This paper extends the use of delayed reference controllers to the simultaneous motion and vibration control of flexible link mechanisms. Vibration damping is achieved by introducing an “equivalent damping force” into the system through the computation of a suitable delayed time. The delayed time, which is based on the measured vibrations, is then employed in the trajectory planner to set the reference input. The stability of the controller is discussed and its effectiveness is proved by applying it to a four-bar planar linkage with flexible links.

References

References
1.
Caracciolo
,
R.
,
Richiedei
,
D.
,
Trevisani
,
A.
, and
Zanotto
,
V.
, 2005, “
Robust Mixed-Norm Position and Vibration Control of Flexible Link Mechanisms
,”
Mechatronics
,
15
, pp.
767
791
.
2.
Boscariol
,
P.
,
Gasparetto
,
A.
, and
Zanotto
,
V.
, 2010, “
Active Position and Vibration Control of a Flexible Links Mechanism Using Model-Based Predictive Control
,”
ASME J. Dyn. Syst., Meas., Control
,
132
,
014506
.
3.
Trevisani
,
A.
, 2003, “
Simultaneous Rigid-Body Motion and Vibration Control of a Flexible Four-Bar Linkage
,”
J. Sound Vib.
,
268
, pp.
947
970
.
4.
Singer
,
N. C.
, and
Seering
,
W. P.
, 1990, “
Preshaping Command Inputs to Reduce System Vibration
,”
ASME J. Dyn. Syst., Meas., Control
,
112
, pp,
76
82
.
5.
Rhim
,
S.
,
Hu
,
A.
,
Sadegh
,
P. N.
, and
Book
,
W. J.
, 2001, “
Combining a Multirate Repetitive Learning Controller With Command Shaping for Improved Flexible Manipulator Control
,”
ASME J. Dyn. Syst., Meas., Control
,
123
, pp.
385
390
.
6.
Bazaz
,
S. A.
, and
Tondu
,
B.
, 1999, “
Minimum Time On-Line Joint Trajectory Generator Based on Low Order Spline Method for Industrial Manipulators
,”
Robot. Auton. Syst.
,
29
, pp.
257
268
.
7.
Kang
,
W.
,
Xi
,
N.
, and
Tan
,
J.
, 1999, “
Analysis and Design of Non-Time Based Motion Controller for Mobile Robots
,”
Proceedings of the IEEE International Conference on Robotics and Automation
, Detroit.
8.
Li
,
P. Y.
, 1999, “
Coordinate Contour Following Control for Machining Operation—a Survey
,”
Proceedings of the American Control Conference
, San Diego.
9.
Gallina
,
P.
, 2006, “
Delayed Reference Control for Hotwire Cutting of Expandable Polystyrene Foam
,”
J. Manuf. Sci. Eng.
,
128
, pp.
360
366
.
10.
Wu
,
Y.
,
Tarn
,
T. J.
, and
Xi
,
N.
, 1995, “
Force and Transition Control with Environmental Uncertainties
,”
Proceedings of the IEEE International Conference on Robotics and Automation
, Nagoya, Japan.
11.
Park
,
J. H.
,
Park
,
J. Y.
, and
Moon
,
S. J.
, 2004, “
Real-Time Bilateral Control for an Internet-Based Telerobotic System
,”
JSME Int. J., Ser. C
,
47
, pp.
708
714
.
12.
Poulakakis
,
I.
, and
Grizzle
,
J. W.
, 2009, “
The Spring Loaded Inverted Pendulum as the Hybrid Zero Dynamics of an Asymmetric Hopper
,”
IEEE Trans. Autom. Control
,
54
, pp.
1779
1793
.
13.
Gallina
,
P.
, and
Trevisani
,
A.
, 2004, “
Delayed Reference Control of a Two Mass Elastic System
,”
J. Vib. Control
,
10
, pp.
135
159
.
14.
Gallina
,
P.
, and
Trevisani
,
A.
, 2005, “
Synthesis and Experimental Validation of a Delayed Reference Controller for Active Vibration Suppression in Mechanical Systems
,”
J. Appl. Mech.
,
72
, pp.
623
627
.
15.
Richiedei
,
D.
, and
Trevisani
,
A.
, 2009, “
Design of Delayed Reference Controllers for Simultaneous Path Tracking and Active Vibration Damping of Multi-Degree-of-Freedom Linear Systems
,”
J. Vib. Control
,
15
, pp.
323
346
.
16.
Giovagnoni
,
M.
, 1994, “
A Numerical and Experimental Analysis of a Chain of Flexible Bodies
,”
ASME J. Dyn. Syst., Meas., Control
,
116
, pp.
73
80
17.
Caracciolo
,
R.
,
Richiedei
,
D.
, and
Trevisani
,
A.
, 2008, “
Robust Piecewise-Linear State Observers for Flexible Link Mechanisms
,”
ASME J. Dyn. Syst., Meas., Control
,
130
,
031011
.
18.
Preumont
,
A.
, 2002,
Vibration Control of Active Structures, An Introduction
,
2nd ed.
,
Kluwer
,
Dordrecht, The Netherlands
.
19.
Boyd
,
S.
, and
Vandenberghe
,
L.
, 2004,
Convex Optimization
, Cambridge University, Cambridge, United Kingdom.
You do not currently have access to this content.