On the stability of the equilibrium of the double pendulum with follower force: Some new results

2022 ◽  
pp. 116699
Author(s):  
Volodymyr Puzyrov ◽  
Jan Awrejcewicz ◽  
Nataliya Losyeva ◽  
Nina Savchenko
Keyword(s):  
Follower Force ◽  
Double Pendulum ◽  
The Stability

The Stability of a Damped Elastic System with a Follower Force

1975 ◽  
Vol 17 (3) ◽  
pp. 163-179 ◽  
Author(s):  
S. S. Saw ◽  
W. G. Wood
Keyword(s):  
Experimental Analysis ◽  
Elastic System ◽  
Follower Force ◽  
Double Pendulum ◽  
Theoretical Predictions ◽  
The Stability ◽  
The Masses

A theoretical and experimental analysis is made of the behaviour of a double pendulum with viscoelastic hinges subjected to a follower force. The effects of variations in the masses, stiffnesses, geometry and the internal and external velocity-dependent forces on the stability of the system are examined in detail. The picture that emerges shows all these factors to be important. In all cases, instability occurs in the first mode of flutter motion and the results accurately confirm theoretical predictions.

Novel robust controller design for load sway reduction in double-pendulum overhead cranes

2018 ◽  
Vol 233 (12) ◽  
pp. 4359-4371 ◽  
Author(s):  
Huimin Ouyang ◽  
Xin Deng ◽  
Huan Xi ◽  
Jinxin Hu ◽  
Guangming Zhang ◽  
...  
Keyword(s):  
Controller Design ◽  
Dynamic Performance ◽  
Optimization Method ◽  
Linear Matrix ◽  
Double Pendulum ◽  
Control Performance ◽  
Mass Property ◽  
Length Changes ◽  
The Stability ◽  
Dynamic Performance Analysis

It is seen that when the hook mass is larger than the load mass or the load has distributed mass property, the load sway of the crane system presents as double-pendulum effect. In this situation, crane system has two different natural frequencies so that the sway characteristic becomes more complex and greatly increases the difficulty of the dynamic performance analysis and controller design. Moreover, the rope length changes significantly affect the stability and control performance of the crane system. In order to solve the aforementioned problems, the linear dynamics of a two-dimensional overhead crane with double-pendulum effect is derived based on a disturbance observer, and is decoupled for controller design by modal analysis. Next, a state feedback controller is presented to achieve robust control performance for a given range of rope length changes. The controller gains are obtained via linear matrix inequality optimization method. Finally, numerical simulations and experimental results validate that the proposed method has superior control performance.

Stability of Human Balance With Reflex Delays Using Galerkin Approximations

2015 ◽  
Vol 11 (4) ◽  
Author(s):  
Zaid Ahsan ◽  
Thomas K. Uchida ◽  
Akash Subudhi ◽  
C. P. Vyasarayani
Keyword(s):  
Differential Equation ◽  
Galerkin Approximation ◽  
The Elderly ◽  
Double Pendulum ◽  
Neutral Delay ◽  
Stability Margins ◽  
Human Balance ◽  
The Stability ◽  
The Galerkin Method ◽  
Delay Differential

Falling is the leading cause of both fatal and nonfatal injury in the elderly, often requiring expensive hospitalization and rehabilitation. We study the stability of human balance during stance using inverted single- and double-pendulum models, accounting for physiological reflex delays in the controller. The governing second-order neutral delay differential equation (NDDE) is transformed into an equivalent partial differential equation (PDE) constrained by a boundary condition and then into a system of ordinary differential equations (ODEs) using the Galerkin method. The stability of the ODE system approximates that of the original NDDE system; convergence is achieved by increasing the number of terms used in the Galerkin approximation. We validate our formulation by deriving analytical expressions for the stability margins of the double-pendulum human stance model. Numerical examples demonstrate that proportional–derivative–acceleration (PDA) feedback generally, but not always, results in larger stability margins than proportional–derivative (PD) feedback in the presence of reflex delays.

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