Fractional-disturbance-observer-based Sliding Mode Control for Fractional Order System with Matched and Mismatched Disturbances

This paper addresses the sliding mode control for a class of fractional order systems with matched and mismatched disturbances. Firstly, fractional disturbance observer is presented to estimate both the matched and mismatched disturbances, and the boundedness of the estimation error can be guaranteed. Secondly, sliding mode surface is constructed based on the output of the observer. The bounded stability of the closed-loop system under the designed controller is revealed by theoretical analysis. Finally, simulation results show that the proposed control strategy can effectively suppress the effect of the matched and mismatched disturbances on the system.

[1]  Zhen Wang,et al.  Control of an uncertain fractional order economic system via adaptive sliding mode , 2012, Neurocomputing.

[2]  Fuad E. Alsaadi,et al.  Adaptive fuzzy prescribed performance controller design for a class of uncertain fractional-order nonlinear systems with external disturbances , 2017, Neurocomputing.

[3]  Weihua Deng,et al.  Remarks on fractional derivatives , 2007, Appl. Math. Comput..

[4]  Manuel A. Duarte-Mermoud,et al.  Lyapunov functions for fractional order systems , 2014, Commun. Nonlinear Sci. Numer. Simul..

[5]  Mohammad Pourmahmood Aghababa,et al.  A Lyapunov-based control scheme for robust stabilization of fractional chaotic systems , 2014 .

[6]  Yiming Fang,et al.  Sliding mode control for continuous casting mold oscillatory system driven by servo motor , 2017 .

[7]  Xin-Ping Guan,et al.  Smooth dynamic output feedback control for multiple time-delay systems with nonlinear uncertainties , 2016, Autom..

[8]  Baoli Ma,et al.  Adaptive sliding mode control for a class of Caputo type fractional-order interval systems with perturbation , 2017 .

[9]  Shouming Zhong,et al.  LMI based design of a sliding mode controller for a class of uncertain fractional-order nonlinear systems , 2013, 2013 American Control Conference.

[10]  Yuquan Chen,et al.  Stability for nonlinear fractional order systems: an indirect approach , 2017 .

[11]  Shengli Shi,et al.  Extended disturbance observer based sliding mode control for fractional-order systems , 2017, 2017 36th Chinese Control Conference (CCC).

[12]  N. Derbel,et al.  On Observer Design for Nonlinear Caputo Fractional‐Order Systems , 2018 .

[13]  Chunbo Zhu,et al.  A physics-based fractional order model and state of energy estimation for lithium ion batteries. Part I: Model development and observability analysis , 2017 .

[14]  Linlin Hou,et al.  Disturbance attenuation and rejection for stochastic Markovian jump system with partially known transition probabilities , 2018, Autom..

[15]  Xiaozhong Liao,et al.  Integral sliding mode control for fractional-order systems with mismatched uncertainties , 2013 .

[16]  Shuyi Shao,et al.  Adaptive sliding mode synchronization for a class of fractional-order chaotic systems with disturbance , 2016 .

[17]  Hamid Reza Karimi,et al.  $\mathscr {L}_\infty$ Control for Positive Delay Systems With Semi-Markov Process and Application to a Communication Network Model , 2019, IEEE Transactions on Industrial Electronics.

[18]  M. P. Aghababa.  Control of Fractional-Order Systems Using Chatter-Free Sliding Mode Approach , 2014 .

[19]  M. Bettayeb,et al.  Observation and sliding mode observer for nonlinear fractional-order system with unknown input. , 2016, ISA transactions.

[20]  R. Wu,et al.  Adaptive sliding-mode control for fractional-order uncertain linear systems with nonlinear disturbances , 2015 .

[21]  Shabnam Pashaei,et al.  A new fractional-order sliding mode controller via a nonlinear disturbance observer for a class of dynamical systems with mismatched disturbances. , 2016, ISA transactions.

[22]  Jin-Hua She,et al.  Robust disturbance rejection for uncertain fractional-order systems , 2018, Appl. Math. Comput..

[23]  D. Matignon.  Stability results for fractional differential equations with applications to control processing , 1996 .

[24]  António M. Lopes,et al.  Stabilization of Uncertain Multi‐Order Fractional Systems Based on the Extended State Observer , 2018 .

[25]  Mahdi Tavakoli,et al.  An adaptive order/state estimator for linear systems with non-integer time-varying order , 2017, Autom..

[26]  H. Momeni,et al.  Linear Matrix Inequality Based Fractional Integral Sliding-Mode Control of Uncertain Fractional-Order Nonlinear Systems , 2017 .