Disturbance attenuation of nonlinear control systems using an observer-based fuzzy feedback linearization control. (English) Zbl 1136.93023
Summary: The almost disturbance decoupling and trajectory tracking of nonlinear control systems using an observer-based fuzzy feedback linearization control (FLC) is developed. Because not all of the state variables of the nonlinear dynamic equations are available, a nonlinear state observer is employed to estimate the state variables. The feedback linearization control guarantees the almost disturbance decoupling performance and the uniform ultimate bounded stability of the tracking error system. Once the tracking errors are driven to touch the global final attractor with the desired radius, the fuzzy logic control is immediately applied via human expert’s knowledge to improve the convergence rate. One example, which cannot be solved by the first paper on the almost disturbance decoupling problem, is proposed in this paper to exploit the fact that the tracking and the almost disturbance decoupling performances are easily achieved by our proposed approach. In order to demonstrate the practical applicability, the study has investigated a pendulum control system.
MSC:
| 93C42 | Fuzzy control/observation systems |
| 93C10 | Nonlinear systems in control theory |
| 93B18 | Linearizations |
| 93B52 | Feedback control |
| 70Q05 | Control of mechanical systems |
References:
| [1] | Alleyne A. A systematic approach to the control of electrohydraulic servosystems. In: Proceedings of the American control conference, Philadelphia (PA), June, 1998. p. 833-7.; Alleyne A. A systematic approach to the control of electrohydraulic servosystems. In: Proceedings of the American control conference, Philadelphia (PA), June, 1998. p. 833-7. |
| [2] | Ball, J. A.; Helton, J. W.; Walker, M. L., \(H^∞\) control for nonlinear systems with output feedback, IEEE Trans Automat Contr, 38, April, 546-559 (1993) · Zbl 0782.93032 |
| [3] | Bedrossian NS. Approximate feedback linearization: the car-pole example. In: Proceedings of the 1992 IEEE international conference on robotics and automation, France, Nice, May, 1992. p. 1987-92.; Bedrossian NS. Approximate feedback linearization: the car-pole example. In: Proceedings of the 1992 IEEE international conference on robotics and automation, France, Nice, May, 1992. p. 1987-92. |
| [4] | Bowong, S.; Kakmeni, F. M.M., Synchronization of uncertain chaotic systems via backstepping approach, Chaos, Solitons & Fractals, 21, 4, 999-1011 (2004) · Zbl 1045.37011 |
| [5] | Chen, B. S.; Lee, C. H.; Chang, Y. C., \(H^∞\) tracking design of uncertain nonlinear SISO systems: adaptive fuzzy approach, IEEE Trans Fuzzy Syst, 4, 1, 32-43 (1996) |
| [6] | Corless, M. J.; Leitmann, G., Continuous state feedback guaranteeing uniform ultimate boundedness for uncertain dynamic systems, IEEE Trans Automat Contr, 26, 5, 1139-1144 (1981) · Zbl 0473.93056 |
| [7] | Gopalswamy, S.; Hedrick, J. K., Tracking nonlinear nonminimum phase systems using sliding control, Int J Contr, 57, May, 1141-1158 (1993) · Zbl 0772.93030 |
| [8] | Henson, M. A.; Seborg, D. E., Critique of exact linearization strategies for process control, J Process Contr, 1, 122-139 (1991) |
| [9] | Huang, X.; Cao, J.; Huang, D. S., LMI-based approach for delay-dependent exponential stability analysis of BAM neural networks, Chaos, Solitons & Fractals, 24, 3, 885-898 (2005) · Zbl 1071.82538 |
| [10] | Huang, J.; Rugh, W. J., On a nonlinear multivariable servomechanism problem, Automatica, 26, June, 963-992 (1990) · Zbl 0717.93019 |
