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research-article

Robust and optimal output-feedback control for interval state-space Model: Application to a 2-DoF piezoelectric tube actuator

[+] Author and Article Information
Mounir Hammouche

Automatic Control and MicroMechatronic Systems department, FEMTO-ST Institute, Université Bourgogne Franche-Comté, 24, rue Alain Savary, Besançon France
mounir.hammouche@femto-st.fr

Philippe Lutz

Automatic Control and MicroMechatronic Systems department, FEMTO-ST Institute, Université Bourgogne Franche-Comté, 24, rue Alain Savary, Besançon France
plutz@femto-st.fr

Micky Rakotondrabe

Automatic Control and MicroMechatronic Systems department, FEMTO-ST Institute, Université Bourgogne Franche-Comté, 24, rue Alain Savary, Besançon France
mrakoton@femto-st.fr

1Corresponding author.

ASME doi:10.1115/1.4040977 History: Received January 24, 2018; Revised July 18, 2018

Abstract

The problem of robust and optimal output feedback design for interval state-space systems is investigated using regional eigenvalues placement and Linear Quadratic (LQ) tracker design techniques. The design method is robust in the sense that the eigenvalues of the interval system are designed to cluster inside a desired region. Indeed, an algorithm based on Set Inversion Via Interval Analysis (SIVIA) combined with interval eigenvalues computation and eigenvalues clustering techniques is proposed. This recursive SIVIA-based algorithm allows to approximate with subpaving the set solutions [K] that satisfy the inclusion of the eigenvalues of the closed-loop system in the desired region. However, the LQ tracker design is used to find from the set solutions [K] the optimal solution that minimizes the inputs/outputs energy and ensures the best behaviors of the closed-loop system. The proposed algorithm can be also used for robust state-feedback, both for interval and for non-interval systems. Finally, the effectiveness of the algorithm is illustrated by a real experimentation on a piezoelectric tube actuator

Copyright (c) 2018 by ASME
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