Discrete-time variable structure control systems

Gao, Wei-Bing; Wang, Yufu; Homaifa, A.

doi:10.1109/41.370376

Cited by 1,347 publications

(115 citation statements)

References 7 publications

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“…Let us derive the greatest possible value of the left-hand side of (19) (20) Using (19) and (20) we obtain that if (18) In order to prove the finite time convergence of the representative point to the sliding hyperplane we will determine the parameter λ i such that…”

Section: Sufficient Conditionmentioning

confidence: 99%

“…In this approach the control signal is computed in order to satisfy a predefined evolution of the sliding variable. Originally, the reaching law method was introduced for continuous time systems [19], and then developed for discrete time ones [20]. Recently, a large number of new reaching laws were presented [21][22][23][24][25][26][27][28][29][30].…”

Section: Introductionmentioning

confidence: 99%

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The problem of state constraints in designing the discrete time sliding mode controller

Jaskula

Pietrala

Leśniewski

2017

PAR

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Section: Sufficient Conditionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The problem of state constraints in designing the discrete time sliding mode controller

Jaskula

Pietrala

Leśniewski

2017

PAR

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“…Also, Lyapunov's second method as a powerful design and analysis technique has not been used Manuscript [4,[6][7][8][9][10][11], which are among scarce papers, where the method is primarily used. There are no papers with exponential stability of sliding subspace, except, some authors speak about exponential changes of, in general case vector variable usually designated e.g.…”

Section: Introductionmentioning

confidence: 98%

“…[9], which are more focused on, later in the work, through the both simulation and experimental application, under the same condition. The [9] was chosen, for the reference was pretty frequently cited in literature, although the author, in [9], neither speaks explicitly about exponential changes of s, what is actually happened, nor uses Lyapunov's method.…”

Section: Introductionmentioning

confidence: 98%

Discrete-time chattering free exponentially stabilizing sliding mode scalar control via Lyapunov’s method

Bučevac

Jovanović

2016

Int. J. Control Autom. Syst.

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Linear time-invariant discrete-time plant, with no restrictions on the form of the state equation and with scalar control, is considered. The exponentially stabilizing state feedback control algorithm is developed by Lyapunov's second method leading to the variable structure system with chattering free sliding modes. Essentially, the control algorithm drives the system from an arbitrary initial state to a prescribed so-called sliding subspace S, in finite time and with prescribed velocity estimate. Inside the sliding subspace S, the system is switched to the sliding mode regime and stays in it forever. The proposed algorithm is tested on the real system in practice, direct current (DC) servo motor, and simulation and experimental results are given. Also, it is compared with another already known algorithm from literature.

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“…Thus, system states adjudicate within a QSM band having less than half bandwidth as given in [37]. From [33] MROF based algorithm using an advanced reaching law can be attained.…”

Section: Introductionmentioning

confidence: 99%

Vibration Annihilation of Sandwiched Beam with MROF DTSMC

Rathi¹,

Khan²

2017

ENG

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In the present paper, an analytical model of a flexible beam fixed at an end with embedded shear sensors and actuators is developed. The smart cantilever beam model is evolved using a piezoelectric sandwich beam element, which accommodates sensor and actuator embedded at distinct locations and a regular sandwiched beam element, having rigid foam at the core. A FE model of a piezoelectric sandwich beam is evolved using laminated beam theory in MATLAB®. Each layer behaves as a Timoshenko beam and the cross-section of the beam remains plane and rotates about the neutral axis of the beam, but it does not remain normal to the deformed longitudinal axis. Keeping the sensor and actuator location fixed in a MIMO system, state space models of the smart cantilever beam is obtained. The proper selection of control strategy is very crucial in order to obtain the better control. In this paper a DSM controller designed to control the first three modes of vibration of the smart cantilever beam and their performances are represented on the basis of control signal input, sensor output and sliding functions. It is found that DSM controller provides superior control than other conventional controllers and also MROF DSM controller is much better than SISO DSM controller.

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Discrete-time variable structure control systems

Cited by 1,347 publications

References 7 publications

The problem of state constraints in designing the discrete time sliding mode controller

The problem of state constraints in designing the discrete time sliding mode controller

Discrete-time chattering free exponentially stabilizing sliding mode scalar control via Lyapunov’s method

Vibration Annihilation of Sandwiched Beam with MROF DTSMC

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