Abstract
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.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
S. Pashaei, and M. Badamchizadeh, “A new fractional-order sliding mode controller via a nonlinear disturbance observer for a class of dynamical systems with mismatched disturbances,” ISA Transactions, vol. 63, pp. 39–48, July 2016.
X. Li, K. Pan, G. Fan, R. Lu, C. Zhu, G. Rizzoni, and M. Canova, “A physics-based fractional order model and state of energy estimation for lithium ion batteries. Part I: Model development and observability analysis,” Journal of Power Sources, vol. 367, pp. 187–201, November 2017.
R. Liu, Z. Nie, M. Wu, and J. She, “Robust disturbance rejection for uncertain fractional-order systems,” Applied Mathematics and Computation, vol. 322, pp. 79–88, April 2018.
Y. Chen, Y. Wei, X. Zhou, and Y. Wang, “Stability for nonlinear fractional order systems: an indirect approach,” Nonlinear Dynamics, vol. 89, no. 2, pp. 1011–1018, April 2017.
H. Liu, S. Li, J. Cao, G. Li, A. Alsaedi, and F. Alsaadi, “Adaptive fuzzy prescribed performance controller design for a class of uncertain fractional-order nonlinear systems with external disturbances,” Neurocomputing, vol. 219, no. 1, pp. 422–430, January 2017.
S. Tabatabaei, H. Talebi, and M. Tavakoli, “An adaptive order/state estimator for linear systems with non-integer time-varying order,” Automatica, vol. 84, no. 10, pp. 1–9, October 2017.
C. Hua, and X. Guan, “Smooth dynamic output feedback control for multiple time-delay systems with nonlinear uncertainties,” Automatica, vol. 68, pp. 1–8, June 2016.
H. Sun, Y. Li, G. Zong, L. Hou, “Disturbance attenuation and rejection for stochastic Markovian jump system with partially known transition probabilities,” Automatica, vol. 89, pp. 349–357, March 2018.
W. Qi, G. Zong, and H. Karimi, “ L ∞ control for positive delay systems with semi-Markov process and application to a communication network model,” IEEE Transactions on Industrial Electronics, vol. 66, no. 3, pp. 2081–2091, March 2019.
S. Shi, K. Kang, J. Li, and Y. Fang, “Sliding mode control for continuous casting mold oscillatory system driven by servo motor,” International Journal of Control, Automation, and Systems, vol. 15, no. 4, pp. 1669–1674, June 2017.
Z. Wang, X. Huang, and H. Shen, “Control of an uncertain fractional order economic system via adaptive sliding mode,” Neurocomputing, vol. 83, no. 6, pp. 83–88, April 2012.
M. Aghababa, “Control of fractional-order systems using chatter-free sliding mode approach,” Journal of Computational and Nonlinear Dynamics, vol. 9, no. 3, pp. 1081–1089, February 2014.
M. Aghababa, “A Lyapunov-based control scheme for robust stabilization of fractional chaotic systems,” Nonlinear Dynamics, vol. 78, no. 3, pp. 2129–2140, November 2014.
Y. Chun, Y. Chen, and S. M. Zhong, “LMI based design of a sliding mode controller for a class of uncertain fractional-order nonlinear systems,” Proc. of American Control Conference, pp. 6511–6516, June 2013.
S. Dadras, S. Dadras, and H. Momeni, “Linear matrix inequality based fractional integral sliding-mode control of uncertain fractional-order nonlinear systems,” Journal of Dynamic Systems Measurement and Control, vol. 139, no. 11, pp. 111003-1-7, July 2017.
Z. Gao, and X. Z. Liao, “Integral sliding mode control for fractional-order systems with mismatched uncertainties,” Nonlinear Dynamics, vol. 72, no. 1–2, pp. 27–35, April 2013.
L. Chen, R. Wu, Y. He, and Y. Chai, “ Adaptive sliding-mode control for fractional-order uncertain linear systems with nonlinear disturbances,” Nonlinear Dynamics, vol. 80, no. 1–2, pp. 51–58, April 2015.
