© The Institution of Engineering and Technology
In this study, an intelligent digital redesign (IDR) technique is proposed for an observer-based sampled-data fuzzy controller of non-linear systems. By using a Takagi–Sugeno fuzzy model, the pre-designed analog and sampled-data fuzzy controllers are supposed, and these discretised closed-loop systems are obtained, respectively. Based on the IDR problem, the authors guarantee both stability and state-matching conditions. Unlike the previous techniques, the proposed IDR not only improves the state-matching performance using the state-matching error cost function, but is also derived in the strict linear matrix inequality format. In a numerical example, the effectiveness of the proposed technique and the results of the improved performance are shown.
References
-
-
1)
-
1. Lien, C.-H.: ‘Robust observer-based control of systems with state perturbations via LMI approach’, IEEE Trans. Autom. Control, 2004, 49, (8), pp. 1365–1370 (doi: 10.1109/TAC.2004.832660).
-
2)
-
35. Ding, B., Sun, H., Yang, P.: ‘Further studies on LMI-based relaxed stabilization conditions for nonlinear systems in Takagi–Sugeno's form’, Automatica, 2006, 42, pp. 503–508 (doi: 10.1016/j.automatica.2005.11.005).
-
3)
-
4. chen, W.-H.: ‘Disturbance observer based control for nonlinear systems’, IEEE/ASME Trans. Mechatron., 2004, 9, (4), pp. 706–710 (doi: 10.1109/TMECH.2004.839034).
-
4)
-
11. Tseng, C.S., Chen, B.S.: ‘Robust fuzzy observer-based fuzzy control design for nonlinear discrete-time systems with persistent bounded disturbances’, IEEE Trans. Fuzzy Syst., 2009, 17, (3), pp. 711–723 (doi: 10.1109/TFUZZ.2008.928604).
-
5)
-
36. Guerra, T.M., Bernal, M., Guelton, K., et al : ‘Non-quadratic local stabilization for continuous-time Takagi–Sugeno models’, Fuzzy Sets Syst., 2012, 201, pp. 40–54 (doi: 10.1016/j.fss.2011.12.003).
-
6)
-
39. Boulkroune, A., Tadjine, M., M'Saad, M., et al : ‘Design of a unified adaptive fuzzy observer for uncertain nonlinear systems’, Inf. Sci., 2014, 265, pp. 139–153 (doi: 10.1016/j.ins.2013.12.026).
-
7)
-
26. Sung, H.C., Park, J.B., Joo, Y.H.: ‘Observer-based sampled-data control for nonlinear systems: Robust intelligent digital redesign approach’, Int. J. Control Autom. Syst., 2014, 12, (3), pp. 486–496 (doi: 10.1007/s12555-013-0129-2).
-
8)
-
42. Boulkroune, A., Msaad, M., Farza, M.: ‘State and output feedback fuzzy variable structure controllers for multivariable nonlinear systems subject to input nonlinearities’, Int. J. Manuf. Technol., 2014, 71, pp. 539–556 (doi: 10.1007/s00170-013-5453-4).
-
9)
-
15. Lee, H.J., Kim, H., Joo, Y.H., Chang, W., Park, J.B.: ‘A new intelligent digital redesign: Global approach’, IEEE Trans. Fuzzy Syst., 2004, 12, (2), pp. 274–284 (doi: 10.1109/TFUZZ.2003.819826).
-
10)
-
16. Lee, H.J., Park, J.B., Joo, Y.H.: ‘Digitalizing a fuzzy observer-based output-feedback control: Intelligent digital redesign approach’, IEEE Trans. Fuzzy Syst., 2005, 13, (5), pp. 701–716 (doi: 10.1109/TFUZZ.2005.856556).
-
11)
-
9. Lin, C., Wang, Q.-G., Lee, T.H.: ‘Improvement on observer-based H∞ control for T–S fuzzy systems’, Automatica, 2005, 41, pp. 1651–1656 (doi: 10.1016/j.automatica.2005.04.004).
-
12)
-
14. Chen, T., Francis, B.: ‘Optimal sampled-data control systems’ (Springer, London, 1995).
-
13)
-
3. Leon, A.E., Mauricio, J.M., Solsona, J.A.: ‘Multi-machine power system stability improvement using an observer-based nonlinear controller’, Electr. Power Syst. Res., 2012, 89, pp. 204–214 (doi: 10.1016/j.epsr.2012.01.022).
