A multivariable super-twisting sliding mode approach

Nagesh, Indira; Edwards, Christopher

doi:10.1016/j.automatica.2013.12.032

Cited by 277 publications

(198 citation statements)

References 16 publications

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“…As in [44,45], the trajectories of the system (39) will cross and not stay on the subspace Ω 1 \ {0}. Thus, the stability of the system (39) can be guaranteed if the time derivative of V (s(t), ϖ(t)) in (40) along with the system (39) is negative definite for…”

Section: Design Of the Sliding Mode Controllermentioning

confidence: 99%

“…Among these, the Lyapunov method is popular because Lyapunov stability theory for linear systems can be recalled, and the finite-time convergence and robustness can also be achieved even when the super-twisting algorithm is not homogeneous [44]. Recently, a multivariable super-twisting algorithm has been presented [45] to extend the classical case [46] where the control gains are constant. In practice, if the disturbances are also bounded by functions of the states, then the constant gain super-twisting algorithm is not applicable.…”

Section: Introductionmentioning

confidence: 99%

“…By following similar arguments to [44,45], the finite time convergence of s(t),ṡ(t), z(t) can be derived. Since the integral sliding mode paradigm is used in this paper, the sliding surface (8) can be reached from the initial time.…”

mentioning

confidence: 99%

“…When the unperturbed dynamics with the variable gain super-twisting algorithm is considered, the algorithm (39) can be regarded as an extension of the variable gain super-twisting algorithm in [44] to the multi-input case and an extension of the constant gain multivariable supertwisting algorithm in [45] to the variable gain case. In the multi-input case, although it is also possible to implement the variable gain super-twisting algorithm in [44] by using the decoupling method [2], the variable gain super-twisting algorithm (39) is more elegant and convenient since it is inherently multivariable.…”

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confidence: 99%

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Integral sliding mode control for Markovian jump T–S fuzzy descriptor systems based on the super‐twisting algorithm

Zhang

Yan

et al. 2017

IET Control Theory & Applications

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This paper investigates integral sliding mode control problems for Markovian jump T-S fuzzy descriptor systems via the super-twisting algorithm. A new integral sliding surface which is continuous is constructed and an integral sliding mode control scheme based on a variable gain super-twisting algorithm is presented to guarantee the well-posedness of the state trajectories between two consecutive switchings. The stability of the sliding motion is analyzed by considering the descriptor redundancy and the properties of fuzzy membership functions. It is shown that the proposed variable gain super-twisting algorithm is an extension of the classical single-input case to the multi-input case. Finally, a bio-economic system is numerically simulated to verify the merits of the method proposed.

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Section: Design Of the Sliding Mode Controllermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Integral sliding mode control for Markovian jump T–S fuzzy descriptor systems based on the super‐twisting algorithm

Zhang

Yan

et al. 2017

IET Control Theory & Applications

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“…From these available measurements, moreover, the detection, identification and reconstruction of exogenous signals, representing faults, is achieved. The present scheme is inspired by the observer design proposed (for non DAE systems) in [17].…”

Section: Introductionmentioning

confidence: 99%

Second‐order sliding mode observers for fault reconstruction in power networks

Mellucci

Menon

Edwards

et al. 2017

IET Control Theory & Applications

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This paper proposes a 2-sliding mode observer to detect and reconstruct a certain class of load altering faults in a power network. The observer design is based on the recently proposed multivariable super-twisting structure. The IEEE benchmark power networks used to test the scheme are modelled as a semi-explicit class of differential algebraic equations (DAEs). For the purpose of developing the detection scheme, only the phase angles of the generators are measured, which represent a subset of the differential states of the DAEs. The objective is to estimate the differential states (the phase angles and frequencies of the generators), the algebraic states (the phase angles of the load bus tensions) and to reconstruct a class of load altering faults affecting the network. The proposed observer is assessed in simulation on two IEEE benchmarks: the 9-bus and 14-bus networks, so as to verify its capability to correctly estimate the differential and algebraic states of the network in spite of its complexity and uncertainty. Moreover, the capability of the proposed scheme to detect the presence of a load altering fault, to exactly identify its position in the network, and to precisely reconstruct the shape of the fault itself is shown and discussed.

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A modified super‐twisting sliding mode control with inner feedback and adaptive gain schedule

Yang

Qin

Jiang

2016

Adaptive Control & Signal

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SummaryIn order to deal with the overestimation of matched uncertainty and improve the convergence of sliding variable in sliding mode control, a modified structure of super‐twisting algorithm (STA) with inner feedback and adaptive gain schedule is presented in this paper. The foremost characteristic of the modified STA is that an inner feedback mechanism is built in the standard STA so as to regulate the dynamic behavior of sliding variable effectively. The damping effect produced by the inner feedback can restrain the overshoot and enhance the performance of faster convergence of the sliding variable. Furthermore, the adaptive gain schedule can effectively decrease the chattering amplitude without knowing the upper bound of uncertainty. The numerical simulations and experiments on DC servo system with low speed are carried out to validate the effectiveness and performance advantages of the proposed methodology. Copyright © 2016 John Wiley & Sons, Ltd.

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A multivariable super-twisting sliding mode approach

Cited by 277 publications

References 16 publications

Integral sliding mode control for Markovian jump T–S fuzzy descriptor systems based on the super‐twisting algorithm

Integral sliding mode control for Markovian jump T–S fuzzy descriptor systems based on the super‐twisting algorithm

Second‐order sliding mode observers for fault reconstruction in power networks

A modified super‐twisting sliding mode control with inner feedback and adaptive gain schedule

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