Y. Guo, B. Ma, L. Chen, and R. Wu, “Adaptive sliding mode control for a class of Caputo type fractional-order interval systems with perturbation,” IET Control Theory and Applications, vol. 11, no. 1, pp. 57–65, January 2017.
N. Djeghali, S. Djennoune, M. Bettayeb, M. Ghanes, and J. Barbot, “Observation and sliding mode observer for nonlinear fractional-order system with unknown input,” ISA Transactions, vol. 63, pp. 1–10, July 2016.
S. Shao, M. Chen, and X. Yan, “Adaptive sliding mode synchronization for a class of fractional-order chaotic systems with disturbance,” Nonlinear Dynamics, vol. 83, no. 4, pp. 1855–1866, March 2016.
S. Shi, “Extended disturbance observer based sliding mode control for fractional-order systems,” Proc. of the 36th Chinese Control Conference, pp. 11385–11389, July 2017.
J. Yang, S. Li, and X. Yu, “Sliding mode control for systems with mismatched uncertainties via a disturbance observer,” IEEE Transactions on Industrial Electronics, vol. 60, no. 1, pp. 160–169, January 2013.
A. Norelys, D. Manuel, and G. Javier, “Lyapunov functions for fractional order systems,” Communications in Nonlinear Science and Numerical Simulation, vol. 19, no. 9, pp. 2951–2957, September 2014.
D. Matignon, “Stability results for fractional differential equations with applications to control processing,” Computational Engineering in Systems Applications, vol. 2, pp. 963–968, 1996.
L. Chen, G. Chen, R. Wu, J. Machado, A. Lopes, and S. Ge, “Stabilization of uncertain multi-order fractional systems based on the extended state observer,” Asian Journal of Control, vol. 20, no. 3, pp. 1263–1273, May 2018.
C. Li and W. Deng, “Remarks on fractional derivatives,” Applied Mathematics and Computation, vol. 187, no. 2, pp. 777–784, April 2007.
A. Jmal, O. Naifar, A. Makhouf, N. Derbel, and M. Hammami, “On observer design for nonlinear Caputo fractional-order systems,” Asian Journal of Control, vol. 20, no. 4, pp. 1533–1540, July 2018.
Author information
Authors and Affiliations
Corresponding author
Additional information
Recommended by Associate Editor Guangdeng Zong under the direction of Editor Hamid Reza Karimi. This work was supported in part by National Natural Science Foundation of China under grants 61873226 and 61803327, Natural Science Foundation of Hebei Province under grants F2017203304 and F2018203370, High Level Talent Support Project of Hebei Province under grant A2016015002, the doctoral foundation of Yanshan University under grant B925, and the young teachers independent research program of Yanshan University grant 15LGA017.
Sheng-Li Shi received his B.S. degree in Mathematics from Shandong University in 2002, and his Ph.D. degree in control science and engineering from Yanshan University in 2014. He is currently a lecturer with the School of Science, Yanshan University. His research interests include robust control and disturbance compensation.
Jian-Xiong Li received the B.S. and Ph.D. degrees in control science and engineering from Yanshan University, in 2004 and 2012, respectively. He is currently an associate professor with the School of Electrical Engineering, Yanshan University. His research interests include robust adaptive control theory with applications to electro-hydraulic servo motor system.
Yi-Ming Fang received his B.S. and Ph.D. degrees in control science and engineering from Yanshan University, in 1985 and 2003, respectively. He is currently a professor with the School of Electrical Engineering, Yanshan University. His research interests include automation technology and application of continuous casting and steel rolling, modeling and controlling of complex system, adaptive robust control theory and application.
Rights and permissions
About this article
Cite this article
Shi, SL., Li, JX. & Fang, YM. Fractional-disturbance-observer-based Sliding Mode Control for Fractional Order System with Matched and Mismatched Disturbances. Int. J. Control Autom. Syst. 17, 1184–1190 (2019). https://doi.org/10.1007/s12555-018-0654-0
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12555-018-0654-0