Disturbance-tailored super-twisting algorithms: properties and design framework. (English) Zbl 1415.93075
Summary: Second- and higher-order sliding mode techniques are able to avoid the chattering effect associated with first-order sliding. The super-twisting algorithm is one of the most popular second-order sliding mode techniques. Existing modifications of the super-twisting algorithm allow for improved disturbance rejection capability. In this paper, we introduce a new class of generalizations of the super-twisting algorithm that are able to keep the main advantages of standard super-twisting while rejecting disturbances bounded in forms for which the existing algorithms may be not directly applicable. Our results thus broaden the applicability of second-order sliding-mode techniques. We give conditions for stability and finite-time convergence, and provide a complete design framework based on given disturbance bounds.
MSC:
| 93B12 | Variable structure systems |
| 93B35 | Sensitivity (robustness) |
| 93D20 | Asymptotic stability in control theory |
Keywords:
sliding modes; super-twisting algorithm; stability; finite-time convergence; disturbance rejectionReferences:
| [1] | Castillo, I.; Fridman, L.; Moreno, J. A., Super-twisting algorithm in presence of time and state dependent perturbations, International Journal of Control (2017) · Zbl 1403.93062 |
| [2] | Clarke, F. H.; Ledyaev, Y. S.; Stern, R. J., Asymptotic stability and smooth Lyapunov functions, Journal of Differential Equations, 149, 1, 69-114 (1998) · Zbl 0907.34013 |
| [3] | Cruz-Zavala, E.; Moreno, J. A., Homogeneous high-order sliding mode design: a Lyapunov approach, Automatica, 80, 232-238 (2017) · Zbl 1370.93073 |
| [4] | Davila, J.; Fridman, L.; Levant, A., Second-order sliding-mode observer for mechanical systems, IEEE Transactions on Automatic Control, 50, 11, 1785-1789 (2005) · Zbl 1365.93071 |
| [5] | Emel’yanov, S. V.; Korovin, S. K.; Levant, A., High-order sliding modes in control systems, Computational Mathematics and Modeling, 7, 3, 294-318 (1996) |
| [6] | Filippov, A. F., Differential equations with discontinuous righthand sides (1988), Kluwer Academic Publishers · Zbl 0664.34001 |
| [7] | Sliding modes after the first decade of the 21st century: state of the art, (Fridman, L.; Moreno, J.; Iriarte, R., Lecture notes in control and information sciences (2011), Springer) |
| [8] | Haimovich, H.; De Battista, H., Disturbance-tailored super-twisting algorithms, (XVII Reunión de trabajo en procesamiento de la información y control (RPIC) (2017), Mar del Plata: Mar del Plata Argentina) |
| [9] | Jakovljevic, B.; Pisano, A.; Rapaic, M. R.; Usai, E., On the sliding-mode control of fractional-order nonlinear uncertain dynamics, International Journal of Robust and Nonlinear Control, 26, 4, 782-798 (2016) · Zbl 1333.93071 |
| [10] | Levant, A., Sliding order and sliding accuracy in sliding mode control, International Journal of Control, 58, 6, 1247-1263 (1993) · Zbl 0789.93063 |
| [11] | Levant, A., Robust exact differentiation via sliding mode technique, Automatica, 34, 3, 379-384 (1998) · Zbl 0915.93013 |
| [12] | Levant, A., Universal single-input single-output (siso) sliding-mode controllers with finite-time convergence, IEEE Transactions on Automatic Control, 46, 9, 1447-1451 (2001) · Zbl 1001.93011 |
| [13] | Levant, A., Homogeneity approach to high-order sliding mode design, Automatica, 41, 823-830 (2005) · Zbl 1093.93003 |
| [14] | Moreno, J. A., A linear framework for the robust stability analysis of a generalized super-twisting algorithm, (6th Int’l Conf. on electrical engineering, computing science and automatic control (CCE) (2009)) |
| [15] | Moreno, J. A., On strict Lyapunov functions for some non-homogeneous super-twisting algorithms, Journal of the Franklin Institute, 351, 1902-1919 (2014) · Zbl 1372.93177 |
| [16] | Moreno, J. A.; Osorio, M., A Lyapunov approach to second-order sliding mode controllers and observers, (Proc. 47th IEEE Conf. on decision and control (2008)), 2856-2861 |
| [17] | Moreno, J. A.; Osorio, M., Strict Lyapunov functions for the super-twisting algorithm, IEEE Transactions on Automatic Control, 57, 4, 1035-1040 (2012) · Zbl 1369.93568 |
| [18] | Picó, J.; Picó-Marco, E.; Vignoni, A.; De Battista, H., Stability preserving maps for finite-time convergence: Super-twisting sliding-mode algorithm, Automatica, 49, 2, 534-539 (2013) · Zbl 1259.93036 |
| [19] | Polyakov, A.; Efimov, D.; Perruquetti, W., Finite-time and fixed-time stabilization: implicit Lyapunov function approach, Automatica, 51, 332-340 (2015) · Zbl 1309.93135 |
| [20] | Polyakov, A.; Poznyak, A., Lyapunov function design for finite-time convergence analysis: twisting controller for second-order sliding mode realization, Automatica, 45, 444-448a (2009) · Zbl 1158.93401 |
| [21] | Polyakov, A.; Poznyak, A., Reaching time estimation for super-twisting second order sliding mode controller via Lyapunov function designing, IEEE Transactions on Automatic Control, 54, 8, 1951-1955b (2009) · Zbl 1367.93127 |
| [22] | Poznyak, A., Stochastic super-twist sliding mode controller, IEEE Transactions on Automatic Control (2017) · Zbl 1395.93513 |
| [23] | Riachy, S.; Orlov, Y.; Floquet, T.; Santiesteban, R.; Richard, J.-P., Second-order sliding mode control of underactuated mechanical systems I: Local stabilization with application to an inverted pendulum, International Journal of Robust and Nonlinear Control, 18, 4-5, 529-543 (2008) · Zbl 1284.93064 |
| [24] | Saif, M.; Chen, W.; Wu, Q., (Modern sliding mode control theory. Chapter high order sliding mode observers and differentiators-application to fault diagnosis problem. Modern sliding mode control theory. Chapter high order sliding mode observers and differentiators-application to fault diagnosis problem, Lecture notes in control and information sciences (2008), Springer), 321-344 · Zbl 1145.93315 |
| [25] | Seeber, R.; Reichhartinger, M.; Horn, M., A Lyapunov function for an extended super-twisting algorithm, IEEE Transactions on Automatic Control (2018) · Zbl 1423.93083 |
| [26] | Shtessel, Y.; Edwards, C.; Fridman, L.; Levant, A., Sliding mode control and observation (2014), Springer |
| [27] | Utkin, V. I., Variable structure systems with sliding modes, IEEE Transactions on Automatic Control, AC-22, 2, 212-222 (1977) · Zbl 0382.93036 |
| [28] | Vladimir, I., Bogachev (2007), Measure Theory: Measure Theory Volume I. Springer |
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