The Lyapunov approach

Author(s):  
Jamal Daafouz ◽  
Denis Arzelier ◽  
Germain Garcia ◽  
Jacques Bernussou
Keyword(s):  
2013 ◽  
Vol 62 (8) ◽  
pp. 673-678 ◽  
Author(s):  
Lassi Paunonen ◽  
Hans Zwart

Author(s):  
Kerem Gurses ◽  
Bradley J. Buckman ◽  
Edward J. Park

This paper presents a novel feedback sensing approach for actively suppressing vibrations of a single-link flexible manipulator. Slewing of the flexible link by a rotating hub induces vibrations in the link that persist long after the hub stops rotating. These vibrations are suppressed through a combined scheme of PD-based hub motion control and proposed piezoelectric (PZT) actuator control, which is a composite linear and velocity feedback controller. Lyapunov approach was used to synthesize the controller based on a finite element model of the system. Its realization was possible due to the availability of both linear and angular velocity feedback provided by a unique, commercially-available fiber optic curvature sensor array, called ShapeTape™. It is comprised of an array of fiber optic curvature sensors, laminated on a long, thin ribbon tape, geometrically arranged in such a way that, when it is embedded into the flexible link, the bend and twist of the link’s centerline can be measured. Experimental results show the effectiveness of the proposed approach.


Author(s):  
Kazuhiko Hiramoto ◽  
Taichi Matsuoka ◽  
Akira Fukukita ◽  
Katsuaki Sunakoda

We address a simultaneous optimal design problem of a semi-active control law and design parameters in a vibration control device for civil structures. The Vibration Control Device (VCD) that is being developed by authors is used as the semi-active control device in the present paper. The VCD is composed of a mechanism of a ball screw with a flywheel for the inertial resistance force and an electric motor with an electric circuit for the damping resistance force. A new bang-bang type semi-active control law referred to as Inverse Lyapunov Approach is proposed as the semi-active control law. In the Inverse Lyapunov Approach the Lyapunov function is searched so that performance measures in structural vibration control are optimized in the premise of the bang-bang type semi-active control based on the Lyapunov function. The design parameters to determine the Lyapunov function and the design parameters of the VCD are optimized for the good performance of the semi-active control system. The Genetic Algorithm is employed for the optimal design.


2013 ◽  
Vol 46 (2) ◽  
pp. 397-402 ◽  
Author(s):  
Yuri Shtessel ◽  
Alain Glumineau ◽  
Franck Plestan ◽  
Martin Weiss

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