became an Associate Professor and a Full Professor in 1994 and 1997, respectively. He has authored or co-authored over 300 research articles, two research monographs, and 20 edited books. His current research interests include system analysis, stability theory, hybrid dynamical systems, impulsive control, complex dynamical networks, and communication security.