Digital second-order sliding mode control for uncertain nonlinear systems. (English) Zbl 0995.93012
The discrete-time implementation of a second-order sliding mode control (2-SMC) scheme is analyzed. In Section 2, the control problem is formulated. In Section 3, the direct discretization of a continuous-time 2-SMC scheme is analyzed, and sufficient conditions for the finite-time reaching of an \(O(T^2)\)-vicinity of the sliding manifold are derived. In Section 4, sufficient conditions under which a sliding motion occurs in an \(O(T^3)\) boundary layer of the desired manifold are derived. Simulations confirm the effectiveness of the proposed method.
Reviewer: Kunihiko Ichikawa (Tokyo)
MSC:
| 93B12 | Variable structure systems |
| 93C55 | Discrete-time control/observation systems |
| 93C62 | Digital control/observation systems |
| 93C10 | Nonlinear systems in control theory |
References:
| [1] | Bartolini, G.; Ferrara, A.; Usai, E., Chattering avoidance by second order sliding mode control, IEEE Transactions Automatic Control, 43, 241-246 (1998) · Zbl 0904.93003 |
| [2] | Bartolini, G.; Ferrara, A.; Utkin, V. I., Adaptive sliding mode control in discrete time systems, Automatica, 31, 769-773 (1995) · Zbl 0825.93097 |
| [3] | Bartolini, G., Ferrara, A., Levant, A., & Usai, E. (1999a). On second order sliding mode controllers. In K.D. Young, & U. Ozguner (Eds.), Variable structure systemssliding mode and nonlinear control; Bartolini, G., Ferrara, A., Levant, A., & Usai, E. (1999a). On second order sliding mode controllers. In K.D. Young, & U. Ozguner (Eds.), Variable structure systemssliding mode and nonlinear control · Zbl 0940.93018 |
| [4] | Bartolini, G.; Ferrara, A.; Pisano, A.; Usai, E., Adaptive reduction of the control effort in chattering free sliding mode control of uncertain nonlinear systems, Journal of Applied Mathematics and Computer Science, 8, 51-71 (1998) · Zbl 0900.93051 |
| [5] | Bartolini, G., Pisano, A., & Usai, E. (1999b). Variable structure control of nonlinear sampled data systems by second order sliding modes. In K.D. Young, & U. Ozguner (Eds.), Variable structure systemssliding mode and nonlinear control; Bartolini, G., Pisano, A., & Usai, E. (1999b). Variable structure control of nonlinear sampled data systems by second order sliding modes. In K.D. Young, & U. Ozguner (Eds.), Variable structure systemssliding mode and nonlinear control · Zbl 0938.93014 |
| [6] | Corradini, M. L. (1998). A variable structure approach to the robust stabilization of a class of discrete-time nonlinear systems. Proceedings of the IFAC Symposium on Nonlinear Control Systems—NOLCOS; Corradini, M. L. (1998). A variable structure approach to the robust stabilization of a class of discrete-time nonlinear systems. Proceedings of the IFAC Symposium on Nonlinear Control Systems—NOLCOS |
| [7] | Drakunov, S. V., Özguner, Ü., & Su, W. C. (1996). Implementation of variable structure control for sampled-data systems. In F. Garofalo, & L. Glielmo (Eds.), Robust control via variable structure and Lyapunov techniques; Drakunov, S. V., Özguner, Ü., & Su, W. C. (1996). Implementation of variable structure control for sampled-data systems. In F. Garofalo, & L. Glielmo (Eds.), Robust control via variable structure and Lyapunov techniques · Zbl 0859.93012 |
| [8] | Furuta, K.; Pan, Y., Variable structure control with sliding sector, Automatica, 36, 211-228 (2000) · Zbl 0938.93011 |
| [9] | Isidori, A., Nonlinear control systems (1995), Springer: Springer New York · Zbl 0569.93034 |
| [10] | Levant, A., Sliding order and sliding accuracy in sliding mode control, International Journal of Control, 58, 1247-1263 (1993) · Zbl 0789.93063 |
| [11] | Milosavljevic, C., General conditions for the existence of a quasisliding mode on the switching hyperplane in discrete variable structure systems, Automation Remote Control, 46, 307-314 (1985) · Zbl 0583.93043 |
| [12] | Utkin, V. I., Sliding modes in control and optimization (1992), Springer: Springer Verlag, Berlin · Zbl 0748.93044 |
| [13] | Utkin, V. I., & Drakunov, S. V. (1989). On discrete-time sliding mode control. Proceedings of the IFAC Symposium on Nonlinear Control Systems—NOLCOS; Utkin, V. I., & Drakunov, S. V. (1989). On discrete-time sliding mode control. Proceedings of the IFAC Symposium on Nonlinear Control Systems—NOLCOS |
| [14] | Young, K. K.D.; Özguner, Ü.; Utkin, V. I., A control engineers guide to sliding mode control, IEEE Transactions on Control Systems Technology, 7, 328-342 (1999) |
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.
