| Title:
|
A new LMI-based robust finite-time sliding mode control strategy for a class of uncertain nonlinear systems (English) |
| Author:
|
Mobayen, Saleh |
| Author:
|
Tchier, Fairouz |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 (print) |
| ISSN:
|
1805-949X (online) |
| Volume:
|
51 |
| Issue:
|
6 |
| Year:
|
2015 |
| Pages:
|
1035-1048 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
This paper presents a novel sliding mode controller for a class of uncertain nonlinear systems. Based on Lyapunov stability theorem and linear matrix inequality technique, a sufficient condition is derived to guarantee the global asymptotical stability of the error dynamics and a linear sliding surface is existed depending on state errors. A new reaching control law is designed to satisfy the presence of the sliding mode around the linear surface in the finite time, and its parameters are obtained in the form of LMI. This proposed method is utilized to achieve a controller capable of drawing the states onto the switching surface and sustain the switching motion. The advantage of the suggested technique is that the control scheme is independent of the order of systems model and then, it is fairly simple. Therefore, there is no complexity in the utilization of this scheme. Simulation results are provided to illustrate the effectiveness of the proposed scheme. (English) |
| Keyword:
|
robust tracking |
| Keyword:
|
finite-time control |
| Keyword:
|
sliding mode control |
| Keyword:
|
nonlinear system |
| Keyword:
|
LMI |
| Keyword:
|
uncertainties |
| MSC:
|
35F20 |
| MSC:
|
37N35 |
| MSC:
|
93C10 |
| MSC:
|
93D09 |
| idZBL:
|
Zbl 06537794 |
| idMR:
|
MR3453684 |
| DOI:
|
10.14736/kyb-2015-6-1035 |
| . |
| Date available:
|
2016-01-21T18:33:31Z |
| Last updated:
|
2018-01-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144823 |
| . |
| Reference:
|
[1] Bandyopadhyay, B., Deepak, F., Kim, K. S.: Sliding mode control using novel sliding surfaces..Springer-Verlag, Berlin/Heidelberg 2009. MR 2548194, 10.1007/978-3-642-03448-0 |
| Reference:
|
[2] Chesi, G.: LMI techniques for optimization over polynomials in control: a survey..IEEE Trans. Automat. Control 55 (2010), 2500-2510. MR 2721892, 10.1109/tac.2010.2046926 |
| Reference:
|
[3] Fridman, E., Shaked, U.: $H_{\infty}$-control of linear state-delay descriptor systems: an LMI approach..Linear Algebra Appl. 351 (2002), 271-302. Zbl 1006.93021, MR 1917482, 10.1016/s0024-3795(01)00563-8 |
| Reference:
|
[4] García, A. E. G., Azhmyakov, V., Basin, M. V.: Optimal control processes associated with a class of discontinuous control systems: applications to sliding mode dynamics..Kybernetika 50 (2014), 5-18. Zbl 1302.93222, MR 3195001, 10.14736/kyb-2014-01-005 |
| Reference:
|
[5] Gouaisbaut, F., Dambrine, M., Richard, J. P.: Robust control of delay systems: a sliding mode control design via LMI..Sys. Control Lett. 46 (2002), 219-230. Zbl 0994.93004, MR 2010239, 10.1016/s0167-6911(01)00199-2 |
| Reference:
|
[6] Hassanzadeh, I., Mobayen, S., Harifi, A.: Input-output feedback linearization cascade controller using genetic algorithm for rotary inverted pendulum system..Am. J. Appl. Sci. 5 (2008), 1322-1328. 10.3844/ajassp.2008.1322.1328 |
| Reference:
|
[7] Ignaciuk, P.: Linear-quadratic optimal sliding plane design for networked control of dynamical systems..In: Proc. 13th International Workshop on Variable Structure Systems (VSS) 2014, pp. 1-6. 10.1109/vss.2014.6881113 |
| Reference:
|
[8] Jiang, X., Han, Q. L.: On designing fuzzy controllers for a class of nonlinear networked control systems..IEEE Trans. Fuzzy Syst. 16 (2008), 1050-1060. 10.1109/tfuzz.2008.917293 |
| Reference:
|
[9] Kim, K. S., Park, Y.: Sliding mode design via quadratic performance optimization with pole-clustering constraint..Siam J. Control Optim. 43 (2004), 670-684. Zbl 1101.93024, MR 2086178, 10.1137/s0363012901388476 |
| Reference:
|
[10] Mobayen, S.: Design of a robust tracker and disturbance attenuator for uncertain systems with time delays..Complexity 21 (2015), 1, 340-348. 10.1002/cplx.21569 |
| Reference:
|
[11] Mobayen, S.: Design of LMI-based global sliding mode controller for uncertain nonlinear systems with application to Genesio's chaotic system..Complexity 21 (2015), 1, 94-98. 10.1002/cplx.21545 |
| Reference:
|
[12] Mobayen, S.: Design of CNF-based nonlinear integral sliding surface for matched uncertain linear systems with multiple state-delays..Nonlinear Dyn. 77 (2014), 1047-1054. Zbl 1314.93023, 10.1007/s11071-014-1362-9 |
| Reference:
|
[13] Mobayen, S.: Fast terminal sliding mode controller design for nonlinear second-order systems with time-varying uncertainties..Complexity 21 (2015), 2, 239-244. 10.1002/cplx.21600 |
| Reference:
|
