Advances in High Order and Adaptive Sliding Mode Control – Theory and Applications

Plestan, Franck; Brégeault, Vincent; Glumineau, Alain; Shtessel, Yuri B.; Moulay, Emmanuel

doi:10.1007/978-3-642-22164-4_17

Cited by 10 publications

(9 citation statements)

References 21 publications

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“…The complete controller is nonanticipative sinceū eq k depends only on the model parameters andx k . Moreoverū s k is the unique solution to (14) given that CB * > 0, using similar arguments as in Lemma 4. This controller retains the structure of the continuous-time sliding mode controller.…”

Section: Exact Discrete Equivalent Controlmentioning

confidence: 93%

“…Lemma 5. If CB * is a P-matrix, then the only equilibrium pair of the system (14) is (σ * ,ū s * ) = (0, 0). Proof.…”

Section: Exact Discrete Equivalent Controlmentioning

confidence: 99%

“…In this section, we investigate the stability of the auxiliary system (14) and some convergence properties of the control inputū s when the sampling period tends to 0. In the nominal case we are able to prove convergence of the sliding variable to 0, using Lyapunov technique, under some structural conditions that match closely the ones for the continuous-time sliding mode controller.…”

Section: Stability and Convergence Propertiesmentioning

confidence: 99%

“…In these past research efforts, most of the focus was on the discontinuous part of the control, since it introduces numerical chattering. Several solutions to alleviate numerical chattering (that is solely due to the time discretization [9]- [13]) have been proposed [1]- [7], [14]- [16], most of them using a so-called quasi-sliding surface [5] or a boundary layer, associated with an explicit discretization of u s . The works in [2] and [6] depart from these discretetime controllers and propose an algorithm which allows the sliding variable to take exactly the zero value at sampling times.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Lyapunov Stability and Performance Analysis of the Implicit Discrete Sliding Mode Control

Huber

Acary

Brogliato

2016

IEEE Trans. Automat. Contr.

104

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Discrete-time sliding mode controllers with an implicit discretization of the signum function are considered. With a proper choice of the equivalent part of the control, the resulting controller is shown to be Lyapunov stable with finitetime convergence of the sliding variable to 0. The convergence of the control input, as the sampling period goes to 0, to the continuous-time one is shown. The robustness with respect to matching perturbations is also investigated. The discretization performance in terms of the error order is studied for different discretizations of the equivalent part of the input. Numerical and experimental results illustrate and support the analysis.

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Section: Exact Discrete Equivalent Controlmentioning

confidence: 93%

“…Lemma 5. If CB * is a P-matrix, then the only equilibrium pair of the system (14) is (σ * ,ū s * ) = (0, 0). Proof.…”

Section: Exact Discrete Equivalent Controlmentioning

confidence: 99%

Section: Stability and Convergence Propertiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Lyapunov Stability and Performance Analysis of the Implicit Discrete Sliding Mode Control

Huber

Acary

Brogliato

2016

IEEE Trans. Automat. Contr.

104

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show abstract

“…Proof: It is known from the sliding mode control theory [41] that, once the state trajectories of the attitude tracking system reach the sliding surface, that is, s = 0, one has…”

Section: Finite-time Sliding Mode Surface Designmentioning

confidence: 99%

Finite‐time fault tolerant attitude control for over‐activated spacecraft subject to actuator misalignment and faults

Zhang

Friswell

2013

IET Control Theory & Applications

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A finite-time attitude compensation control scheme is developed for an over-activated rigid spacecraft subject to actuator faults, misalignment, external disturbances and uncertain inertia parameters. The controller is synthesised based on the sliding mode control theory, and guarantees the finite-time reachability of the system states. A sufficient condition for the controller to accommodate misalignment and faults of actuator is presented. An optimised control allocation algorithm based on the Karush-Kuhn-Tucker condition is then applied to distribute the commanded control to each actuator, and optimise the consumption of energy. Numerical simulation results are presented that highlight the performance benefits of the control law.

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An adaptive sliding mode controller for electro‐hydraulic servo systems combining offline training and online estimation

Gao,

2023

Asian Journal of Control

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In order to improve the tracking accuracy of electro‐hydraulic servo systems under nonlinear disturbance, an adaptive sliding mode controller (SMC) based on generalized regression neural network (GRNN) is proposed. The nonlinear factors and external disturbances of systems are considered in the controller, and an improved GRNN is used. In addition, the neural network achieves nonlinear approximation of the unknown part by online learning, determines the parameters of the SMC in real time by training the model offline, and reduces the impact of online estimation errors on the system to improve control accuracy. Finally, the effectiveness of the control method is verified by simulation.

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Advances in High Order and Adaptive Sliding Mode Control – Theory and Applications

Cited by 10 publications

References 21 publications

Lyapunov Stability and Performance Analysis of the Implicit Discrete Sliding Mode Control

Lyapunov Stability and Performance Analysis of the Implicit Discrete Sliding Mode Control

Finite‐time fault tolerant attitude control for over‐activated spacecraft subject to actuator misalignment and faults

An adaptive sliding mode controller for electro‐hydraulic servo systems combining offline training and online estimation

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