Adjustable-Smooth Polynomial Command-Shaping Control With Linear Hoisting

2018 ◽  
Vol 140 (6) ◽  
Author(s):  
Khalid A. Alghanim ◽  
Majed A. Majeed ◽  
Khaled A. Alhazza
Keyword(s):  
Input Signal ◽  
Polynomial Function ◽  
Equation Of Motion ◽  
Modal Parameters ◽  
Input Shaping ◽  
Overhead Crane ◽  
Command Shaping ◽  
System Parameters ◽  
Cable Length ◽  
Simple Pendulum

Great amount of work has been dedicated to eliminate residual vibrations in rest-to-rest motion. Considerable amount of these methods is based on convolving a general input signal with a sequence of timed impulses. These impulses usually have large jumps in their profiles and are chosen depending on the system modal parameters. Furthermore, classical input shaping methods are usually used for constant cable length and are sensitive to any change in the system parameters. To overcome these limitations, polynomial command shapers with adjustable maneuvering time are proposed. The equation of motion of a simple pendulum with the effect of hoisting is derived, linearized, and solved in order to eliminate residual vibrations in rest-to-rest maneuvers. Several cases including smooth, semi-smooth and unsmooth continuous shapers are simulated numerically and validated experimentally on an experimental overhead crane. Numerical and experimental results show that the proposed polynomial command shaper eliminates residual vibrations effectively. The effect of linear hoisting is also included and discussed. To enhance the shaper performance, extra parameters are added to the polynomial function to reduce shaper sensitivity. Results show that the effect of adding these parameters greatly enhances the shaper performance.

Adjustable maneuvering time wave-form command shaping control with variable hoisting speeds

2016 ◽  
Vol 23 (7) ◽  
pp. 1095-1105 ◽  
Author(s):  
Khaled A Alhazza
Keyword(s):  
Continuous Wave ◽  
Equation Of Motion ◽  
Approximation Technique ◽  
Wave Form ◽  
Input Shaping ◽  
Overhead Crane ◽  
Algorithm Optimization ◽  
Optimization Scheme ◽  
Command Shaping ◽  
Pendulum Model

Classical input shaping is based on convolving a general input signal with a sequence of timed impulses. These impulses are chosen to match certain modal parameters of the system under control to eliminate residual vibrations in rest-to-rest maneuvers. This type of input shaping is strongly dependent on the system period. In this work, an adjustable maneuvering time wave form command shaper is presented. The equation of motion of a simple pendulum model of a crane is derived and solved in order to eliminate residual vibrations at the end of motion. Several cases are simulated numerically and validated experimentally on an experimental model of an overhead crane. Results show that the proposed command shaper is capable of eliminating residual vibrations effectively with a single continuous wave form command. The work is extended to include the effect of hoisting on the shaper performance. Several functions are used to simulate hoisting. To overcome the added complexity of hoisting on the system, an approximation technique is used to determine initial shaped command parameters, which are later used in a genetic algorithm optimization scheme. Numerical and experimental results prove that the proposed command shaper can effectively eliminate residual vibrations in rest-to-rest maneuvers.

Experimental and Numerical Validation on a Continuous Modulated Wave-Form Command Shaping Control Considering the Effect of Hoisting

2013 ◽  
Author(s):  
Khaled A. Alhazza
Keyword(s):  
Optimization Technique ◽  
Large Body ◽  
Initial Point ◽  
Pattern Search ◽  
Wave Form ◽  
Input Shaping ◽  
Time Varying ◽  
Scaled Model ◽  
Command Shaping ◽  
Cable Length

A large body of research has been dedicated to input-shaping control techniques. Most of the research assumes constant cable length, due to the complexity of the dynamics associated with changing cable length (hoisting). Current techniques tend to split maneuvers into three consecutive stages, raising the payload from an initial point, then moving it horizontally using input-shaping, and finally lowering it to a final location. These techniques are effective, however, they involve significant time penalties. In this work, a new modulated wave-form command shaping technique is proposed to enable concurrent hoisting and travel maneuvers. The time varying ordinary differential equation of motion is derived and used to determine the parameters and frequency of the proposed shaped-command. Assuming linear hoisting, the equation is solved analytically by assuming small changes in the time varying terms. This approach results in some error which can be corrected by using pattern search optimization technique. It is shown that, the proposed method is capable of eliminating the travel and residual oscillations for different maneuvers involving linear hoisting. Performance is simulated numerically and validated experimentally on a scaled model of an overhead crane.

Adaptive output-based command shaping for sway control of a 3D overhead crane with payload hoisting and wind disturbance

2018 ◽  
Vol 98 ◽  
pp. 157-172 ◽  
Author(s):  
Auwalu M. Abdullahi ◽  
Z. Mohamed ◽  
H. Selamat ◽  
Hemanshu R. Pota ◽  
M.S. Zainal Abidin ◽  
...  
Keyword(s):  
Wind Disturbance ◽  
Overhead Crane ◽  
Command Shaping

On a Certain Class of Expanding Systems

2010 ◽  
Vol 17 (2) ◽  
pp. 299-306
Author(s):  
Adam Żuchowski
Keyword(s):  
Transfer Function ◽  
Input Signal ◽  
Initial Conditions ◽  
System Optimization ◽  
Gain Coefficient ◽  
Time Intervals ◽  
System Parameters ◽  
Linear Dynamic ◽  
Subsequent Time ◽  
Input Signals

On a Certain Class of Expanding Systems The interesting properties of a class of expanding systems are discussed. The operation of the considered systems can be described as follows: the input signal is processed by a linear dynamic converter in subsequent time intervals, each of them is equal to Ti. Processing starts at the moments n · Ti, always after zeroing of converter initial conditions. For smooth input signals and a given transfer function of the converter one can suitably choose Ti and the gain coefficient in order to realize the postulated linear operations on input signals, which is quite different comparing it to the operation realized by the converter. The errors of postulated operations are mainly caused by non-smooth components of the input signal. The principles for choice of system parameters and rules for system optimization are presented in the paper. The referring examples are attached too.

