Control of underactuated mechanical systems with two degrees of freedom and symmetry

2000 ◽  
Author(s):  
R. Olfati-Saber
Keyword(s):  
Degrees Of Freedom ◽  
Mechanical Systems ◽  
Underactuated Mechanical Systems ◽  
Two Degrees Of Freedom

Stable Control of Under-Actuated Mechanical System Acrobot

2014 ◽  
Vol 971-973 ◽  
pp. 727-730
Author(s):  
Min Wu ◽  
Hai Pu
Keyword(s):  
Asymptotic Stability ◽  
Mechanical System ◽  
Degrees Of Freedom ◽  
Mechanical Systems ◽  
Vertical Plane ◽  
Drive System ◽  
Control Input ◽  
Underactuated Mechanical Systems ◽  
Two Degrees Of Freedom ◽  
Stable Control

The mechanical system with one control input and two degrees of freedom is one kind of simple under-drive system, As a typical of two-DOF underactuated mechanical systems , Two-link underactuated mechanical arms is a system scholars always research of.This paper mainly take the two link underactuated mechanical arms-Acrobot which motivate in the vertical plane as object to discusses the asymptotic stability of control

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.

An Extension of Rayleigh's Principle

1994 ◽  
Vol 22 (2) ◽  
pp. 83-90
Author(s):  
Alfonso Díaz-Jiménez ◽  
Gentil A. Estévez-Bretón
Keyword(s):  
Present Article ◽  
Degrees Of Freedom ◽  
Mechanical Systems ◽  
Natural Generalization ◽  
Vibrational Frequencies ◽  
Exact Results ◽  
Two Degrees Of Freedom ◽  
Elegant Method ◽  
Three Degrees Of Freedom

Steidel's extension of Rayleigh's method for calculating the natural vibrational frequencies of mechanical systems with two degrees of freedom provides an elegant method to obtain exact results. In the present article this approach, which perhaps has not been exploited as much as it could be, is first reviewed and then several examples of the procedure are given. An extension of the method to three degrees of freedom is presented, and a natural generalization of Rayleigh's principle is suggested.

Non-linear vibrations in mechanical systems with one or two degrees of freedom

2018 ◽  
Author(s):  
Д.А. Гришко ◽  
◽  
В.В. Лапшин ◽  
Е.С. Студенников ◽  
А.Н. Тарасенко ◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Mechanical Systems ◽  
Two Degrees Of Freedom ◽  
Non Linear ◽  
Linear Vibrations
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