Fuzzy Adaptive Fixed-time Sliding Mode Control with State Observer for A Class of High-order Mismatched Uncertain Systems

Abstract

Using state observer has attracted a notable interest of researchers in control community to provide an on-line state estimator for control systems instead of measuring them physically by sensors which is costly, inaccurate, and easy to contaminate by noise. Some challenges ahead to design state observer in control systems are using estimated data by observer in the designed controller as well as the system stability analysis by using controller and observer simultaneously. This paper proposes Fuzzy Adaptive Fixed-time Sliding Mode Control (FAFSMC) technique for trajectory tracking of a class of high-order nonlinear systems with mismatched external disturbances and uncertainties. Meanwhile, the fixed-time state observer is proposed to incorporate with the controller for estimating the unmeasured even states (velocity) and providing on-line data in the controller. A proper candidate Lyapunov function is defined to verify the system global fixed-time stability by considering designed control law, state observer term, and adaptive law, simultaneously. The simulation results of three simulation examples, ship course system, two-link robotic manipulator, and three-link robotic manipulator, are carried out in Simulink/MATLAB to reveal the effectiveness of the proposed FAFSMC scheme compared with the other three conventional methods for solving trajectory tracking problem. Two performance criteria, Integral of the Square Value (ISV) and Integral of the Absolute value of the Error (IAE), are used to make a comprehensive comparison among the proposed FAFSMC method with state observer and the other three methods.

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Correspondence to Ali Soltani Sharif Abadi.

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Recommended by Associate Editor Hongyi Li under the direction of Editor Euntai Kim. The authors would like to acknowledge the financial support received from the University of Malaya, Malaysia, through the faculty of engineering research grant (GPF013A-2019).

Ali Soltani Sharif Abadi received his B. Eng. degree in Electrical Engineering from Urmia University, Urmia, Iran in 2016. He has graduated with M.Eng. in Control from Yazd University, Yazd, Iran, in 2019. His research interests include control systems, robust control, nonlinear control, fuzzy logic, state and disturbance observer, stability analysis, finite/fixed and predefined time methods.

Pooyan Alinaghi Hosseinabadi received his B.Eng. degree in Electrical Engineering from Najafabad Branch, Islamic Azad University, Isfahan, Iran in 2012. He graduated in M.Eng. with Distinction in Industrial Electronic and Control from University of Malaya in 2018. He has been working as a researcher and a Research Assistant in Power Electronics and Renewable Energy Research Laboratory (PEARL) in the Department of Electrical Engineering, University of Malaya since September 2017. His research interests include control systems, robust control, adaptive control, fuzzy logic, observer, and stability analysis.

Saad Mekhilef received his B.Eng. degree in Electrical Engineering from University of Setif, in 1995, and his Master of Engineering Science and Ph.D. from University of Malaya, in 1998 and 2003, respectively. He is a Professor and the Dean of Faculty of Engineering and the Director of Power Electronics and Renewable Energy Research Laboratory (PEARL) in the Department of Electrical Engineering, University of Malaya. He is also a Distinguished Adjunct Professor at the Swinburne University of Technology. He is a Distinguished Adjunct Professor at the Center of Research Excellence in Renewable Energy and Power Systems, King Abdulaziz University. His research interests include power conversion techniques, control of power converters, renewable energy, energy efficiency, and control systems.

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Abadi, A.S.S., Hosseinabadi, P.A. & Mekhilef, S. Fuzzy Adaptive Fixed-time Sliding Mode Control with State Observer for A Class of High-order Mismatched Uncertain Systems. Int. J. Control Autom. Syst. 18, 2492–2508 (2020). https://doi.org/10.1007/s12555-019-0650-z

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Keywords

  • Adaptive
  • fixed-time
  • fuzzy
  • mismatched uncertainties
  • sliding mode
  • state observer