Stabilization of a class of underactuated mechanical systems via total energy shaping

2003 ◽  
Author(s):  
F. Gomez-Estern ◽  
R. Ortega ◽  
F.R. Rubio ◽  
J. Aracil
Keyword(s):  
Total Energy ◽  
Mechanical Systems ◽  
Underactuated Mechanical Systems ◽  
Energy Shaping

Total Energy Shaping for Underactuated Mechanical Systems

2001 ◽  
Vol 34 (6) ◽  
pp. 1135-1140
Author(s):  
Fabio Gómez-Estern ◽  
Romeo Ortega ◽  
Mark W. Spong
Keyword(s):  
Total Energy ◽  
Mechanical Systems ◽  
Underactuated Mechanical Systems ◽  
Energy Shaping

Synchronization Control for a Class of Underactuated Mechanical Systems via Energy Shaping

2012 ◽  
Vol 134 (4) ◽  
Author(s):  
Dongfang Zhu ◽  
Di Zhou ◽  
Jingyang Zhou ◽  
Kok Lay Teo
Keyword(s):  
Control System ◽  
Mechanical Systems ◽  
Synchronization Control ◽  
Underactuated Mechanical Systems ◽  
Tracking Errors ◽  
Energy Shaping ◽  
Synchronization Errors ◽  
Shaping Technique ◽  
Passivity Based Control ◽  
Control Methodology

A synchronization control strategy for a class of underactuated mechanical systems is proposed by using the energy shaping technique, aiming to achieve the required performance of the synchronization motion. A synchronization controller is designed based on the interconnection and damping assignment passivity-based control methodology. It will guarantee that the position tracking errors and the synchronization errors of the underactuated mechanical systems are to converge to zero asymptotically. Experiments on a synchronization control system with two single-inverted pendulums as well as simulations of a synchronization control system consisting of four ball-beam devices are presented to demonstrate the effectiveness of the proposed method.

Total Energy Shaping Control of Mechanical Systems: Simplifying the Matching Equations Via Coordinate Changes

2007 ◽  
Vol 52 (6) ◽  
pp. 1093-1099 ◽  
Author(s):  
G. Viola ◽  
R. Ortega ◽  
R. Banavar ◽  
J. A. Acosta ◽  
A. Astolfi
Keyword(s):  
Total Energy ◽  
Mechanical Systems ◽  
Energy Shaping ◽  
Coordinate Changes

scholarly journals Observer-based robust integral of the sign of the error control of class I of underactuated mechanical systems: Theory and real-time experiments

2021 ◽  
pp. 014233122110313
Author(s):  
Afef Hfaiedh ◽  
Ahmed Chemori ◽  
Afef Abdelkrim
Keyword(s):  
Real Time ◽  
Error Control ◽  
Degrees Of Freedom ◽  
Sliding Mode ◽  
Mechanical Systems ◽  
Class I ◽  
Control Input ◽  
Underactuated Mechanical Systems ◽  
Control Scheme ◽  
And Performance

In this paper, the control problem of a class I of underactuated mechanical systems (UMSs) is addressed. The considered class includes nonlinear UMSs with two degrees of freedom and one control input. Firstly, we propose the design of a robust integral of the sign of the error (RISE) control law, adequate for this special class. Based on a change of coordinates, the dynamics is transformed into a strict-feedback (SF) form. A Lyapunov-based technique is then employed to prove the asymptotic stability of the resulting closed-loop system. Numerical simulation results show the robustness and performance of the original RISE toward parametric uncertainties and disturbance rejection. A comparative study with a conventional sliding mode control reveals a significant robustness improvement with the proposed original RISE controller. However, in real-time experiments, the amplification of the measurement noise is a major problem. It has an impact on the behaviour of the motor and reduces the performance of the system. To deal with this issue, we propose to estimate the velocity using the robust Levant differentiator instead of the numerical derivative. Real-time experiments were performed on the testbed of the inertia wheel inverted pendulum to demonstrate the relevance of the proposed observer-based RISE control scheme. The obtained real-time experimental results and the obtained evaluation indices show clearly a better performance of the proposed observer-based RISE approach compared to the sliding mode and the original RISE controllers.

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