<abstract xmlns="http://www.w3.org/1999/xhtml"><p>This study presents a new, reference trajectory based sliding mode control strategy for disturbed discrete time dynamical systems. The desired trajectory, which is generated externally according to an existing switching type reaching law, determines the properties of the emerging sliding motion of the system. It is proved that an appropriate choice of the trajectory generator parameters ensures the existence of the quasi-sliding motion of the system according to the definition by Gao <italic>et al.</italic> (1995) in spite of the influence of disturbances. Moreover, the paper shows that the application of the desired trajectory based reaching law results in a significant reduction in the quasi-sliding mode band width and errors of all state variables. Therefore, in comparison with Gao’s control method, the system’s robustness is increased. The paper also presents an additional modification of the reaching law, which guarantees a further reduction in the quasi-sliding mode band in the case of slowly varying disturbances. The results are confirmed with a simulation example.</p></abstract>

This study presents a new, reference trajectory based sliding mode control strategy for disturbed discrete time dynamical systems. The desired trajectory, which is generated externally according to an existing switching type reaching law, determines the properties of the emerging sliding motion of the system. It is proved that an appropriate choice of the trajectory generator parameters ensures the existence of the quasi-sliding motion of the system according to the definition by Gao et al. (1995) in spite of the influence of disturbances. Moreover, the paper shows that the application of the desired trajectory based reaching law results in a significant reduction in the quasi-sliding mode band width and errors of all state variables. Therefore, in comparison with Gao’s control method, the system’s robustness is increased. The paper also presents an additional modification of the reaching law, which guarantees a further reduction in the quasi-sliding mode band in the case of slowly varying disturbances. The results are confirmed with a simulation example.

A Reference Trajectory Based Discrete Time Sliding Mode Control Strategy

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"A Reference Trajectory Based Discrete Time Sliding Mode Control Strategy"}

This study presents a new, reference trajectory based sliding mode control strategy for disturbed discrete time dynamical systems. The desired trajectory,...

A Reference Trajectory Based Discrete Time Sliding Mode Control Strategy

Published Online: Sep 28, 2019

Page range: 517 - 525

Received: Dec 04, 2018

Accepted: Apr 19, 2019

DOI: https://doi.org/10.2478/amcs-2019-0038

Keywords
discrete time systems, sliding mode control, reaching law, reference trajectory

© 2019 Andrzej Bartoszewicz et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

A Reference Trajectory Based Discrete Time Sliding Mode Control Strategy

Published Online: Sep 28, 2019

Page range: 517 - 525

Received: Dec 04, 2018

Accepted: Apr 19, 2019

DOI: https://doi.org/10.2478/amcs-2019-0038

Keywordsdiscrete time systems, sliding mode control, reaching law, reference trajectory

© 2019 Andrzej Bartoszewicz et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
discrete time systems, sliding mode control, reaching law, reference trajectory