Application of Dynamic Input Shaping for a Dual-Mirror System

2021 ◽  
Author(s):  
Alicia Dautt-Silva ◽  
Raymond de Callafon
Keyword(s):  
Input Signal ◽  
Inverse Kinematic ◽  
Open Loop ◽  
Mirror System ◽  
Image Motion ◽  
Step Response ◽  
Input Shaping ◽  
Input Signals ◽  
Compensation Device ◽  
Operating Constraints

Abstract The task of trajectory planning for a dual-mirror optical pointing system greatly benefits from carefully designed dynamic input signals. This paper summarizes the application of multivariable input shaping (IS) for a dual-mirror system, starting from initial open-loop step-response data. The optical pointing system presented consists of two Fast Steering Mirrors (FSM) for which dynamically coupled input signals are designed, while adhering to mechanical and input signal constraints. For the solution, the planned trajectories for the dual-mirrors are determined via (inverse) kinematic analysis. A linear program (LP) problem is used to compute the dynamic input signal for each of the FSMs, with one of the mirrors acting as an image motion compensation device that guarantees tracking of a planned trajectory within a specified accuracy and the operating constraints of the FSMs.

Dynamics of a Continuous System With Clearance and Motion Limiting Stops

1999 ◽  
Author(s):  
P. Metallidis ◽  
S. Natsiavas
Keyword(s):  
Piecewise Linear ◽  
Research Work ◽  
Continuous System ◽  
Continuous Model ◽  
Equation Of Motion ◽  
Model System ◽  
Periodic Motions ◽  
System Parameters ◽  
Rigid Rods ◽  
The Stability

Abstract The present study generalises previous research work on the dynamics of discrete oscillators with piecewise linear characteristics and investigates the response of a continuous model system with clearance and motion-limiting constraints. More specifically, in the first part of this work, an analysis is presented for determining exact periodic response of a periodically excited deformable rod, whose motion is constrained by a flexible obstacle. This methodology is based on the exact solution form obtained within response intervals where the system parameters remain constant and its behavior is governed by a linear equation of motion. The unknowns of the problem are subsequently determined by imposing an appropriate set of periodicity and matching conditions. The analytical part is complemented by a suitable method for determining the stability properties of the located periodic motions. In the second part of the study, the analysis is applied to several cases in order to investigate the effect of the system parameters on its dynamics. Special emphasis is placed on comparing these results with results obtained for similar but rigid rods. Finally, direct integration of the equation of motion in selected areas reveals the existence of motions, which are more complicated than the periodic motions determined analytically.

Reducing Trajectory Tracking Error of Flexible Mobile Robots Using Command Shaping With Error-Limiting Constraints

2017 ◽  
Author(s):  
Gerald Eaglin ◽  
Joshua Vaughan
Keyword(s):  
Mobile Robots ◽  
Trajectory Tracking ◽  
Tracking Error ◽  
Input Shaping ◽  
Flexible Systems ◽  
Command Shaping ◽  
Modeling Errors ◽  
Temporal Tracking ◽  
Point Motion ◽  
Point To Point

The ability to track a trajectory without significant error is a vital requirement for mobile robots. Numerous methods have been proposed to mitigate tracking error. While these trajectory-tracking methods are efficient for rigid systems, many excite unwanted vibration when applied to flexible systems, leading to tracking error. This paper analyzes a modification of input shaping, which has been primarily used to limit residual vibration for point-to-point motion of flexible systems. Standard input shaping is modified using error-limiting constraints to reduce transient tracking error for the duration of the system’s motion. This method is simulated with trajectory inputs constructed using line segments and Catmull-Rom splines. Error-limiting commands are shown to improve both spatial and temporal tracking performance and can be made robust to modeling errors in natural frequency.

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.

scholarly journals The Time Delay Filtering Method for Cancelling Vibration on Overhead Transportation Systems Modelled as a Physical Pendulum

2007 ◽  
Vol 14 (1) ◽  
pp. 53-64 ◽  
Author(s):  
G. Peláez ◽  
J. Doval-Gandoy ◽  
N. Caparrini ◽  
J.C. García-Prada
Keyword(s):  
Time Delay ◽  
Dynamic Response ◽  
Transportation Systems ◽  
Overhead Crane ◽  
Physical Pendulum ◽  
Filtering Method ◽  
Overhead Cranes ◽  
Simple Pendulum ◽  
Pendulum Model

An investigation of the response of a physical pendulum to time delay filtered inputs was conducted. It was shown that the physical pendulum model is more accurate than the simple pendulum for modelling the dynamic response of overhead cranes with loads hanging from hooks. Based on the physical pendulum model a Specified Time Delay filter for an experimental mini overhead crane was synthesized. While somewhat limited in the scope by the hardware conditions placed in the system, the results provide basic insights into the successful application of the Time Delay Filtering method to overhead cranes.

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