[14] Mobayen, S.: Finite-time stabilization of a class of chaotic systems with matched and unmatched uncertainties: An LMI approach..Published online (2014). Complexity. 10.1002/cplx.21624 |
| Reference:
|
[15] Mobayen, S.: An LMI-based robust controller design using global nonlinear sliding surfaces and application to chaotic systems..Nonlinear Dyn. 79 (2015), 1075-1084. MR 3302754, 10.1007/s11071-014-1724-3 |
| Reference:
|
[16] Mobayen, S., Majd, V. J., Sojoodi, M.: An LMI-based composite nonlinear feedback terminal sliding-mode controller design for disturbed MIMO systems..Math. Comp. Simul. 85 (2012), 1-10. Zbl 1258.93043, MR 2999847, 10.1016/j.matcom.2012.09.006 |
| Reference:
|
[17] Mobayen, S., Yazdanpanah, M. J., Majd, V. J.: A finite-time tracker for nonholonomic systems using recursive singularity-free FTSM..In: Proc. American Control Conference (ACC) 2011, pp. 1720-1725. 10.1109/acc.2011.5991040 |
| Reference:
|
[18] Moulay, E., Peruquetti, W.: Finite time stability and stabilization of a class of continuous systems..J. Math. Anal. Appl. 323 (2006), 1430-1443. MR 2260193, 10.1016/j.jmaa.2005.11.046 |
| Reference:
|
[19] Niu, Y., Ho, D. W. C., Wang, X.: Robust $H_{\infty}$ control for nonlinear stochastic systems: a sliding-mode approach..IEEE Trans. Automat. Control 53 (2008), 1695-1701. MR 2446384, 10.1109/tac.2008.929376 |
| Reference:
|
[20] Pujol, G., Rodellar, J., Rossell, J. M., Pozo, F.: Decentralised reliable guaranteed cost control of uncertain systems: an LMI design..IET Control Theory Appl. 1 (2007), 779-785. 10.1049/iet-cta:20050364 |
| Reference:
|
[21] Rabiee, A., Mohammadi-Ivatloo, B., Moradi-Dalvand, M.: Fast dynamic economic power dispatch problems solution via optimality condition decomposition..IEEE Trans. Power Syst. 29 (2014), 982-983. 10.1109/tpwrs.2013.2288028 |
| Reference:
|
[22] Rabiee, A., Soroudi, A., Mohammadi-Ivatloo, B., Parniani, M.: Corrective voltage control scheme considering demand response and stochastic wind power..IEEE Trans. Power Syst. 29 (2014), 2965-2973. 10.1109/tpwrs.2014.2316018 |
| Reference:
|
[23] Soroudi, A., Rabiee, A.: Optimal multi-area generation schedule considering renewable resources mix: a real-time approach..IET Gener. Transm. Dis. 7 (2013), 1011-1026. 10.1049/iet-gtd.2012.0735 |
| Reference:
|
[24] Soroudi, A., Mohammadi-Ivatloo, B., Rabiee, A.: Energy hub management with intermittent wind power..In: Large Scale Renewable Power Generation, Springer, Singapore 2014, pp. 413-438. 10.1007/978-981-4585-30-9_16 |
| Reference:
|
[25] Tai, T. L., Lu, Y. S.: Global sliding mode control with chatter alleviation for robust eigenvalue assignment..J. Sys. Control Engrg. 220 (2006), 573-584. 10.1243/09596518jsce197 |
| Reference:
|
[26] Tan, H., Shu, S., Lin, F.: An optimal control approach to robust tracking of linear systems..Int. J. Control 82 (2009), 525-540. Zbl 1168.49030, MR 2503276, 10.1080/00207170802187239 |
| Reference:
|
[27] Valiloo, S., Khosrowjerdi, M. J., Salari, M.: LMI based sliding mode surface design with mixed $H_2$/$H_{\infty}$ optimization..J. Dyn. Sys. Meas. Control 136 (2013), 011016. 10.1115/1.4025553 |
| Reference:
|
[28] Wu, H.: Adaptive robust state observers for a class of uncertain nonlinear dynamical systems with delayed state perturbations..IEEE Trans. Automat. Control 54 (2009), 1407-1412. MR 2532639, 10.1109/tac.2009.2017960 |
| Reference:
|
[29] Zhang, B. L., Han, Q. L., Zhang, X. M., Yu, X.: Sliding mode control with mixed current and delayed states for offshore steel jacket platforms..IEEE Trans. Control Syst. Technol. 22 (2014), 1769-1783. 10.1109/tcst.2013.2293401 |
| Reference:
|
[30] Zhang, H., Liu, X., Wang, J., Karimi, H. R.: Robust $H_{\infty}$ sliding mode control with pole placement for a fluid power electrohydraulic actuator (EHA) system..Int. J. Adv. Manuf. Tech. 73 (2014), 1095-1104. 10.1007/s00170-014-5910-8 |
| Reference:
|
[31] Zhang, B. L., Ma, L., Han, Q.L.: Sliding mode $H_{\infty}$ control for offshore steel jacket platforms subject to nonlinear self-excited wave force and external disturbance..Nonlinear Anal. Real World Appl. 14 (2013), 163-178. Zbl 1254.93062, MR 2969826, 10.1016/j.nonrwa.2012.05.010 |
| Reference:
|
[32] Zadeh, I. H., Mobayen, S.: PSO-based controller for balancing rotary inverted pendulum..J. Appl. Sci. 16 (2008), 2907-2912. 10.3923/jas.2008.2907.2912 |
| Reference:
|
[33] Zhang, J., Xia, Y.: Design of static output feedback sliding mode control for uncertain linear systems..IEEE Trans. Ind. Elec. 57 (2010), 2161-2170. 10.1109/tie.2009.2033485 |
| Reference:
|
[34] Zheng, B. C., Yang, G. H.: $H_2$ control of linear uncertain systems considering input quantization with encoder/decoder mismatch..ISA Trans. 52 (2013), 577-582. MR 3085982, 10.1016/j.isatra.2013.06.002 |
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