Modeling and Control of Cable Driven Parallel Manipulators with Elastic Cables: Singular Perturbation Theory

2011 ◽  
pp. 455-464 ◽  
Author(s):  
Alaleh Vafaei ◽  
Mohammad A. Khosravi ◽  
Hamid D. Taghirad
Keyword(s):  
Perturbation Theory ◽  
Singular Perturbation ◽  
Parallel Manipulators ◽  
Singular Perturbation Theory ◽  
Modeling And Control ◽  
And Control ◽  
Elastic Cables

DYNAMIC ANALYSIS AND CONTROL OF CABLE DRIVEN ROBOTS WITH ELASTIC CABLES

2011 ◽  
Vol 35 (4) ◽  
pp. 543-557 ◽  
Author(s):  
Mohammad A. Khosravi ◽  
Hamid D. Taghirad
Keyword(s):  
Control Algorithm ◽  
Closed Loop ◽  
Parallel Manipulators ◽  
Lyapunov Theorem ◽  
Closed Loop System ◽  
Modeling And Control ◽  
Internal Forces ◽  
And Control ◽  
Flexible Cables ◽  
Elastic Cables

In this paper modeling and control of cable driven redundant parallel manipulators with flexible cables, are studied in detail. Based on new results, in fully constrained cable robots, cables can be modeled as axial linear springs. Considering this assumption the system dynamics formulation is developed using Lagrange approach. Since in this class of robots, all the cables should remain in tension for the whole workspace, the notion of internal forces are introduced and incorporated in the proposed control algorithm. The control algorithm is developed in cable coordinates in which the internal forces play an important role. Finally, asymptotic stability of the closed loop system is analyzed through Lyapunov theorem, and the performance of the proposed algorithm is studied by simulations.

scholarly journals Renormalization group and fractional calculus methods in a complex world: A review

2021 ◽  
Vol 24 (1) ◽  
pp. 5-53
Author(s):  
Lihong Guo ◽  
YangQuan Chen ◽  
Shaoyun Shi ◽  
Bruce J. West
Keyword(s):  
Perturbation Theory ◽  
Renormalization Group ◽  
Fractional Calculus ◽  
Singular Perturbation ◽  
World View ◽  
Singular Perturbation Theory ◽  
Asymptotic Behavior Of Solutions ◽  
Quantum Field ◽  
Self Similarity ◽  
Way Of Thinking

Abstract The concept of the renormalization group (RG) emerged from the renormalization of quantum field variables, which is typically used to deal with the issue of divergences to infinity in quantum field theory. Meanwhile, in the study of phase transitions and critical phenomena, it was found that the self–similarity of systems near critical points can be described using RG methods. Furthermore, since self–similarity is often a defining feature of a complex system, the RG method is also devoted to characterizing complexity. In addition, the RG approach has also proven to be a useful tool to analyze the asymptotic behavior of solutions in the singular perturbation theory. In this review paper, we discuss the origin, development, and application of the RG method in a variety of fields from the physical, social and life sciences, in singular perturbation theory, and reveal the need to connect the RG and the fractional calculus (FC). The FC is another basic mathematical approach for describing complexity. RG and FC entail a potentially new world view, which we present as a way of thinking that differs from the classical Newtonian view. In this new framework, we discuss the essential properties of complex systems from different points of view, as well as, presenting recommendations for future research based on this new way of thinking.

Periodic solutions for equations with distributed delays

2006 ◽  
Vol 136 (6) ◽  
pp. 1317-1325 ◽  
Author(s):  
Guojian Lin ◽  
Rong Yuan
Keyword(s):  
Perturbation Theory ◽  
Singular Perturbation ◽  
Periodic Solutions ◽  
General Theorem ◽  
Linear Chain ◽  
Distributed Delays ◽  
Singular Perturbation Theory ◽  
Geometric Singular Perturbation Theory ◽  
Geometric Singular Perturbation ◽  
Existence Of Periodic Solutions

A general theorem about the existence of periodic solutions for equations with distributed delays is obtained by using the linear chain trick and geometric singular perturbation theory. Two examples are given to illustrate the application of the general the general therom.

On voltage stability from the viewpoint of singular perturbation theory

1994 ◽  
Vol 16 (6) ◽  
pp. 409-417 ◽  
Author(s):  
N. Yorino ◽  
H. Sasaki ◽  
Y. Masuda ◽  
Y. Tamura ◽  
M. Kitagawa ◽  
...  
Keyword(s):  
Perturbation Theory ◽  
Singular Perturbation ◽  
Voltage Stability ◽  
Singular Perturbation Theory
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