Robust two-scale command shaping for residual vibration mitigation in nonlinear systems

2019 ◽  
Vol 462 ◽  
pp. 114927
Author(s):  
J. Justin Wilbanks ◽  
Michael J. Leamy
Keyword(s):  
Nonlinear Systems ◽  
Residual Vibration ◽  
Vibration Mitigation ◽  
Command Shaping

Residual Vibration Suppression for Duffing Nonlinear Systems With Electromagnetical Actuation Using Nonlinear Command Shaping Techniques

2006 ◽  
Vol 128 (6) ◽  
pp. 778-789 ◽  
Author(s):  
Kuo-Shen Chen ◽  
Tian-Shiang Yang ◽  
Jui-Feng Yin
Keyword(s):  
Nonlinear Systems ◽  
Vibration Suppression ◽  
Residual Vibration ◽  
Single Degree Of Freedom ◽  
Weakly Nonlinear ◽  
Command Shaping ◽  
Magnetically Actuated ◽  
Highly Nonlinear ◽  
Parameter Variations ◽  
Residual Vibration Suppression

Residual vibration control is crucial for numerous applications in precision machinery with negligible damping such as magnetically actuated systems. In certain magnetically actuated applications, the systems could also be highly nonlinear and conditionally stable. Although traditional command shaping techniques work well for linear and weakly nonlinear systems, they show little effects for dealing with systems with both strong structural and actuation nonlinearities. In this paper, a general input shaper design methodology for single degree of freedom systems with both Duffing spring and electromagnetic forcing nonlinearities is successfully devised using an energy approach. Following this method, two-step and three-step shapers are developed, which in the linear limit reduce to the traditional zero-vibration (ZV) and zero-vibration-and-derivative (ZVD) shapers, respectively. The robustness of these nonlinear shapers is investigated numerically through several case studies and the results show that the three-step shaper is sufficiently robust to resist significant amounts of parameter variations without exciting significant residual vibration. The two-step shaper, however, is somewhat less robust with respect to parameter variations. Meanwhile, an electromagnetically driven Duffing mechanical system is also constructed so that the performances and robustness of the nonlinear shapers in vibration suppression can be examined. It is shown that the nonlinear shapers result in a significant improvement in residual vibration suppression and settling time reduction in comparison with the traditional linearized ZV and ZVD shapers.

Friction-Compensating Command Shaping for Vibration Reduction

2004 ◽  
Vol 127 (4) ◽  
pp. 307-314 ◽  
Author(s):  
Jason Lawrence ◽  
William Singhose ◽  
Keith Hekman
Keyword(s):  
Steady State ◽  
Coulomb Friction ◽  
Vibration Reduction ◽  
Input Shaping ◽  
Residual Vibration ◽  
Command Shaping ◽  
Point Motion ◽  
Common Operation ◽  
Point To Point ◽  
Theoretical Developments

Fast and accurate point-to-point motion is a common operation for industrial machines, but vibration will frequently corrupt such motion. This paper develops commands that can move machines without vibration, even in the presence of Coulomb friction. Previous studies have shown that input shaping can be used on linear systems to produce point-to-point motion with no residual vibration. This paper extends command-shaping theory to nonlinear systems, specifically systems with Coulomb friction. This idea is applied to a PD-controlled mass with Coulomb friction to ground. The theoretical developments are experimentally verified on a solder cell machine. The results show that the new commands allow the proportional gain to be increased, resulting in reduced rise time, settling time, and steady-state error.

Design of command shapers for residual vibration suppression in Duffing nonlinear systems

Mechatronics ◽  
2009 ◽  
Vol 19 (2) ◽  
pp. 184-198 ◽  
Author(s):  
Kuo-Shen Chen ◽  
Tian-Shiang Yang ◽  
Kuang-Shun Ou ◽  
Jui-Feng Yin
Keyword(s):  
Nonlinear Systems ◽  
Vibration Suppression ◽  
Residual Vibration ◽  
Residual Vibration Suppression

Arresting Motion in Nonlinear Systems Using Two-Scale Command Shaping

2021 ◽  
Author(s):  
Alexander Alyukov ◽  
Michael Leamy
Keyword(s):  
Nonlinear Systems ◽  
Command Shaping

Command Shaping Slewing Motions for Tower Cranes

2010 ◽  
Vol 132 (1) ◽  
Author(s):  
Jason Lawrence ◽  
William Singhose
Keyword(s):  
Nonlinear Dynamics ◽  
Rotational Motion ◽  
Effective Control ◽  
Input Shaping ◽  
Residual Vibration ◽  
Command Shaping ◽  
Tower Crane ◽  
Control Scheme ◽  
Point To Point ◽  
Gantry Cranes

Input shaping has been shown to be a practical and effective control scheme for reducing payload swing on industrial bridge and gantry cranes. However, when applied to tower cranes, standard input shapers will have degraded performance due to the nonlinear dynamics of rotational motion. To alleviate this problem, two new command generators for tower cranes are developed for a point-to-point slewing motion. It is shown that standard shaping techniques greatly reduce oscillation and the new tower crane command generators cause even less residual vibration. Simulations and experiments verify the results.

New Command Shaping Methods for Reduced Vibration of a Suspended Payload With Constrained Trolley Motion

2007 ◽  
Author(s):  
Aaron R. Enes ◽  
Timothy Y. Hsu ◽  
Angela A. Sodemann
Keyword(s):  
System Modeling ◽  
Small Scale ◽  
Residual Vibration ◽  
Conveyor System ◽  
Command Shaping ◽  
Common Task ◽  
Modeling Errors ◽  
Point To Point ◽  
Manufacturing Environments ◽  
Command Signal

In manufacturing environments, a common task is to quickly move a suspended payload point-to-point along a fixed overhead conveyor track without inducing significant payload vibration. Recent research in command shaping has shown remarkably effective ways to reduce the swing of a suspended payload providing the motion of the trolley is not constrained. However, the development of a command shaper where the trajectory of the trolley is constrained to follow a fixed curvilinear path has not been explored. This paper will present the development of a simple feedforward command shaper for fast, low vibration, point-to-point movement of a payload suspended from a trolley constrained to follow a fixed generalized path. The command shaping method involves modifying the command signal by convolving it with a series of impulses. Prior work has suggested command shaping to be very effective for fast, low-vibration movement of flexible systems. In this paper, command shaping methods are applied to an overhead conveyor system constrained to move along a fixed curvilinear path. Two new command shapers are presented for canceling payload vibration induced by motion of the trolley along the path. The designed Tangential Vibration (TV) shaper reduces payload vibrations induced by tangential accelerations of the trolley along the path, while the Centripetal-Tangential Vibration (CTV) shaper reduces vibrations induced by both tangential and centripetal accelerations. A key result of this study is that a command shaper having at least three impulses is required to yield zero residual vibration for motion along a curvilinear path. A simple pendulum payload attached to an actual small-scale overhead trolley following a constrained path is used to evaluate the performance of the designed command shapers. It is shown that the designed shapers significantly reduce payload swing compared to unshaped performance. An experimental sensitivity analysis shows the designed shapers are robust to system modeling errors and variations in path parameters.

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