Abstract
This paper concerns with fixed-time control for the mismatched uncertain system. We propose a fixed-time disturbance observer (DO). Then, a non-singular fixed-time sliding-mode surface and controller are designed based on the estimations of proposed DO. Existing DO-based sliding-mode control (DOSMC) and finite-time DOSMC schemes can eliminate the mismatched uncertain problem by using traditional sliding-mode control (TSMC). However, the convergence times of these DOSMC schemes are infinite or related to the initial system conditions. Unlike existing approaches, the proposed fixed-time DOSMC can guarantee the convergence time is uniformly bounded and the upper bound is independent on initial system conditions, which implies that the proposed scheme can provide similar convergence performance with the same control parameters under different initial conditions. Simulation result shows the excellent convergence performance of the proposed scheme.
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F. Castanos and L. Fridman, “Analysis and design of integral sliding manifolds for systems with unmatched perturbations,” IEEE Transactions on Automatic Control, vol. 51, no. 5, pp. 853–858, May 2006.
S. Ding, J. H. Park, and C.-C. Chen, “Second-order sliding mode controller design with output constraint,” Automatica, vol. 121, pp. 108704, February 2020.
K.-S. Kim, Y. Park, and S.-H. Oh, “Designing robust sliding hyperplanes for parametric uncertain systems: A Riccati approach,” Automatica, vol. 36, no. 7, pp. 1041–1048, July 2000.
J. Wang, J. Yang, B. Wu, S. Li, and Q. Li, “Extended state observer-based sliding mode control for PWM-based DC—DC buck power converter systems with mismatched disturbances,” IET Control Theory & Applications, vol. 9, no. 4, pp. 579–586, February 2015.
Y. Wang, H. Shen, and H. R. Karimi, “Dissipativity-based fuzzy integral sliding mode control of continuous-time TS fuzzy systems,” IEEE Transactions on Fuzzy Systems, vol. 26, no. 3, pp. 1164–1176, June 2018.
H. Li, P. Shi, and D. Yao, “Observer-based adaptive sliding mode control for nonlinear Markovian jump systems,” Automatica, vol. 64, pp. 133–142, February 2016.
X. Wang and J. Wang, “Partial integrated missile guidance and control with finite time convergence,” Journal of Guidance, Control, and Dynamics, vol. 36, no. 5, pp. 1399–1409, September 2013.
X. Wang, J. Wang, and G. Gao, “Partial integrated missile guidance and control with state observer,” Nonlinear Dynamics, vol. 79, no. 4, pp. 2497–2514, March 2015.
Z. Zhu, D. Xu, J. Liu, and Y. Xia, “Missile guidance law based on extended state observer,” IEEE Transactions on Industrial Electronics, vol. 60, no. 12, pp. 5882–5891, December 2013.
R. Zhang, L. Dong, and C. Sun, “Adaptive nonsingular terminal sliding mode control design for near space hypersonic vehicles,” IEEE/CAA Journal of Automatica Sinica, vol. 1, no. 2, pp. 155–161, April 2014.
S. D. Brierley and R. Longchamp, “Application of sliding-mode control to air-air interception problem,” IEEE Transactions on Aerospace and Electronic Systems, vol. 26, no. 2, pp. 306–325, March 1990.
T. Shima, M. Idan, and O. M. Golan, “Sliding-mode control for integrated missile autopilot guidance,” Journal of Guidance, Control, and Dynamics, vol. 29, no. 2, pp. 250–260, March 2006.
W. R. Errouissi, M. Ouhrouche, and A. M. Trzynadlowski, “Robust nonlinear predictive controller for permanent-magnet synchronous motors with an optimized cost function,” IEEE Transactions on Industrial Electronics, vol. 59, no. 7, pp. 2849–2858, July 2012.
W. R. Abdul-Adheem, I. K. Ibraheem, and A. J. Humaidi, “Model-free active input-output feedback linearization of a single-link flexible joint manipulator: An improved active disturbance rejection control approach,” Measurement & Control, vol. 54, no. 5, pp. 856–871, May 2021.
K.-S. Kim, Y. Park, and S.-H. Oh, “Designing robust sliding hyperplanes for parametric uncertain systems: A Riccati approach,” Automatica, vol. 36, no. 7, pp. 1041–1048, July 2000.
J.-L. Chang, “Dynamic output integral sliding-mode control with disturbance attenuation,” IEEE Transactions on Automatic Control, vol. 54, no. 11, pp. 2653–2658, November 2009.
H. H. Choi, “LMI-based sliding surface design for integral sliding mode control of mismatched uncertain systems,” IEEE Transactions on Automatic Control, vol. 52, no. 4, pp. 736–742, April 2007.
H. H. Choi, “An explicit formula of linear sliding mode surfaces for a class of uncertain dynamic systems with mismatched uncertainties,” Automatica, vol. 34, no. 8, pp. 1015–1020, August 1998.
P. Park, D. J. Choi, and S. G. Kong, “Output feedback variable structure control for linear systems with uncertainties and disturbances,” Automatica, vol. 43, no. 1, pp. 72–79, January 2007.
C.-C. Wen and C.-C. Cheng, “Design of sliding mode for mismatched uncertain systems to achieve asymptotical stability,” Journal of the Franklin Institute, vol. 345, no. 8, pp. 926–941, November 2008.
J. Yang, W.-H. Chen, and S. Li, “Non-linear disturbance observer-based robust control for systems with mismatched disturbances/uncertainties,” IET Control Theory & Applications, vol. 5, no. 18, pp. 2053–2062, December 2011.
