Abstract
This paper presents a new method of controlling the end effector position and orientation of a flexible planar three-link mechanism. The coupled dynamic model was formulated using a method based on the Udwadia–Kalaba equations of motion for constrained systems. Lyapunov's theory was used to develop a nonlinear control law using piezoelectric actuators and the unconstrained link dynamic models. Numerical simulation was used to demonstrate the system tracking performance of the end effector using a reduced order controller applied to a higher order truth dynamic model.
Issue Section:
Research Papers
References
1.
Asada
,
H.
, and
Slotine
,
J.
, 1986
, Robot Analysis and Control
, 1st ed.,
Wiley
, New York
.2.
Craig
,
J.
, 2017
, Introduction to Robotics
, 4th ed.,
Pearson
, London
.3.
Spong
,
M.
,
Hutchinson
,
S.
, and
Vidyasagar
,
M.
, 2006
, Robot Modeling and Control
, 2nd ed.,
Wiley
, New York
.4.
Dwivedy
,
S.
, and
Eberhard
,
P.
, 2006
, “
Dynamic Analysis of Flexible Manipulators
,” Mech. Mach. Theory
,
41
(7
), pp. 749
–777
.10.1016/j.mechmachtheory.2006.01.0145.
Crawley
,
E. F.
, and
de Luis
,
J.
, 1987
, “
Piezoelectric Actuators as Elements of Intelligent Structures
,” AIAA J.
,
25
(10
), pp. 1373
–1385
.10.2514/3.97926.
Dosch
,
J.
,
Inman
,
D.
, and
Garcia
,
E.
, 1992
, “
A Self-Sensing Piezoelectric Actuator for Collocated Control
,” J. Intell. Mater. Syst. Struct.
,
3
(1
), pp. 166
–185
.10.1177/1045389X92003001097.
Sun
,
D.
, and
Mills
,
J.
, 1999
, “
Study on Piezoelectric Actuators in Control of a Single-Link Flexible Manipulator
,” Proceedings IEEE International Conference on Robotics and Automation
,
IEEE Xplore
, Vol. 2
, Detroit, MI
, May 10–15, pp. 849
–854
.10.1109/ROBOT.1999.7723968.
Sangpet
,
T.
,
Kuntanapreeda
,
S.
, and
Schmidt
,
R.
, 2018
, “
An Adaptive Pid-Like Controller for Vibration Suppression of Piezo-Actuated Flexible Beams
,” J. Vib. Control
,
24
(12
), pp. 2656
–2670
.10.1177/10775463176921609.
Karagiannis
,
A.
,
Clayton
,
G.
, and
Nataraj
,
C.
, 2016
, “
Boundary Control of Harmonic Disturbances of Flexible Cantilever Beams Using Piezoelectric Patch
,” J. Vib. Control
,
22
(18
), pp. 3916
–3929
.10.1177/107754631456772310.
He
,
W.
,
Yang
,
C.
,
Zhu
,
J.
,
Liu
,
J.
, and
He
,
X.
, 2017
, “
Active Vibration Control of a Nonlinear Three-Dimensional Euler-Bernoulli Beam
,” J. Vib. Control
,
23
(19
), pp. 3196
–3215
.10.1177/107754631562772211.
Gerses
,
K.
, 2007
, “
Vibration Control of a Single-Link Flexible Manipulator Using a Combined Linear and Angular Velocity Feedback Controller
,” Master of Applied Science,
University of Victoria
, Victoria, BC
.12.
Chu
,
Z.
, and
Cui
,
J.
, 2015
, “
Control of a Two-Link Flexible Manipulator Using an Input Shaper and Adaptivepositive Position Feedback
,” Adv. Mech. Eng.
,
7
(10
), pp. 1–13.10.1177/168781401561046613.
Mirzaee
,
E.
,
Eghtesad
,
M.
, and
Fazelzadeh
,
S.
, 2010
, “
Maneuver Control and Active Vibration Suppression of a Two-Link Flexible Arm Using a Hybrid Variable Structure/Lyapunov Control Design
,” Acta Astronaut.
,
67
(9–10
), pp. 1218
–1232
.10.1016/j.actaastro.2010.06.05414.
Karagülle
,
H.
,
Malgaca
,
L.
,
Dirilmiş
,
M.
,
Akdağ
,
M.
, and
Yavuz
,
Ş.
, 2017
, “
Vibration Control of a Two-Link Flexible Manipulator
,” Eng. Comput.
,
23
(12
), pp. 2023
–2034
.10.1177/107754631560769415.
Sayahkarajy
,
M.
,
Mohamed
,
Z.
,
Faudzi
,
A.
, and
Supriyanto
,
E.
, 2016
, “
Hybrid Vibration and Rest-to-Rest Control of a Two-Link Flexible Robotic Arm Using
Loop Shaping Control Design
,” Eng. Comput.
,
33
(2
), pp. 395
–409
.10.1108/EC-11-2014-022816.
Wu
,
S.
,
Tang
,
S.
, and
Huang
,
K.
, 2018
, “
Vibration Attenuation of a Two-Link Arm Carried by a Translational Stage
,” J. Vib. Control
,
24
(23
), pp. 5650
–5664
.10.1177/107754631876343717.
Zhang
,
W.
, 2018
, “
The Impulse Spectrum Method for Vibration Suppression of a Flexible Multilink Robot
,” J. Vib. Control
,
24
(17
), pp. 3865
–3881
.10.1177/107754631771418418.
Kilicaslan
,
S.
,
Ozgoren
,
M.
, and
Ider
,
S.