-
14)
-
13. Joo, Y.H., Shieh, L.-S., Chen, G.: ‘Hybrid state-space fuzzy model-based controller with dual-rate sampling for digital control of chaotic systems’, IEEE Trans. Fuzzy Syst., 1999, 7, (4), pp. 394–408 (doi: 10.1109/91.784199).
-
15)
-
12. Nguang, S.K., Shi, P.: ‘Robust fuzzy observer-based fuzzy control design for nonlinear discrete-time systems with persistent bounded disturbances’, IEEE Trans. Fuzzy Syst., 2003, 11, (3), pp. 331–340 (doi: 10.1109/TFUZZ.2003.812691).
-
16)
-
17)
-
25. Koo, G.B., Park, J.B., Joo, Y.H.: ‘Intelligent digital redesign for nonlinear systems using a guaranteed cost control method’, Int. J. Control Autom. Syst., 2013, 11, (6), pp. 1075–1083 (doi: 10.1007/s12555-013-0093-x).
-
18)
-
10. Chen, B., Liu, X.-P., Tong, S.-C., et al : ‘Observer-based stabilization of T–S fuzzy systems with input delay’, IEEE Trans. Fuzzy Syst., 2008, 16, (3), pp. 652–663 (doi: 10.1109/TFUZZ.2007.903329).
-
19)
-
32. Kim, D.W., Lee, H.J., Tomizuka, M.: ‘Fuzzy stabilization of nonlinear systems under sampled-data feedback: an exact discrete-time model approach’, IEEE Trans. Fuzzy Syst., 2010, 18, (2), pp. 251–260.
-
20)
-
19. Lee, H.J., Shieh, L.-S., Kim, D.W.: ‘Digital control of nonlinear systems: optimal linearisation-based digital redesign approach’, IET Control Theory Appl., 2008, 2, (4), pp. 337–351 (doi: 10.1049/iet-cta:20070074).
-
21)
-
29. Tong, S., Li, Y., Shi, P.: ‘Observer-based adaptive fuzzy backstepping output feedback control of uncertain mimo pure-feedback nonlinear systems’, IEEE Trans. Fuzzy Syst., 2012, 20, (4), pp. 771–85 (doi: 10.1109/TFUZZ.2012.2183604).
-
22)
-
18. Lee, H.J., Park, J.B., Joo, Y.H.: ‘An efficient observer-based sampled-data control: digital redesign approach’, IEEE Trans. Circuits Syst. I, 2003, 50, (12), pp. 1595–1601 (doi: 10.1109/TCSI.2003.819832).
-
23)
-
17. Chang, W., Park, J.B., Lee, H.J., et al : ‘LMI approach to digital redesign of linear time-invariant systems’, IEE Proc. Control Theory Appl., 2002, .
-
24)
-
41. Boulkroune, A., Bouzeriba, A., Hamel, S., et al : ‘A projective synchronization scheme based on fuzzy adaptive control for unknown multivariable chaotic systems’, Nonlinear Dyn., 2014, 78, pp. 433–447 (doi: 10.1007/s11071-014-1450-x).
-
25)
-
21. Sung, H.C., Park, J.B., Joo, Y.H.: ‘Robust control of observer-based sampled-data systems: Digital redesign approach’, IET Control Theory Appl., 2012, 6, (12), pp. 1842–1850 (doi: 10.1049/iet-cta.2010.0580).
-
26)
-
20. Kim, D.W., Park, J.B., Joo, Y.H.: ‘Robust stabilisation of sampled-data control systems with non-linear perturbations via digital redesign’, IET Control Theory Appl., 2009, 3, (8), pp. 1070–1080 (doi: 10.1049/iet-cta.2008.0133).
-
27)
-
16. Shieh, L.S., Wang, W.M., Tsai, J.S.H.: ‘Digital modelling and digital redesign of sampled-data uncertain systems’, IEE Proc. Control Theory Appl., 1995, 42, pp. 585–594 (doi: 10.1049/ip-cta:19952217).
-
28)
-
15. Hu, L.S., Bai, T., Shi, P., et al : ‘Sampled-data control of networked linear control systems’, Automatica, 2007, 43, pp. 903–911 (doi: 10.1016/j.automatica.2006.11.015).
