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Discrete-time sliding mode control of linear systems with input saturation

Veselić Boban, Milosavljević Čedomir, Peruničić-Draženović Branislava, Huseinbegović Senad, Petronijević Milutin

International Journal of Applied Mathematics and Computer Science

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2020

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Vol. 30, no. 3

517--528

EN

The paper proposes a discrete-time sliding mode controller for single input linear dynamical systems, under requirements of the fast response without overshoot and strong robustness to matched disturbances. The system input saturation is imposed during the design due to inevitable limitations of most actuators. The system disturbances are compensated by employing nonlinear estimation by integrating the signum of the sliding variable. Hence, the proposed control structure may be regarded as a super-twisting-like algorithm. The designed system stability is analyzed as well as the sliding manifold convergence conditions are derived using a discrete-time model of the system in the δ-domain. The results obtained theoretically have been verified by computer simulations.

2

Robust stabilization using a sampled-data strategy of uncertain neutral state-delayed systems subject to input limitations

El Fezazi N., El Haoussi F., Tissir E. H., Alvarez T., Tadeo F.

International Journal of Applied Mathematics and Computer Science

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2018

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Vol. 28, no. 1

111--122

EN

Stabilization of neutral systems with state delay is considered in the presence of uncertainty and input limitations in magnitude. The proposed solution is based on simultaneously characterizing a set of stabilizing controllers and the associated admissible initial conditions through the use of a free weighting matrix approach. From this mathematical characterization, state feedback gains that ensure a large set of admissible initial conditions are calculated by solving an optimization problem with LMI constraints. Some examples are presented to compare the results with previous approaches in the literature.

3

BIBO stabilisation of continuous-time Takagi–Sugeno systems under persistent perturbations and input saturation

Salcedo J. V., Martínez M., García-Nieto S., Hilario A.

International Journal of Applied Mathematics and Computer Science

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2018

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Vol. 28, no. 3

457--472

EN

This paper presents a novel approach to the design of fuzzy state feedback controllers for continuous-time non-linear systems with input saturation under persistent perturbations. It is assumed that all the states of the Takagi–Sugeno (TS) fuzzy model representing a non-linear system are measurable. Such controllers achieve bounded input bounded output (BIBO) stabilisation in closed loop based on the computation of inescapable ellipsoids. These ellipsoids are computed with linear matrix inequalities (LMIs) that guarantee stabilisation with input saturation and persistent perturbations. In particular, two kinds of inescapable ellipsoids are computed when solving a multiobjective optimization problem: the maximum volume inescapable ellipsoids contained inside the validity domain of the TS fuzzy model and the smallest inescapable ellipsoids which guarantee a minimum *-norm (upper bound of the 1-norm) of the perturbed system. For every initial point contained in the maximum volume ellipsoid, the closed loop will enter the minimum *-norm ellipsoid after a finite time, and it will remain inside afterwards. Consequently, the designed controllers have a large domain of validity and ensure a small value for the 1-norm of closed loop.

4

Nonlinear robust control for single-machine infinite-bus power systems with input saturation

Wan Y.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2017

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Vol. 65, nr 1

3--9

EN

In this paper, a new control scheme is proposed to achieve stability for a single-machine infinite-bus power system. A power system model simultaneously considering input saturation and time-varying uncertainties is presented. A sufficient condition for the system convergence is given and based on this result, a switching excitation control law with auxiliary system is designed. The stability analysis and simulation results all show that the developed controller is effective.

5

Adaptacyjne sterowanie manipulatorem z ograniczeniem momentu

Kabziński J.

Przegląd Elektrotechniczny

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2012

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R. 88, nr 4b

104-109

PL

Na przykładzie sterowania manipulatorem przedstawiono koncepcję modyfikacji algorytmu adaptive backstepping pozwalającą na jego stosowanie w przypadku ograniczenia sygnału sterującego. Wykorzystano koncepcję filtru różnicy miedzy sygnałem na wejściu i wyjściu elementu ograniczającego. Wszystkie parametry obiektu, łącznie ze wzmocnieniem sygnału sterującego mogą być nieznane.

EN

Using nonlinear manipulator as an example we propose modification of adaptive backstepping control, which allows to use it in case of actuator saturation. We apply an idea of filtering the difference between saturation input and output. All plant parameters, also the control gain may be unknown.