J. Yang, S. Li, and W.-H. Chen, “Nonlinear disturbance observer-based control for multi-input multi-output nonlinear systems subject to mismatching condition,” International Journal of Control, vol. 85, no. 8, pp. 1071–1082, April 2012.
S. Li, J. Yang, W.-H. Chen, and X. Chen, “Generalized extended state observer based control for systems with mismatched uncertainties,” IEEE Transactions on Industrial Electronics, vol. 59, no. 12, pp. 4792–4802, December 2012.
J. Yang, A. Zolotas, W.-H. Chen, K. Michail, and S. Li, “Robust control of nonlinear MAGLEV suspension system with mismatched uncertainties via DOBC approach,” ISA Transactions, vol. 50, no. 3, pp. 389–396, July 2011.
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 2011.
D. Ginoya, P. D. Shendge, and S. B. Phadke, “Sliding mode control for mismatched uncertain systems using an extended disturbance observer,” IEEE Transactions on Industrial Electronics, vol. 61, no. 4, pp. 1983–1992, April 2014.
M. Zhihong and X. H. Yu, “Terminal sliding mode control of MIMO linear systems,” IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, vol. 44, no. 11, pp. 1065–1070, November 1997.
Y. Feng, X. Yu, and Z. Man, “Non-singular terminal sliding mode control of rigid manipulators,” Automatica, vol. 38, no. 12, pp. 2159–2167, December 2002.
L. Yang and J. Yang, “Nonsingular fast terminal sliding-mode control for nonlinear dynamical systems,” International Journal of Robust and Nonlinear Control, vol. 21, no. 16, pp. 1865–1879, November 2002.
H. Sun, S. Li, and C. Sun, “Finite time integral sliding mode control of hypersonic vehicles,” Nonlinear Dynamics, vol. 73, no. 1–2, pp. 229–244, July 2013.
J. Yang, S. Li, J. Su, and X. Yu, “Continuous nonsingular terminal sliding mode control for systems with mismatched disturbances,” Automatica, vol. 49, no. 7, pp. 2287–2291, July 2013.
N. P. Nguyen, H. Oh, and Y. Kim, “Disturbance observer-based continuous finite-time sliding mode control against matched and mismatched disturbances,” Complexity, vol. 2020, pp. 2085752, May 2020.
A. Polyakov and L. Fridman, “Stability notions and Lyapunov functions for sliding mode control systems,” Journal of the Franklin Institute, vol. 351, no. 4, pp. 1831–1865, April 2014.
W. Yang, M. Chen, and Y. Song, “Robust fixed-time inverse dynamic control for uncertain robot manipulator system,” Complexity, vol. 2021, pp. 6664750, January 2021.
J. Ni, L. Liu, and C. Liu, “Fast fixed-time nonsingular terminal sliding mode control and its application to chaos suppression in power system,” IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 64, no. 2, pp. 151–155, February 2017.
Z. Y. Zuo, “Non-singular fixed-time terminal sliding mode control of non-linear systems,” IET Control Theory & Applications, vol. 9, no. 4, pp. 545–552, February 2015.
Z. Gao and G. Guo, “Fixed-time sliding mode formation control of AUVs based on a disturbance observer,” IEEE/CAA Journal of Automatica Sinica, vol. 7, no. 2, pp. 539–545, March 2020.
S. P. Bhat and D. S. Bernstein, “Finite-time stability of continuous autonomous systems,” SIAM Journal on Control and Optimization, vol. 38, no. 3, pp. 751–766, March 2000.
A. Polyakov, “Nonlinear feedback design for fixed-time stabilization of linear control systems,” IEEE Transactions on Automatic Control, vol. 57, no. 8, pp. 2106–2110, August 2012.
Y. Su and C. Zheng, “Fixed-time inverse dynamics control for robot manipulators,” Journal of Dynamic Systems, Measurement, and Control, vol. 141, no. 6, p. 064502, June 2019.
R. Cruz-Zavala, J. A. Moreno, and L. M. Fridman, “Uniform robust exact differentiator,” IEEE Transactions on Automatic Control, vol. 56, no. 11, pp. 2727–2733, November 2011.
L. P. Xin, B. Yu, and L. Zhao, “Adaptive fuzzy backstepping control for a two continuous stirred tank reactors process based on dynamic surface control approach,” Applied Mathematics and Computation, vol. 377, pp. 125138, July 2020.
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This work was supported by the Natural Science Basic Research Program of Shaanxi (2021JQ-880,2021JM-533,2020JM-646), Scientific Research Program Funded by Shaanxi Provincial Education Department (Program No.21JK0956, Program No.21JK0960) and the Scientific Research Fund for High-Level Talents of Xijing University (XJ21B01).
Yang Wang received his B.S., M.S., and Ph.D. degrees in 2011, 2014, and 2018 respectively from Northwestern Polytechnical University, China. His research interests include nonlinear control system theory and robust control
Mingshu Chen received her M.S. degree from Xi’an University of Architecture and Technology, China. Her research interests include robot and FPGA design
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Wang, Y., Chen, M. Fixed-time Disturbance Observer-based Sliding Mode Control for Mismatched Uncertain Systems. Int. J. Control Autom. Syst. 20, 2792–2804 (2022). https://doi.org/10.1007/s12555-021-0097-x
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DOI: https://doi.org/10.1007/s12555-021-0097-x