Adaptive sliding mode output tracking control based-FODOB for a class of uncertain fractional-order nonlinear time-delay
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https://doi.org/10.1007/s11431-019-1476-4
Adaptive sliding mode output tracking control based-FODOB for a class of uncertain fractional-order nonlinear time-delayed systems WANG Zhen1, WANG XinHe1, XIA JianWei2, SHEN Hao3 & MENG Bo1* 1 College
of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China; 2 School of Mathematics Science, Liaocheng University, Liaocheng 252059, China; 3 School of Electrical Engineering and Information, Anhui University of Technology, Maanshan 243002, China Received August 7, 2019; accepted November 7, 2019; published online May 11, 2020
An adaptive sliding mode control (ASMC) method, based on fractional-order disturbance-observer (FODOB), is presented for a class of fractional-order nonlinear time-delay systems (FONTDS) with uncertainties to solve the target output tracking problem. The external disturbances are estimated by FODOB, and the unknown internal perturbations of the system are adaptively estimated by sliding mode control (SMC). Furthermore, Gronwall’s inequality approach is used to ensure that the output tracking error is uniformly bounded for FONTDS. Firstly, a fractional-order sliding mode control (FOSMC) based FODOB is proposed for a fractional-order linear time-delay system (FOLTDS). Secondly, combined with adaptive estimation, the ASMC of FONTDS is studied. Finally, a numerical example of FONTDS is used to verify the effectiveness of the proposed methods. adaptive sliding mode control, fractional-order, disturbance-observer, time-delay, uncertainty Citation:
Wang Z, Wang X H, Xia J W, et al. Adaptive sliding mode output tracking control based-FODOB for a class of uncertain fractional-order nonlinear time-delayed systems. Sci China Tech Sci, 2020, 63, https://doi.org/10.1007/s11431-019-1476-4
1 Introduction In recent decades, fractional calculus (FC) has been widely applied in information science, engineering technology, economic systems, biological systems, and mechanical systems [1–5]. Notably, electro-magnetic suspension systems are modeled and controlled by FC [6, 7]. FC was founded by Leibniz over 300 years ago as a generalization of integerorder calculus [8]. It benefited from the rapid development of fractional differential equations (FDE) theory and fractionalorder systems (FOS). With the introduction of pseudo-state space description for FOS [9], the FDE’s numerical computing has been studied using Matlab Toolbox. Presently, system theory and control methods have made great progress. Dissipative control [10, 11], synchronous *Corresponding author (email: [email protected])
control [12, 13], neural network control [14–16], eventtriggered control [17, 18], and sliding mode control (SMC) [19–21] have been widely studied. As a form of nonlinear control, SMC has rapidly developed and is widely used [22]. Some examples of this are: second order SMC, high order SMC, super twisting SMC, and integral SMC. In terms of the composite control method, adaptive sliding mode control (ASMC) has a w
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