| [11] | Isidori, A., Nonlinear control system (1989), Springer-Verlag: Springer-Verlag New York · Zbl 0674.93052 |
| [12] | Isidori, A., \(H^∞\) control via measurement feedback for affine nonlinear systems, Int J Robust Nonlinear Contr (1994) · Zbl 0806.93016 |
| [13] | Isidori, A.; Byrnes, C. I., Output regulation of nonlinear systems, IEEE Trans Automat Contr, 35, February, 131-140 (1990) · Zbl 0704.93034 |
| [14] | Isidori, A.; Kang, W., \(H^∞\) control via measurement feedback for general nonlinear systems, IEEE Trans Automat Contr, 40, March, 466-472 (1995) · Zbl 0822.93029 |
| [15] | Joo, S. J.; Seo, J. H., Design and analysis of the nonlinear feedback linearizing control for an electromagnetic suspension system, IEEE Trans Automat Contr, 5, 1, 135-144 (1997) |
| [16] | Kawamoto, S.; Tada, K.; Ishigame, A.; Taniguchi, T., An approach to stability analysis of second order fuzzy systems, IEEE Int Conf Fuzzy Syst, 1427-1434 (1992) |
| [17] | Khalil, H. K., Nonlinear systems (1996), Prentice-Hall: Prentice-Hall New Jersey · Zbl 0626.34052 |
| [18] | Khorasani, K.; Kokotovic, P. V., A corrective feedback design for nonlinear systems with fast actuators, IEEE Trans Automat Contr, 31, 67-69 (1986) · Zbl 0582.93054 |
| [19] | Kim, J. H.; Park, C. W.; Kim, E.; Park, M., Adaptive synchronization of T-S fuzzy chaotic systems with unknown parameters, Chaos, Solitons & Fractals, 24, 5, 1353-1361 (2005) · Zbl 1092.37512 |
| [20] | Lam, H. K.; Leung, F. H.F.; Tam, P. K.S., Fuzzy state feedback controller for nonlinear systems: Stability analysis and design, IEEE Int Conf Fuzzy Syst, 2, 677-681 (2002) |
| [21] | Lee SY, Lee JI, Ha IJ. A new approach to nonlinear autopilot design for bank-to-turn missiles. In: Proceedings of the 36th conference on decision and control, San Diego (CA), December, 1997. p. 4192-7.; Lee SY, Lee JI, Ha IJ. A new approach to nonlinear autopilot design for bank-to-turn missiles. In: Proceedings of the 36th conference on decision and control, San Diego (CA), December, 1997. p. 4192-7. |
| [22] | Lee KW, Singh SN. Robust control of chaos in Chua’s circuit based on internal model principle. Chaos, Solitons & Fractals, in press, doi:10.1016/j.chaos.2005.10.058.; Lee KW, Singh SN. Robust control of chaos in Chua’s circuit based on internal model principle. Chaos, Solitons & Fractals, in press, doi:10.1016/j.chaos.2005.10.058. · Zbl 1143.93313 |
| [23] | Marino, R.; Kokotovic, P. V., A geometric approach to nonlinear singularly perturbed systems, Automatica, 24, 31-41 (1988) · Zbl 0633.93033 |
| [24] | Marino, R.; Respondek, W.; Van Der Schaft, A. J., Almost disturbance decoupling for single-input single-output nonlinear systems, IEEE Trans Automat Contr, 34, 9, 1013-1017 (1989) · Zbl 0693.93030 |
| [25] | Marino, R.; Tomei, P., Nonlinear output feedback tracking with almost disturbance decoupling, IEEE Trans Automat Contr, 44, 1, 18-28 (1999) · Zbl 0967.93042 |
| [26] | Miller, R. K.; Michel, A. N., Ordinary differential equations (1982), Academic Press: Academic Press New York · Zbl 0499.34024 |
| [27] | Nijmeijer, H.; Van Der Schaft, A. J., Nonlinear dynamical control systems (1990), Springer-Verlag: Springer-Verlag New York · Zbl 0701.93001 |
| [28] | Park, J. H.; Kwon, O. M., LMI optimization approach to stabilization of time-delay chaotic systems, Chaos, Solitons & Fractals, 23, 2, 445-450 (2005) · Zbl 1061.93509 |
| [29] | Peroz, H.; Ogunnaike, B.; Devasia, S., Output tracking between operating points for nonlinear processes: Van de Vusse example, IEEE Trans Contr Syst Technol, 10, 4, 611-617 (2002) |
