Backstepping sliding mode control with functional tuning based on an instantaneous power approach applied to an underwater vehicle

ABSTRACT

In this paper, we present a modified backstepping sliding mode control to deal with Euler–Lagrange systems. The controller is applied in an underwater vehicle in order to show the effectiveness of the approach proposed. Instantaneous power data provided by the propulsion system are used to tune the controller in order to guarantee robust performance and energy saving. Thanks to the combination of an internal Proportional Integral and Derivative (PID) controller, it is possible implement high gains to deal with the influence of disturbances and uncertainties. A comparative study among this backstepping sliding mode controller and standard sliding mode controls is presented.

KEYWORDS:

• Roboltics
• backstepping control
• sliding mode control

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Erratum

Acknowledgments

The authors are grateful to Unioeste, UFSC, Araucaria Foundation and UTFPR for supporting this research.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. Stable error dynamics in closed-loop.

2. In this work, the forces and moments induced by the waves and wind are considered as main disturbances.

3. The Boundary Layer method was applied in standard controllers in order to smooth out the control law discontinuity within a vicinity of the sliding surface and thus avoid the chattering problem.

Additional information

Notes on contributors

Carlos Henrique Farias dos Santos

Carlos Henrique Farias dos Santos was born in Recife, Brazil. He received the Graduate's degree in electrical engineering from Pernambuco Federal University, Recife, in 1999 and the M.S. and Ph.D. degrees in electrical engineering from Santa Catarina Federal University, Florianopolis, Brazil, in 2002 and 2006, respectively. He is currently an Associate Professor with theWestern Parana State University, Foz do Iguacu, Brazil. He has experience in electrical engineering with emphasis in feedback control process, concerning the following topics: autonomous mobile robots, fixed and mobile robot manipulators, computational intelligence, hybrid dynamical systems, and nonlinear control.

Mariana Uzeda Cildoz

Mariana Uzeda Cildoz holds a bachelor's degree in Mathematics from the State University of Western Paraná (2008) and a Master's degree in Engineering of Dynamic and Energy Systems from the State University of Western Paraná (2014). He has experience in Applied Mathematics, with emphasis on Dynamic Systems, Control Systems and Biomathematics, working mainly in the areas of: stability analysis and synthesis of control laws applied to autonomous underwater vehicles and analysis of coexistence of species in ecological interactions.

Marco Henrique Terra

Marco Henrique Terra is graduated in Electrical Engineering from Júlio de Mesquita Filho State University (1986), Master's degree in Electrical Engineering from the University of São Paulo (1990), a PhD in Electrical Engineering from the University of São Paulo (1995) and a postdoctoral degree from the University of California at Los Angeles (2002). Coordinator of the robotics committee and president of the Brazilian Automation Society (SBA). Associate editor of the SBA Control & Automation Journal and the Journal of Applied Mathematics. He has experience in the area of Electrical Engineering, systems control, working mainly on the following topics: robust control, robust filtering and robotics.

Edson Roberto De Pieri

Edson Roberto De Pieri was born in Mogi Mirim, Brazil. He received the degree in statistics in 1982, the degree in mathematics in 1983, and the M.Sc. degree in electrical engineering in 1987, all from the Campinas State University, Campinas, Brazil, and the doctoral degree from the Pierre et Marie Curie University, Paris, France, in 1991. In 2004, he received a Coordenacao de Aperfeicoamento de Pessoal de Nivel Superior (Brazil) Grant for a one-year stay with Ecole Normale Sup´erieure de Cachan, Cachan, France. Since 1992, he has been a Professor with the Department of Automation and Systems, Santa Catarina Federal University, Florianopolis, Brazil. His research interests include nonlinear control, automation, and robotics.