Abstract
Conventional sliding mode control, studied in Chap. 2, and second-order sliding mode control (Chap. 4) are the most obvious choices in controlling systems with bounded matched disturbances/uncertainties. Sliding mode control laws allow us achieve to insensitivity of system’s compensated dynamics to these perturbations. The ultimate price for this insensitivity is a high-frequency (that is equal to infinity in an ideal sliding mode) switching control function that after being filtered by the plant yields self-sustained oscillations of almost zero amplitude. The main advantage of higher (second-)order sliding mode control is its ability to guarantee higher accuracy of the sliding variable stabilization at zero than conventional sliding mode control.
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- 1.
- 2.
There exists a method named the locus of a perturbed relay system Locus of Perturbed Relay System (LPRS) [29] that gives an exact analysis of limit cycles in perturbed relay systems. However, the LPRS method is computationally much more intensive than DF method. Conversely, the DF method is simple and efficient and provides accuracy sufficient for the analysis of practical systems.
- 3.
For details see [100].
- 4.
For details, see, for example,[39].
References
Aguilar, L., Boiko, I., Fridman, L., Iriarte, R.: Generating self-excited oscillations for underactuated mechanical systems via two-relay controller. Int. J. Control 82(9), 1678–1691 (2009)
Aguilar, L., Boiko, I., Fridman, L., Iriarte, R.: Oscillations via two-relay controller. IEEE Trans. Automat. Contr. 54(2), 416–420 (2009)
Anosov, D.V.: On stability of equilibrium points of relay systems. Automat. Rem. Contr. 20(2), 135–149 (1959)
Atherton, D.P.: Nonlinear Control Engineering – Describing Function Analysis and Design. Van Nostrand Company Limited, Workingham, Berkshire (1975)
Boiko, I.: Frequency domain analysis of fast and slow motions in sliding modes. Asian J. Control 5(4), 445–453 (2003)
Boiko, I.: Discontinuous Control Systems: Frequency-Domain Analysis and Design. Birkhauser, Boston (2009)
Boiko, I.: On frequency-domain criterion of finite-time convergence of second-order sliding mode control algorithms. Automatica 47(9), 1969–1973 (2011)
Boiko, I., Fridman, L., Castellanos, M.I.: Analysis of second order sliding mode algorithms in the frequency domain. IEEE Trans. on Automat. Contr. 49(6), 946–950 (2004)
Boiko, I., Fridman, L., Pisano, A., Usai, E.: Analysis of chattering in systems with second order sliding modes. IEEE Trans. Automat. Contr. 52(11), 2085–2102 (2007)
Boiko, I., Fridman, L., Pisano, A., Usai, E.: Performance analysis of second-order sliding-mode control systems with fast actuators. IEEE Trans. Automat. Contr. 52(6), 1053–1059 (2007)
Boiko, I., Fridman, L., Pisano, A., Usai, E.: On the transfer properties of the generalized sub-optimal second-order sliding mode control algorithm. IEEE Trans. Automat. Contr. 54(2), 399–403 (2009)
Burlington, R.S.: Handbook of Mathematical Tables and Formulas. McGraw-Hill, New York (1973)
Fridman, L.: An averaging approach to chattering. IEEE Trans. Automat. Contr. 46(8), 1260–1264 (2001)
Fridman, L.: Chattering analysis in sliding mode systems with inertial sensors. Int. J. Control 76(9/10), 906–912 (2003)
Gelb, A., Vander Velde, W.E.: Multiple-Input Describing Functions and Nonlinear System Design. McGraw-Hill, New York (1968)
Kobayashi, S., Furuta, K.: Frequency characteristics of Levant’s differentiator and adaptive sliding mode differentiator. Int. J. Syst. Sci. 38(10), 825–832 (2007)
Pisano, A., Usai, E.: Contact force regulation in wire-actuated pantographs via variable structure control and frequency-domain techniques. Int. J. Control 81(11), 1747–1762 (2008)
Shtessel, Y.B., Lee, Y.J.: New approach to chattering analysis in systems with sliding modes. In: Proceedings of 35th IEEE Conference on Decision and Control, pp. 4014–4019, Kobe, Japan (1996)
Tsypkin, Y.Z.: Relay Control Systems. Cambridge University press, Cambridge (1984)
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Shtessel, Y., Edwards, C., Fridman, L., Levant, A. (2014). Analysis of Sliding Mode Controllers in the Frequency Domain. In: Sliding Mode Control and Observation. Control Engineering. Birkhäuser, New York, NY. https://doi.org/10.1007/978-0-8176-4893-0_5
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