| [30] | Qian, C.; Lin, W., Almost disturbance decoupling for a class of high-order nonlinear systems, IEEE Trans Automat Contr, 45, 6, 1208-1214 (2000) · Zbl 0968.93056 |
| [31] | Van der Schaft, A. J., \(L_2\)-gain analysis of nonlinear systems and nonlinear state feedback \(H^∞\) control, IEEE Trans Automat Contr, 37, June, 770-784 (1992) · Zbl 0755.93037 |
| [32] | Sheen JJ, Bishop RH. Adaptive nonlinear control of spacecraft. In: Proceedings of the American control conference, Baltlmore (MD), June, 1998. p. 2867-71.; Sheen JJ, Bishop RH. Adaptive nonlinear control of spacecraft. In: Proceedings of the American control conference, Baltlmore (MD), June, 1998. p. 2867-71. |
| [33] | Slotine, J. J.E.; Li, W., Applied nonlinear control (1991), Prentice-Hall: Prentice-Hall New York · Zbl 0753.93036 |
| [34] | Swaroop, D.; Hedrick, J. K.; Yip, P. P.; Gerdes, J. C., Dynamic surface control for a class of nonlinear systems, IEEE Trans Automat Contr, 45, 10, 1893-1899 (2000) · Zbl 0991.93041 |
| [35] | Tanaka, K.; Hori, T.; Wang, H. O., A multiple Lyapunov function approach to stabilization of fuzzy control systems, IEEE Int Conf Fuzzy Syst, 11, 4, 582-589 (2003) |
| [36] | Tanaka K, Sugeno M. Stability analysis of fuzzy control systems using Lyapunov’s direct method. In: Proceedings of the NAFIPS’90, 1990. p. 133-6.; Tanaka K, Sugeno M. Stability analysis of fuzzy control systems using Lyapunov’s direct method. In: Proceedings of the NAFIPS’90, 1990. p. 133-6. |
| [37] | Tanaka, K.; Sugeno, M., Stability analysis and design of fuzzy control systems, Fuzzy Sets Syst, 45, 2, 135-156 (1992) · Zbl 0758.93042 |
| [38] | Wang, C. C.; Su, J. P., A new adaptive variable structure control for chaotic synchronization and secure communication, Chaos, Solitons & Fractals, 20, 5, 967-977 (2004) · Zbl 1050.93036 |
| [39] | Wang, H. O.; Tanaka, K.; Griffin, M. F., An approach to fuzzy control of nonlinear systems: stability and design issues, IEEE Trans Fuzzy Syst, 4, 14-23 (1996) |
| [40] | Weiland, S.; Willems, J. C., Almost disturbance decoupling with internal stability, IEEE Trans Automat Contr, AC-34, 3, 277-286 (1989) · Zbl 0674.93014 |
| [41] | Willems, J. C., Almost invariant subspace: an approach to high gain feedback design - Part I: almost controlled invariant subspaces, IEEE Trans Automat Contr, AC-26, 1, 235-252 (1981) · Zbl 0463.93020 |
| [42] | Yager, R. R.; Filev, D. P., Essentials of fuzzy modeling and control (1994), Wiley: Wiley New York |
| [43] | Yan, J. J., \(H_∞\) controlling hyperchaos of the Rössler system with input nonlinearity, Chaos, Solitons & Fractals, 21, 2, 283-293 (2004) · Zbl 1049.93040 |
| [44] | Yan, J. J.; Shyu, K. K.; Lin, J. S., Adaptive variable structure control for uncertain chaotic systems containing dead-zone nonlinearity, Chaos, Solitons & Fractals, 25, 2, 347-355 (2005) · Zbl 1125.93472 |
| [45] | Yip, P. P.; Hedrick, J. K., Adaptive dynamic surface control: a simplified algorithm for adaptive backstepping control of nonlinear systems, Int J Contr, 71, 5, 959-979 (1998) · Zbl 0969.93037 |
| [46] | Zhang, H.; Yu, J., LMI-based stability analysis of fuzzy large-scale systems with time delays, Chaos, Solitons & Fractals, 25, 5, 1193-1207 (2005) · Zbl 1142.93376 |
| [47] | Zhang, J.; Li, C.; Zhang, H.; Yu, J., Chaos synchronization using single variable feedback based on backstepping method, Chaos, Solitons & Fractals, 21, 5, 1183-1193 (2004) · Zbl 1129.93518 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
