Variable measurement step in 2-sliding control

Levant, Arie

Kybernetika, Tome 36 (2000) no. 1, pp. 77-93

Abstract (VO)

Sliding mode is used in order to retain a dynamic system accurately at a given constraint and features theoretically-infinite-frequency switching. Standard sliding modes are known to feature finite time convergence, precise keeping of the constraint and robustness with respect to internal and external disturbances. Having generalized the notion of sliding mode, higher order sliding modes preserve or generalize its main properties, improve its precision with discrete measurements and remove the chattering effect. However, in their standard form, most of higher order sliding controllers are sensitive to measurement errors. A special measurement step feedback is introduced in the present paper, which solves that problem without loss of precision. The approach is demonstrated on a so-called twisting algorithm. Its asymptotic properties are studied in the presence of vanishing measurement errors. A model illustration and simulation results are presented.

Détail

Classification : 93B12, 93B40, 93B51, 93C10
Keywords: sliding mode control; twisting algorithm

Bibliographie

[1] G. G. Bartolini, Ferrara A., Usai E.: Chattering avoidance by second–order sliding mode control. IEEE Trans. Automat. Control 43 (1998), 2, 241–246 | DOI | MR | Zbl

[2] Bartolini G., Ferrara A., Usai E., Utkin V. I.: Second order chattering–free sliding mode control for some classes of multi–input uncertain nonlinear systems. In: Proc. of the 6th IEEE Mediterranean Conference on Control and Systems, Alghero 1998

[3] Ben–Asher J. Z., Gitizadeh R., Levant A., Pridor A., Yaesh I.: 2–sliding mode implementation in aircraft pitch control. In: Proc. of 5th European Control Conference, Karlsruhe 1999

[4] Elmali H., Olgac N.: Robust output tracking control of nonlinear MIMO systems via sliding mode technique. Automatica 28 (1992), 1, 145–151 | DOI | MR

[5] Emelyanov S. V., Korovin S. K., Levantovsky L. V.: Higher order sliding regimes in the binary control systems. Soviet Phys. Dokl. 31 (1986), 4, 291–293

[6] Emelyanov S. V., Korovin S. K., Levant A.: Higher–order sliding modes in control systems. Differential Equations 29 (1993), 11, 1627–1647 | MR

[7] Filippov A. F.: Differential Equations with Discontinuous Right–Hand Side. Kluwer, Dordrecht 1988 | Zbl

[8] Fridman L., Levant A.: Sliding modes of higher order as a natural phenomenon in control theory. In: Robust Control via Variable Structure & Lyapunov Techniques (Lecture Notes in Control and Inform. Sci. 217, F. Garofalo, L. Glielmo, eds.). Springer–Verlag, London 1996, p. 107 | MR

[9] Isidori A.: Nonlinear Control Systems. Springer–Verlag, New York 1989 | MR | Zbl

[10] Levantovsky) A. Levant (L. V.: Sliding order and sliding accuracy in sliding mode control. Internat. J. Control 58 (1993), 6, 1247–1263 | DOI | MR

[11] Levant A.: Robust exact differentiation via sliding mode technique. Automatica 34 (1998), 3, 379–384 | DOI | MR | Zbl

[12] Levant A.: Arbitrary–order sliding modes with finite time convergence. In: Proc. of the 6th IEEE Mediterranean Conference on Control and Systems, Alghero 1998

[13] Levantovsky L. V.: Second order sliding algorithms: their realization. In: Dynamics of Heterogeneous Systems, Institute for System Studies, Moscow 1985, pp. 32–43. In Russian

[14] Sira–Ramírez H.: On the dynamical sliding mode control of nonlinear systems. Internat. J. Control 57 (1993), 5, 1039–1061 | DOI | MR | Zbl

[15] Slotine J.-J. E., Sastry S. S.: Tracking control of non-linear systems using sliding surfaces, with applications to robot manipulators. Internat. J. Control 38 (1983), 465–492 | DOI | MR

[16] Utkin V. I.: Sliding Modes in Optimization and Control Problems. Springer–Verlag, New York 1992 | MR

[17] Zinober A.: Variable Structure and Lyapunov Control. Springer–Verlag, London 1994 | MR | Zbl