The problem of robust and optimal output feedback design for interval state-space systems is addressed in this paper. Indeed, an algorithm based on set inversion via interval analysis (SIVIA) combined with interval eigenvalues computation and eigenvalues clustering techniques is proposed to seek for a set of robust gains. This recursive SIVIA-based algorithm allows to approximate with subpaving the set solutions that satisfy the inclusion of the eigenvalues of the closed-loop system in a desired region in the complex plane. Moreover, the LQ tracker design is employed to find from the set solutions the optimal solution that minimizes the inputs/outputs energy and ensures the best behaviors of the closed-loop system. Finally, the effectiveness of the algorithm is illustrated by a real experimentation on a piezoelectric tube actuator.
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February 2019
Research-Article
Robust and Optimal Output-Feedback Control for Interval State-Space Model: Application to a Two-Degrees-of-Freedom Piezoelectric Tube Actuator
Mounir Hammouche,
Mounir Hammouche
Automatic Control and MicroMechatronic
Systems Department,
FEMTO-ST Institute,
Université Bourgogne Franche-Comté, CNRS,
24, rue Alain Savary,
Besançon 25000, France
Systems Department,
FEMTO-ST Institute,
Université Bourgogne Franche-Comté, CNRS,
24, rue Alain Savary,
Besançon 25000, France
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Philippe Lutz,
Philippe Lutz
Automatic Control and MicroMechatronic
Systems Department,
FEMTO-ST Institute,
Université Bourgogne Franche-Comté, CNRS,
24, rue Alain Savary,
Besançon 25000, France
Systems Department,
FEMTO-ST Institute,
Université Bourgogne Franche-Comté, CNRS,
24, rue Alain Savary,
Besançon 25000, France
Search for other works by this author on:
Micky Rakotondrabe
Micky Rakotondrabe
Automatic Control and MicroMechatronic
Systems Department,
FEMTO-ST Institute,
Université Bourgogne Franche-Comté, CNRS,
24, rue Alain Savary,
Besançon 25000, France
e-mail: mrakoton@femto-st.fr
Systems Department,
FEMTO-ST Institute,
Université Bourgogne Franche-Comté, CNRS,
24, rue Alain Savary,
Besançon 25000, France
e-mail: mrakoton@femto-st.fr
Search for other works by this author on:
Mounir Hammouche
Automatic Control and MicroMechatronic
Systems Department,
FEMTO-ST Institute,
Université Bourgogne Franche-Comté, CNRS,
24, rue Alain Savary,
Besançon 25000, France
Systems Department,
FEMTO-ST Institute,
Université Bourgogne Franche-Comté, CNRS,
24, rue Alain Savary,
Besançon 25000, France
Philippe Lutz
Automatic Control and MicroMechatronic
Systems Department,
FEMTO-ST Institute,
Université Bourgogne Franche-Comté, CNRS,
24, rue Alain Savary,
Besançon 25000, France
Systems Department,
FEMTO-ST Institute,
Université Bourgogne Franche-Comté, CNRS,
24, rue Alain Savary,
Besançon 25000, France
Micky Rakotondrabe
Automatic Control and MicroMechatronic
Systems Department,
FEMTO-ST Institute,
Université Bourgogne Franche-Comté, CNRS,
24, rue Alain Savary,
Besançon 25000, France
e-mail: mrakoton@femto-st.fr
Systems Department,
FEMTO-ST Institute,
Université Bourgogne Franche-Comté, CNRS,
24, rue Alain Savary,
Besançon 25000, France
e-mail: mrakoton@femto-st.fr
1Corresponding author.
Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received January 24, 2018; final manuscript received July 18, 2018; published online October 10, 2018. Assoc. Editor: Dumitru I. Caruntu.
J. Dyn. Sys., Meas., Control. Feb 2019, 141(2): 021008 (14 pages)
Published Online: October 10, 2018
Article history
Received:
January 24, 2018
Revised:
July 18, 2018
Citation
Hammouche, M., Lutz, P., and Rakotondrabe, M. (October 10, 2018). "Robust and Optimal Output-Feedback Control for Interval State-Space Model: Application to a Two-Degrees-of-Freedom Piezoelectric Tube Actuator." ASME. J. Dyn. Sys., Meas., Control. February 2019; 141(2): 021008. https://doi.org/10.1115/1.4040977
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