Comand shaping, a feedforward approach used to control flexible manipulators, performs most effectively when applied to a linear system. In practice, various nonlinearities are present in a given system that will deteriorate the performance of command shaping. In this work, a multirate repetitive learning controller (MRLC) is used in conjunction with a command shaping method known as the optimal arbitrary time-delay filter (OATF) for discrete-time joint control of a single flexible link manipulator containing nonlinearities. With very little a priori knowledge of the given system, a MRLC is able to cancel the repetitive tracking errors caused by nonlinearities at select frequencies and thereby achieve near-perfect tracking of a periodic reference trajectory. By doing this, a MRLC controls the joint of the flexible link manipulator to follow a given shaped command more closely, thus allowing the OATF to more effectively attenuate residual manipulator tip vibrations. It is shown both analytically and experimentally that this combined control strategy is more effective than a conventional PID and OATF controller at attenuating residual tip vibrations.

Issue Section:
Technical Papers
Keywords:
flexible manipulators, multivariable control systems, learning (artificial intelligence), feedforward, control nonlinearities, optimal control, filtering theory, delay filters
Topics:
Control equipment, Flexible manipulators, Vibration, Displacement, Trajectories (Physics), Delays, Errors, Filters, Manipulators, Control systems, Feedforward control
1.
Singer
,
N. C.
, and
Seering
,
W. P.
,
1990
, “
Preshaping Command Inputs to Reduce System Vibration
,”
ASME J. Dyn. Syst., Meas., Control
,
112
, No.
1
, pp.
76
–
82
.
2.
Magee, D. P., and Book, W. J., 1994, “Filtering Schilling Manipulator Commands to Prevent Flexible Structure Vibration,” Proceedings of the American Control Conference, Baltimore, MA, June 29–July 1, pp. 2538–2542.
3.
Rhim, S., and Book, W. J., 1997, “Vibration Cancellation in Complex Support Structures for Precision Robots,” Proceedings of the ASME International Mechanical Engineering Congress and Exposition, Dallas, TX, November 16–21, DSC-Vol. 61, pp. 503–509.
4.
Khorrami
,
F.
,
Jain
,
S.
, and
Tzes
,
A.
,
1994
, “
Experiments on Rigid-body Based Controllers with Input Preshaping for a Two-link Flexible Manipulator
,”
IEEE Trans. Rob. Autom.
,
10
, No.
1
, pp.
55
–
65
.
5.
Khorrami
,
F.
,
Jain
,
S.
, and
Tzes
,
A.
,
1995
, “
Experimental Results on Adaptive Nonlinear Control and Input Preshaping for Multi-link Flexible Manipulators
,”
Automatica
,
31
, No.
1
, pp.
83
–
97
.
6.
Arimoto, S., 1986, “Mathematical Theory of Learning with Applications to Robot Control,” K. S. Narendra, Ed., Adaptive and Learning Systems, Plenum Press, New York, pp. 379–388.
7.
Moore, K. L., 1993, Iterative Learning Control for Deterministic Systems, Springer-Verlag, London.
8.
Magee, D. P., 1996, “Optimal Arbitrary Time-delay Filtering to Minimize Vibration in Elastic Manipulator Systems,” Ph.D. thesis, Georgia Institute of Technology, Atlanta, GA, Aug.
9.
Rhim, S., and Book, W. J., 2000, “Adaptation of Generalized Time-delay Command Shaper for Flexible Manipulator Control,” Proceedings of the IEEE International Conference on Robotics and Automation, San Francisco, CA, Apr. 22–28, pp. 1465–1471.
10.
James, C. D., 1997, “The Design of Robust Multi-rate Repetitive Learning Controllers with Applications to Practical Systems,” Ph.D. thesis, Georgia Institute of Technology, Atlanta, GA, Nov.
11.
James, C., and Sadegh, N., 1999, “Synthesis and Stability of a Multirate Repetitive Learning Controller,” Proceedings of the American Control Conference, San Diego, CA, June 2–4, pp. 358–362.
12.
James, C., Sadegh, N., and Hu, A.-P., 1999, “Synthesis, Stability Analysis, and Experimental Implementation of a Multirate Repetitive Learning Controller,” Proceedings of the IEEE/ASME International Conference on Advanced Intelligent Mechatronics, Atlanta, GA, Sept. 19–23, pp. 653–658.
13.
Sadegh, N., 1991, “Synthesis and Stability Analysis of Repetitive Controllers,” Proceedings of the American Control Conference, Boston, MA, June 26–28, pp. 2634–2639.
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