Optimal interval type-2 fuzzy fractional order super twisting algorithm: A second order sliding mode controller for fully-actuated and under-actuated nonlinear systems

Ehsan Zakeri; Seyed Alireza Moezi; Mohammad Eghtesad

doi:10.1016/j.isatra.2018.10.013

Optimal interval type-2 fuzzy fractional order super twisting algorithm: A second order sliding mode controller for fully-actuated and under-actuated nonlinear systems

ISA Trans. 2019 Feb:85:13-32. doi: 10.1016/j.isatra.2018.10.013. Epub 2018 Oct 17.

Authors

Ehsan Zakeri¹, Seyed Alireza Moezi², Mohammad Eghtesad³

Affiliations

¹ Department of Mechanical Engineering, University of Sistan and Baluchestan, Zahedan, Iran. Electronic address: ehsan8631@gmail.com.
² Department of Mechanical Engineering, Yazd University, Yazd, Iran.
³ School of Mechanical Engineering, Shiraz University, shiraz, Iran.

PMID: 30482550
DOI: 10.1016/j.isatra.2018.10.013

Abstract

In this paper, a novel interval type-2 fuzzy fractional order super twisting algorithm (IT2FFOSTA) which is essentially a second order sliding mode controller is presented. The proposed IT2FFOSTA enhances fractional order super twisting algorithm (FOSTA) by taking advantage of an interval type-2 fuzzy fractional order sliding surface (IT2FFOSS) for some classes of fully-actuated and under-actuated nonlinear systems in presence of uncertainty. The FOSTA significantly reduces the amount of chattering and the IT2FFOSS results in decreasing the tracking error, control effort, and chattering level. In order to control under-actuated systems, a hierarchical sliding surface is employed. The multi-tracker optimization algorithm is utilized to adjust the controller's parameters; this leads to an optimal performance for the IT2FFOSTA. To examine the performance of the IT2FFOSTA, some simulation and experimental tests on three examples of different classes of fully-actuated and under-actuated systems, including ball and plate, inverted pendulum, and ball and beam systems are carried out. The simulation and experimental results demonstrate the superiority of the IT2FFOSTA in reducing the amount of chattering, tracking error, and control effort compared to those of the other control methods.

Keywords: Fractional operators; Hierarchical sliding surface; Interval type-2 fuzzy logic; MTOA; Super twisting algorithm; Under-actuated systems.