Linear unstable plants with saturating actuators: robust stabilization by a time varying sliding surface. (English) Zbl 1140.93467
Summary: This paper proposes the use of a time-varying sliding surface for the robust stabilization of linear uncertain SISO plants with saturating actuators. A constructive procedure for its design is also proposed, and stability of the closed loop system is proved in the null controllable region. The proposed technique does not require plant stability, and can manage any bounded disturbance term satisfying the matching condition. Theoretical results have been validated by simulation using the missile roll angle control problem.
MSC:
| 93D21 | Adaptive or robust stabilization |
| 93C05 | Linear systems in control theory |
| 93C15 | Control/observation systems governed by ordinary differential equations |
Software:
MatlabReferences:
| [1] | Bernstein, D. S.; Michel, A. N., Chronological bibiliography on saturating actuators, International Journal of Robust and Nonlinear Control, 5, 5, 375-380 (1995) · Zbl 0841.93002 |
| [2] | Chen, B. M.; Lee, T. H.; Venkataramanan, V., Composite nonlinear feedback control for linear systems with input saturation: Theory and an application, IEEE Transactions on Automatic Control, AC-48, 3, 427-439 (2003) · Zbl 1364.93294 |
| [3] | De Donà, J. A.; Goodwin, G. C.; Moheiami, S. O.R., Combining switching, over-saturation and scaling to optimise control performance in the presence of model uncertainty and input saturation, Automatica, 38, 1153-1162 (2002) · Zbl 1002.93017 |
| [4] | Emelyanov, S. V.; Korovin, S. K.; Mamedov, I. G., Variable structure control systems: Discrete and digital (1995), Mir Publishers: Mir Publishers Moscow · Zbl 0939.93500 |
| [5] | Fuller, A. T., In the large stability of relay and saturating control systems with linear controllers, International Journal of Control, 10, 4, 457-480 (1969) · Zbl 0176.39302 |
| [6] | Gokcek, C.; Kabamba, P. T.; Merkoov, S. M., An LQR/LQG theory for systems with saturating actuators, IEEE Transactions on Automatic Control, AC-46, 10, 1529-1542 (2001) · Zbl 1007.93078 |
| [7] | Grimm, G.; Teel, A. R.; Zaccarian, L., A linear LMI-based external anti-windup augmentation for stable linear systems, Automatica, 40, 1987-1996 (2004) · Zbl 1059.93048 |
| [8] | Hippe, P.; Wurmthaler, C., Systematic closed-loop design in the presence of input saturations, Automatica, 35, 689-695 (1999) · Zbl 0925.93247 |
| [9] | Hippe, P.; Wurmthaler, C., Windup prevention for unstable systems, Automatica, 39, 1967-1973 (2003) · Zbl 1046.93021 |
| [10] | Hu, T.; Lin, Z.; Qiu, L., Stabilization of exponentially unstable linear systems with saturating actuators, IEEE Transactions on Automatic Control, AC-46, 6, 973-979 (2001) · Zbl 1032.93063 |
| [11] | Lin, Z., Global control of linear systems with saturating actuators, Automatica, 34, 897-905 (1998) · Zbl 0934.93059 |
| [12] | Lin, Z.; Saberi, A., Semi-global exponential stabilization of linear systems subject to input saturation via linear feedbacks, Systems & Control Letters, 21, 225-239 (1993) · Zbl 0788.93075 |
| [13] | Lin, Z.; Saberi, A., Semi-global exponential stabilization of linear discrete-time systems subject to input saturation via linear feedbacks, Systems & Control Letters, 24, 125-132 (1995) · Zbl 0877.93095 |
| [14] | Saberi, A., Lin, Z., & Teel, A. R. (1995). Control of linear systems with saturating actuators. Proceedings of 34th IEEE conference on decision and control; Saberi, A., Lin, Z., & Teel, A. R. (1995). Control of linear systems with saturating actuators. Proceedings of 34th IEEE conference on decision and control · Zbl 0853.93046 |
| [15] | Sontag, E. D., An algebraic approach to bounded controllability of linear systems, International Journal of Control, 39, 181-188 (1984) · Zbl 0531.93013 |
| [16] | Sontag, E. D., & Sussman, H. J., (1990). Nonlinear output feedback design for linear systems with saturating controls. Proceedings of the 29th IEEE conference on decision and control; Sontag, E. D., & Sussman, H. J., (1990). Nonlinear output feedback design for linear systems with saturating controls. Proceedings of the 29th IEEE conference on decision and control |
| [17] | Sussmann, H. J.; Sontag, E. D.; Yang, Y., A general result on the stabilization of linear systems using bounded controls, IEEE Transactions on Automatic Control, AC-39, 2411-2425 (1994) · Zbl 0811.93046 |
| [18] | Sussman, H. J., & Yang, Y., (1991). On the stabilizability of multiple integrators by means of bounded feedback controls. Proceedings of the 30th IEEE conference on decision and control; Sussman, H. J., & Yang, Y., (1991). On the stabilizability of multiple integrators by means of bounded feedback controls. Proceedings of the 30th IEEE conference on decision and control |
| [19] | Teel, A. R., Global stabilization and restricted tracking for multiple integrators with bounded controls, Systems & Control Letters, 18, 165-171 (1992) · Zbl 0752.93053 |
| [20] | Teel, A. R., Anti-windup for exponentially unstable linear systems, International Journal of Robust and Nonlinear Control, 9, 701-716 (1999) · Zbl 0936.93022 |
| [21] | Tibaldi, M., (1993). Note introductive a MATLAB e control system toolbox\( \langle\) http://www.mathworks.com/support/books/book1399.html \(\rangle \); Tibaldi, M., (1993). Note introductive a MATLAB e control system toolbox\( \langle\) http://www.mathworks.com/support/books/book1399.html \(\rangle \) |
| [22] | Utkin, V. I., Sliding modes in control optimization (1992), Springer: Springer Berlin · Zbl 0748.93044 |
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.
