The Lyapunov approach

2007 ◽  
pp. 278-299
Author(s):  
Jamal Daafouz ◽  
Denis Arzelier ◽  
Germain Garcia ◽  
Jacques Bernussou
Keyword(s):  
Lyapunov Approach

A Lyapunov approach to strong stability of semigroups

2013 ◽  
Vol 62 (8) ◽  
pp. 673-678 ◽  
Author(s):  
Lassi Paunonen ◽  
Hans Zwart
Keyword(s):  
Strong Stability ◽  
Lyapunov Approach

Vibration Control of a Flexible Link Manipulator Using an Array of Fiber-Optic Curvature Sensors and Piezoelectric Actuators

2007 ◽  
Author(s):  
Kerem Gurses ◽  
Bradley J. Buckman ◽  
Edward J. Park
Keyword(s):  
Motion Control ◽  
Sensor Array ◽  
Fiber Optic ◽  
Element Model ◽  
Flexible Manipulator ◽  
Flexible Link ◽  
Velocity Feedback ◽  
Lyapunov Approach ◽  
Single Link ◽  
Actuator Control

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.

Simultaneous Optimal Design of the Lyapunov-Based Semi-Active Control and the Semi-Active Vibration Control Device: Inverse Lyapunov Approach

2010 ◽  
Author(s):  
Kazuhiko Hiramoto ◽  
Taichi Matsuoka ◽  
Akira Fukukita ◽  
Katsuaki Sunakoda
Keyword(s):  
Optimal Design ◽  
Lyapunov Function ◽  
Vibration Control ◽  
Active Control ◽  
Control Device ◽  
Ball Screw ◽  
Design Parameters ◽  
Resistance Force ◽  
Control Law ◽  
Lyapunov Approach

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.

Hybrid-Impulsive Second Order Sliding Mode Control: Lyapunov Approach

2013 ◽  
Vol 46 (2) ◽  
pp. 397-402 ◽  
Author(s):  
Yuri Shtessel ◽  
Alain Glumineau ◽  
Franck Plestan ◽  
Martin Weiss
Keyword(s):  
Sliding Mode Control ◽  
Sliding Mode ◽  
Second Order ◽  
Lyapunov Approach ◽  
Mode Control ◽  
Second Order Sliding Mode
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