Flexible Manipulator Control Based on Singular Perturbation Theory Study

2013 ◽  
Vol 346 ◽  
pp. 69-73 ◽  
Author(s):  
Ping Lin Zeng ◽  
San Xiu Wang ◽  
Ji Jian Qiu ◽  
Shou Ren Ma ◽  
Xiao Fei Wan
Keyword(s):  
Perturbation Theory ◽  
Singular Perturbation ◽  
Sliding Mode ◽  
Flexible Manipulator ◽  
Singular Perturbation Theory ◽  
Reference Trajectory ◽  
Flexible Link ◽  
Fast Subsystem ◽  
Slow Subsystem ◽  
Manipulator Control

Aiming at the problem of tracking the reference trajectory and suppressing the beam vibration for flexible manipulator, this paper separated the system of flexible-link manipulator into slow subsystem and fast subsystem two different time scale subsystems based on singular perturbation theory and proposes a simple composite control algorithm. For the slow subsystem, a sliding mode controller is employed to track the desired trajectory, while optimal controller is used to stabilize the fast subsystem to suppress the vibration. Finally, the simulation results demonstrate the good performance of the proposed control strategy.

scholarly journals Modelling and Composite Control of Single Flexible Manipulators with Piezoelectric Actuators

2016 ◽  
Vol 2016 ◽  
pp. 1-14 ◽  
Author(s):  
En Lu ◽  
Wei Li ◽  
Xuefeng Yang ◽  
Mengbao Fan ◽  
Yufei Liu
Keyword(s):  
Vibration Suppression ◽  
Control Method ◽  
Sliding Mode ◽  
Piezoelectric Actuators ◽  
Flexible Manipulator ◽  
Optimal Placement ◽  
Flexible Manipulators ◽  
Linear Quadratic ◽  
Fast Subsystem ◽  
Slow Subsystem

The piezoelectric actuators are used to investigate the active vibration control of flexible manipulators in this paper. Based on the assumed mode method, piezoelectric coupling model, and Hamilton’s principle, the dynamic equation of the single flexible manipulator (SFM) with surface bonded actuators is established. Then, a singular perturbation model consisted of a slow subsystem and a fast subsystem is formulated and used for designing the composite controller. The slow subsystem controller is designed by fuzzy sliding mode control method, and the linear quadratic regulator (LQR) optimal control method is used to design fast subsystem controller. Furthermore, the changing trends of natural frequencies along with the changes in the position of piezoelectric actuators are obtained through the ANSYS Workbench software, by which the optimal placement of actuators is determined. Finally, numerical simulations and experiments are presented. The results demonstrate that the method of optimal placement is feasible based on the maximal natural frequency, and the composite controller presented in this paper can not only realize the trajectory tracking of the SFM and has a good result on the vibration suppression.

Impedance control of a two degree-of-freedom planar flexible link manipulator using singular perturbation theory

Robotica ◽  
2005 ◽  
Vol 24 (2) ◽  
pp. 221-228 ◽  
Author(s):  
G. R. Vossoughi ◽  
A. Karimzadeh
Keyword(s):  
Singular Perturbation ◽  
Sliding Mode ◽  
Impedance Control ◽  
Singular Perturbation Theory ◽  
Flexible Link ◽  
Singular Perturbation Method ◽  
Flexible Links ◽  
Assumed Mode Method ◽  
Mode Method ◽  
Flexible Link Robots

In this article, impedance control of a two link flexible link manipulators is addressed. The concept of impedance control of flexible link robots is rather new and is being addressed for the first time by the authors. Impedance Control provides a universal approach to the control of flexible robots, in both constrained and unconstrained maneuvers. The initial part of the paper concerns the use of Hamilton's principle to derive the mathematical equations governing the dynamics of joint angles, vibration of the flexible links and the constraining forces. The approximate elastic deformations are then derived by means of the Assumed-Mode-Method (AMM). Using the singular perturbation method, the dynamic of the manipulator is decomposed into fast and slow subsystems. The slow dynamic corresponds to the rigid manipulator and the fast dynamic is due to vibrations of flexible links. The sliding mode control (SMC) theory has been used as the means to achieve the 2nd order target impedance for the slow dynamics. A controller based on state feedback is also designed to stabilize the fast dynamics. The composite controller is constructed by using the slow and fast controllers. Simulation results for a 2-DOF robot in which only the 2nd link is flexible confirm that the controller performs remarkably well under various simulation conditions.

The Composite Control for Single-Link Flexible Manipulator Using Dynamic Sliding Mode and Optimal Based on Dynamic Switching

2013 ◽  
Vol 275-277 ◽  
pp. 707-710 ◽  
Author(s):  
Ming Chu ◽  
Xia Deng ◽  
Qing Xuan Jia ◽  
Fei Jie Huang
Keyword(s):  
Sliding Mode ◽  
Flexible Manipulator ◽  
Sliding Mode Controller ◽  
Fast Subsystem ◽  
Composite Control ◽  
Dynamic Switching ◽  
Single Link ◽  
Simulation Results ◽  
Slow Subsystem ◽  
Dynamic Sliding Mode

A composite controller is designed based on the singular perturbation model of single-link flexible manipulators. A dynamic sliding mode controller is designed for the slow subsystem, and optimal controller is designed to stabilize the fast subsystem. Numerical simulation results confirm that the proposed controller not only can perform fast and accurate tracking, but also can reduce the chattering of the sliding-mode control, and the proposed controller can suppress the tip vibration of the flexible manipulator effectively.

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.

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