| Title:
|
Tracking through singularities using sliding mode differentiators (English) |
| Author:
|
Castillo-Toledo, Bernardino |
| Author:
|
Di Gennaro, Stefano |
| Author:
|
López-Cuevas, Armando |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 (print) |
| ISSN:
|
1805-949X (online) |
| Volume:
|
51 |
| Issue:
|
1 |
| Year:
|
2015 |
| Pages:
|
20-35 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this work, an alternative solution to the tracking problem for a SISO nonlinear dynamical system exhibiting points of singularity is given. An inversion-based controller is synthesized using the Fliess generalized observability canonical form associated to the system. This form depends on the input and its derivatives. For this purpose, a robust exact differentiator is used for estimating the control derivatives signals with the aim of defining a control law depending on such control derivative estimates and on the system state variables. This control law is such that, when applied to the system, bounded tracking error near the singularities is guaranteed. (English) |
| Keyword:
|
singularities |
| Keyword:
|
sliding mode differentiator |
| Keyword:
|
tracking |
| MSC:
|
41A30 |
| MSC:
|
93B12 |
| MSC:
|
93C10 |
| idZBL:
|
Zbl 06433830 |
| idMR:
|
MR3333831 |
| DOI:
|
10.14736/kyb-2015-1-0020 |
| . |
| Date available:
|
2015-03-23T18:45:10Z |
| Last updated:
|
2016-01-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144200 |
| . |
| Reference:
|
[1] Becerra, H. M., López-Nicolás, G., Sagués, C.: A sliding-mode-control law for mobile robots based on epipolar visual servoing from three views..IEEE Trans. Robotics 27 (2011), 1, 175-183. 10.1109/tro.2010.2091750 |
| Reference:
|
[2] Benosman, M., Vey, G. Le: Stable inversion of SISO nonminimum phase linear systems through output planning: An experimental application to the one-link flexible manipulator..IEEE Trans. Control Systems Technol. 11 (2003), 4, 588-597. 10.1109/tcst.2003.813372 |
| Reference:
|
[3] Castillo, B.: Output tracking through singular points for a class of nonlinear SISO systems.In: Proc. First European Control Conference 1991, pp. 1496-1498. |
| Reference:
|
[4] Devasia, S., Chen, D., Paden, B.: Nonlinear inversion based-output tracking..IEEE Trans. Automat. Control 41 (1996), 7, 930-942. Zbl 0859.93006, MR 1398777, 10.1109/9.508898 |
| Reference:
|
[5] Devasia, S.: Should model-based inverse inputs be used as feedforward under Plant uncertainty?.IEEE Trans. Automat. Control 47 (2002), 11, 1865-1871. MR 1937698, 10.1109/tac.2002.804478 |
| Reference:
|
[6] Fliess, M.: Generalized controller canonical form for linear and nonlinear dynamics..IEEE Trans. Automat. Control 35 (1990), 9, 994-1001. MR 1065035, 10.1109/9.58527 |
| Reference:
|
[7] Hauser, J., Sastry, S., Kokotovic, P.: Nonlinear control via approximate input-output linearization: The Ball and Beam example..In: Proc. 28th Conference on Decision and Control 1989, pp. 1987-1993. MR 1148727, 10.1109/cdc.1989.70513 |
| Reference:
|
[8] Hauser, J., Sastry, S., Kokotovic, P.: Nonlinear control via approximate input-output linearization: The Ball and Beam example..IEEE Trans. Automat. Control 35 (1992), 3, 392-398. MR 1148727, 10.1109/cdc.1989.70513 |
| Reference:
|