, 2007
, “
Control of Constrained Spatial Three-Link Flexible Manipulators
,” Mediterranean Conference on Control and Automation
,
IEEE Xplore
, Athens, Greece
, July 27–29, pp. 1
–6
.10.1109/MED.2007.443378119.
Zhang
,
X.
, 2009
, “
Dynamic Modeling and Active Vibration Control of a Planar 3-Prr Parallel Manipulator With Three Flexible Links
,” Ph.D. thesis,
University of Toronto
,
Toronto, CA
.20.
6Zhang
,
Q.
,
Li
,
C.
,
Zhang
,
J.
, and
Jin
,
J.
, 2016
, “
Active Vibration Control and Coupled Vibration Analysis of a Parallel Manipulator With Multiple Flexible Links
,” Shock Vib.
,
7474085
(17
), pp. 3865
–3881
.10.1155/2016/747408521.
Khalil
,
H.
, 2002
, Nonlinear Systems
, 3rd ed.,
Prentice Hall
,
Upper Saddle River, NJ
.22.
Vidyasagar
,
M.
, 2002
, Nonlinear Systems
, 2nd ed.,
Prentice Hall
,
Englewood Cliffs, NJ
.23.
Banerjee
,
A.
, 2003
, “
Contributions to Multibody Dynamics to Space Flight: A Brief Review
,” J. Guid. Control, Dyn.
,
26
(3
), pp. 385
–394
.10.2514/2.506924.
Sandor
,
G.
, and
Erdman
,
A.
, 1984
, Advanced Mechanism Design: Analysis and Synthesis
, 1st ed., Vol.
2
,
Prentice Hall
, Englewood Cliffs, NJ
.25.
Shabana
,
A.
, 1997
, “
Flexible Multibody Dynamics: Review of Past and Recent Developments
,” Multibody Syst. Dyn.
,
1
(2
), pp. 189
–222
.10.1023/A:100977350541826.
McMonagle
,
R.
, 2014
, “
Multi-Body Large Displacement Equations of Motion for Flexible Bodies Represented as Finite Element Models
,” AIAA
Paper No. 2014–2646.10.2514/6.2014-264627.
Banerjee
,
A.
, and
Dickens
,
J.
, 1990
, “
Dynamics of an Arbitrary Flexible Body in Large Rotation and Translation
,” J. Guid., Control Dyn.
,
13
(2
), pp. 221
–227
.10.2514/3.2054028.
Kane
,
T.
,
Ryan
,
R.
, and
Banerjee
,
A.
, 1987
, “
Dynamics of a Cantilever Beam Attached to a Moving Base
,” J. Guid., Control Dyn.
,
10
(2
), pp. 139
–151
.10.2514/3.2019529.
Lugrís
,
U.
,
Naya
,
M. A.
,
Pérez
,
J. A.
, and
Cuadrado
,
J.
, 2008
, “
Implementation and Efficiency of Two Geometric Stiffening Approaches
,” Multibody Syst. Dyn.
,
20
(2
), pp. 147
–161
.10.1007/s11044-008-9114-630.
Udwadia
,
F.
, 2008
, “
Optimal Tracking Control of Nonlinear Dynamical Systems
,” Proc. R. Soc. Lond. A
,
464
(2097), pp. 2341
–2363
.10.1098/rspa.2008.004031.
Udwadia
,
F.
, and
Kalaba
,
R.
, 1996
, Analytical Dynamics: A New Approach
,
Cambridge University Press
, New York
.32.
Spada
,
R.
, and
Nicoletti
,
R.
, 2017
, “
Application of the Udwadia-Kalaba Methodology to the Active Control of Shaft
,” J. Vib. Control
,
23
(13
), pp. 2094
–2110
.10.1177/107754631561100333.
Bajodah
,
A.
,
Hodges
,
D.
, and
Chen
,
Y.
, 2003
, “
New Form of Kane's Equations of Motion for Constrained Systems
,” J. Guid., Control, Dyn.
,
26
(1
), pp. 79
–88
.10.2514/2.501734.
Weaver
,
W.
, and
Johnston
,
P.
, 1984
, Finite Elements for Structural Analysis
,
Prentice Hall
, Englewood Cliffs, NJ
.35.
Craig
,
R.
, and
Kurdila
,
A.
, 2006
, Fundamentals of Structural Dynamics
, 2nd ed.,
Wiley
, Hoboken, NJ
.36.
Maciejowski
,
J.
, 1989
, Multivariable Feedback Design
,
Addison-Wesley Publishing Company
, Cornwall, GB
.37.
Seiler
,
P.
,
Packard
,
A.
, and
Gahinet
,
P.
, 2020
, “
An Introduction to Disk Margins
,” IEEE Control Syst. Mag.
,
40
(5
), pp. 78
–95
.10.1109/MCS.2020.300527738.
Cinquemani
,
S.
,
Ferrari
,
D.
, and
Bayati
,
I.
, 2015
, “
Reduction of Spillover Effects on Independent Modal Space Control Through Optimal Placement of Sensors and Actuators
,” Smart Mater. Struct.
,
24
(8
), p. 085006
.10.1088/0964-1726/24/8/08500639.
Matlab
, 2021
, “
R2021a
,”
The MathWorks
, Natick, MA
.40.
Singer
,
N.
, and
Seering
,
P.
, 1990
, “
Preshaping Command Inputs to Reduce System Vibration
,” ASME J. Dyn. Syst., Meas., Control
,
112
(1
), pp. 76
–82
.10.1115/1.2894142Copyright © 2023 by ASME
You do not currently have access to this content.
