Modified Sliding Mode Control for Mismatched Uncertain Systems with Unknown Disturbances

Abstract:

In this paper, a new sliding mode control law is developed for a class of mismatched uncertain systems with more general exogenous disturbances. First, we derive a new existence condition of linear sliding surface in terms of strict linear matrix inequalities such that the reduce-order sliding mode dynamics is is asymptotically stable. Second, we propose an adaptive sliding mode control law such that the system states reach the sliding surface in finite time and stay on its thereafter. Final, a numerical example is used to demonstrate the efficacy of the proposed method.

• Periodical: Applied Mechanics and Materials (Volume 829)
• Pages: 123-127
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.829.123
• Online since: March 2016
• Authors: Van Van Huynh, Thao Phuong Thi Nguyen*
• Keywords: General Disturbances, Linear Matrix Inequalities, Mismatched Uncertain Systems

References

[1] H.H. Choi, A new method for variable-structure control-system design –A linear matrix inequality approach, Automatica, vol. 33, no. 11, pp.2089-2092, (1997).

DOI: 10.1016/s0005-1098(97)00118-0

[2] H.H. Choi, An explicit formula of linear sliding surfaces for a class of uncertain dynamic systems with mismatched uncertainties, Automatica, vol. 34, no. 8, pp.1015-1020, (1998).

DOI: 10.1016/s0005-1098(98)00042-9

[3] K.K. Shyu, Y.W. Tsai, C.K. Lai, A dynamic output feedback controllers for mismatched uncertain variable structure systems, Automatica, vol. 37, no. 5, p.775–779, (2001).

DOI: 10.1016/s0005-1098(01)00014-0

[4] 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, (2007).

DOI: 10.1109/tac.2007.894543

[5] F.J. Bejarano, L.M. Fridman, and A.S. Poznyak, Output integral sliding mode for min-max optimization of multi-plant linear uncertain systems, IEEE Transactions on Automatic Control, vol. 54, no. 11, pp.2611-2620, (2009).

DOI: 10.1109/tac.2009.2031718

[6] M. Rubagotti, A. Estrada, F. Castanos and A. Ferrara, Integral sliding mode control for nonlinear systems with matched and unmatched perturbations, IEEE Transactions on Automatic Control, vol. 56, no. 11, pp.2699-2704, (2011).

DOI: 10.1109/tac.2011.2159420

[7] Y. Gao, B. Sunand G. Lu, Passivity-based integral sliding-mode control of uncertain singularly perturbed systems, IEEE transactions on Circuits and Systems II: Express Briefs, vol. 58, no. 6, pp.386-390, (2011).

DOI: 10.1109/tcsii.2011.2149690

[8] J. Yang, J. Su, S. Liand X. Yu, High-order mismatched disturbance compensation for motion control systems via a continuous dynamic sliding-mode approach, IEEE Transactions on Industrial Informatics, vol. 10 ,  no. 1, pp.604-614, (2013).

DOI: 10.1109/tii.2013.2279232

[9] Q. Gao, G. Feng, L. Liu, J. Qiu and Y. Wang, Robust H∞ control for stochastic T-S fuzzy systems via integral sliding-mode approach, IEEE Transactions on Fuzzy Systems, vol. 22, no. 4, pp.870-881, (2013).

DOI: 10.1109/tfuzz.2013.2277732

[10] D. Ginoya, P. D. Shendge, 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, (2014).

DOI: 10.1109/tie.2013.2271597

[11] H. Yang, Y. Xia, M. Fu and P. Shi, Robust adaptive sliding mode control for uncertain delta operator systems, International Journal of Adaptive Control and Signal Processing, vol. 24, no. 8, pp.623-632, (2010).

DOI: 10.1002/acs.1154