[9] Herrero, P., Jaulin, L., Vehí, J., Sainz, M. A.: Guaranteed set-point computation with application to the control of a sailboat..Int. J. Control Automat. Systems 8 (2010), 1, 1-7. 10.1007/s12555-010-0101-3 |
| Reference:
|
[10] Hirschorn, R. M.: Incremental sliding mode control of the Ball and Beam..IEEE Trans. Automat. Control 47 (2002), 10, 1696-1700. MR 1929943, 10.1109/tac.2002.803538 |
| Reference:
|
[11] Hirschorn, R., Davis, J.: Output tracking for nonlinear systems with singular points..SIAM J. Control Optim. 25 (1987), 3, 547-557. Zbl 0624.93008, MR 0885184, 10.1137/0325030 |
| Reference:
|
[12] Isidori, A.: Nonlinear Control System..Springer Verlag, Berlin 1989. 10.1007/978-3-662-02581-9 |
| Reference:
|
[13] Krener, A.: Approximate linearization by state feedback..SIAM J. Control Optim. 25 (1987), 3, 547-557. Zbl 0555.93027 |
| Reference:
|
[14] Lamnabhi-Lagarrigue, F., Crouch, P. E., Ighneiwa, I.: Tracking through singularities..In: New Trends in Control Theory, Lect. Notes in Control and Inform. Sci. Springer Berlin Heidelberg 122 (1989), pp. 44-53. Zbl 0718.93023, MR 1229764, 10.1007/bfb0043016 |
| Reference:
|
[15] Levant, A.: Robust exact differentiation via sliding mode technique..Automatica 34 (1998), 3, 379-384. Zbl 0915.93013, MR 1623077, 10.1016/s0005-1098(97)00209-4 |
| Reference:
|
[16] Levant, A.: Higher-order sliding modes, differentiation and output feedback control..Int. J. Control 76 (2003), 9/10, 924-945. Zbl 1049.93014, MR 1999375, 10.1080/0020717031000099029 |
| Reference:
|
[17] Levant, A.: Homogeneity approach to high-order sliding mode design..Automatica 41 (2005), 5, 823-830. Zbl 1093.93003, MR 2157713, 10.1016/j.automatica.2004.11.029 |
| Reference:
|
[18] Márton, L., Hodel, A. S., Lantos, B., Hung, J.: Underactuated robot control: Comparing LQR, subspace stabilization, and combined error metric approaches..IEEE Trans. Industr. Electron. 55 (2008), 10, 3724-3730. 10.1109/tie.2008.923285 |
| Reference:
|
[19] Perruquetti, W., Floquet, T.: Homogeneous finite time observer for nonlinear systems with linearizable error dynamics..In: Proc. 46th IEEE Conference on Decision and Control, New Orleans 2007, pp. 12-14. 10.1109/cdc.2007.4434702 |
| Reference:
|
[20] Saif, M., Chen, W., Wu, Q.: High order sliding mode observers and differentiators - application to fault diagnosis problem..In: Modern Sliding Mode Control Theory, Lect. Notes in Control and Inform. Sci. Springer, Berlin - Heidelgerg 375 (2008) pp. 321-344. Zbl 1145.93315, MR 2454142, 10.1007/978-3-540-79016-7_15 |
| Reference:
|
[21] Sira-Ramirez, H.: The differential algebraic approach in nonlinear dynamical feedback controlled landing maneuvers..IEEE Trans. Automat. Control 37 (1992), 4, 518-524. MR 1153118, 10.1109/9.126590 |
| Reference:
|
[22] Tomlin, C., Sastry, S.: Switching through singularities..Systems Control Lett. 35 (1998), 145-154. Zbl 0909.93032, MR 1749610, 10.1016/s0167-6911(98)00046-2 |
| Reference:
|
[23] Utkin, V., Gulden, J., Shi, J.: Sliding Modes in Electromechanical Systems..Taylor and Francis, London 1999. |
| Reference:
|
[24] Yu, Z., Fan, G.: Jianqiang Yi. Indirect adaptive flight control based on nonlinear inversion..In: Proc. 2009 IEEE International Conference on Mechatronics and Automation 2009, pp. 3787-3792. 10.1109/icma.2009.5246179 |
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