-
29)
-
5. Tong, S., Li, Y.: ‘Observer-based fuzzy adaptive control for strict-feedback nonlinear systems’, Fuzzy Sets Syst., 2009, 160, pp. 1749–1764 (doi: 10.1016/j.fss.2008.09.004).
-
30)
-
34. Zhang, H., Yan, H., Yang, F., et al : ‘Quantized control design for impulsive fuzzy networked systems’, IEEE Trans. Fuzzy Syst., 2011, 19, (6), pp. 1153–1162 (doi: 10.1109/TFUZZ.2011.2162525).
-
31)
-
6. Tanaka, K., Wand, H.O.: ‘Fuzzy control systems design and analysis: a linear matrix inequality approach’ (Wiley, New York, 2001).
-
32)
-
7. Tong, S., Li, H.-H.: ‘Observer-based robust fuzzy control of nonlinear systems with parametric uncertainties’, Fuzzy Sets Syst., 2002, 131, pp. 165–184 (doi: 10.1016/S0165-0114(01)00216-0).
-
33)
-
41. de Oliveira, M.C., Bernussou, J., Geromel, J.C.: ‘A new discrete-time robust stability condition’, Syst. Control Lett., 1999, 37, pp. 261–265 (doi: 10.1016/S0167-6911(99)00035-3).
-
34)
-
29. Kim, D.W., Park, J.B., Joo, Y.H.: ‘Effective digital implementation of fuzzy control systems based on approximate discrete-time models’, Automatica, 2007, 43, pp. 1671–1683 (doi: 10.1016/j.automatica.2007.01.025).
-
35)
-
25. Tong, S., Li, Y., Li, Y., Liu, Y.: ‘Observer-based adaptive fuzzy backstepping control for a class of stochastic nonlinear strict-feedback systems’, IEEE Trans. Syst. Man Cybern. B: Cybern., 2011, 41, (6), pp. 1693–1704 (doi: 10.1109/TSMCB.2011.2159264).
-
36)
-
19. He, S., Liu, F.: ‘Finite-time h∞fuzzy control of nonlinear jump systems with time delays via dynamic observer-based state feedback’, IEEE Trans. Fuzzy Syst., 2012, 20, pp. 605–614 (doi: 10.1109/TFUZZ.2011.2177842).
-
37)
-
2. Lin, C., Wang, Z., Yang, F.: ‘Observer-based networked control for continuous-time systems with random sensor delays’, Automatica, 2009, 45, pp. 578–584 (doi: 10.1016/j.automatica.2008.09.009).
-
38)
-
13. Guerra, T.M., Kruszewski, A., Vermeiren, L., et al : ‘Conditions of output stabilization for nonlinear models in the Takagi–Sugeno's form’, Fuzzy Sets Syst., 2006, 157, pp. 1248–1259 (doi: 10.1016/j.fss.2005.12.006).
-
39)
-
27. Kim, D.W., Lee, H.J.: ‘Sampled-data observer-based output-feedback fuzzy stabilization of nonlinear systems: exact discrete-time design approach’, Fuzzy Set Syst., 2012, 201, pp. 20–39 (doi: 10.1016/j.fss.2011.12.017).
-
40)
-
40. Boulkroune, A., Tadjine, M., M'Saad, M., et al : ‘Adaptive fuzzy observer for uncertain nonliear systems’, Control Intell. Syst., 2011, 39, (3), pp. 145–150.
-
41)
-
23. Li, Z., Park, J.B., Joo, Y.H., Zang, B., Chen, G.: ‘Bifurcations and chaos in a permanent magnet synchronous motor’, IEEE Trans. Circuits Syst. I, 2002, 49, (3), pp. 383–389 (doi: 10.1109/81.989176).
-
42)
-
33. Zhang, H., Yan, H., Liu, T., et al : ‘Fuzzy controller design for nonlinear impulsive fuzzy systems with time delay’, IEEE Trans. Fuzzy Syst., 2011, 19, (5), pp. 844–856 (doi: 10.1109/TFUZZ.2011.2147793).
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-cta.2015.0244
Related content
content/journals/10.1049/iet-cta.2015.0244
pub_keyword,iet_inspecKeyword,pub_concept
6
6