In this paper, tip regulation of a flexible one-link manipulator by Learning Variable Structure Control (LVSC) is investigated. Switching surface is designed according to a selected reference model which relocates system poles to be negative real ones, hence link vibration is eliminated. The proposed LVSC incorporates a learning mechanism to improve regulation accuracy. Rigorous proof shows: the tracking error sequence converges uniformly to zero; the uniformly bounded learning control sequence converges to the equivalent control almost everywhere. For practical considerations, the learning mechanism is further conducted in frequency domain by means of Fourier series expansion, hence achieves better regulation performance. Numerical simulations confirm the effectiveness and robustness of the proposed approach. [S0022-0434(00)01804-9]

Issue Section:
Technical Papers
Keywords:
flexible manipulators, variable structure systems, learning systems, pole assignment, control system synthesis, vibration control, convergence, frequency-domain synthesis, Fourier series
Topics:
Control equipment, Design, Errors, Flexible manipulators, Fourier series, Manipulators, Poles (Building), Robustness, Vibration, Computer simulation, Trajectories (Physics), Steady state, Dynamic models, Control systems, Variable structure systems, Vibration control
1.
Utkin, V. I., 1992, Sliding Modes in Control and Optimizations, Springer-Verlag, Berlin, Germany.
2.
Fu
,
L.-C.
, and
Liao
,
T.-L.
,
1990
, “
Globally Stable Robust Tracking of Nonlinear Systems Using Variable Structure Control and With an Application to a Robotic Manipulator
,”
IEEE Trans. Autom. Control
,
35
, No.
12
, pp.
1345
–
1350
.
3.
Zinober, A. S. I., Ed. 1994, Lecture Notes in Control and Information Sciences, Variable Structure and Lyapunov Control, Springer-Verlag, London.
4.
Man
,
Z.
,
Paplinkski
,
A. P.
, and
Wu
,
H. R.
,
1994
, “
A Robust Mimo Terminal Sliding Mode Control Scheme for Rigid Robotics Manipulators
,”
IEEE Trans. Autom. Control
,
39
, No.
12
, pp.
2464
–
2469
.
5.
Edwards
,
C.
, and
Spurgeon
,
S. K.
,
1996
, “
Robust Output Tracking Using a Sliding Mode Controller/Observer
,”
Int. J. Control
,
64
, No.
5
, pp.
967
–
983
.
6.
Misawa
,
E. A.
,
1997
, “
Discrete-Time Sliding Mode Control for Nonlinear Systems With Unmatched Uncertainties and Uncertain Control Vector
,”
ASME J. Dyn. Syst., Meas., Control
,
119
, No.
3
, pp.
503
–
512
.
7.
Yu
,
X.
, and
Man
,
Z.
,
1998
, “
Multi-Input Uncertain Linear Systems With Terminal Sliding-Mode Control
,”
Automatica
,
34
, No.
3
, pp.
389
–
392
.
8.
Bartolini
,
G.
, and
Ferrara
,
A.
,
1999
, “
On the Parameter Convergence Properties of a Combined Vs/Adaptive Control Scheme During Sliding Motion
,”
IEEE Trans. Autom. Control
,
44
, No.
1
, pp.
70
–
76
.
9.
Qian
,
W. T.
, and
Ma
,
C. C. H.
,
1992
, “
A New Controller Design for a Flexible One-Link Manipulator
,”
IEEE Trans. Autom. Control
,
37
, No.
1
, pp.
132
–
137
.
10.
Young
,
K. D.
, and
Ozguner
,
U.
,
1993
, “
Frequency Shaping Compensator Design for Sliding Mode
,”
Int. J. Control
,
57
, pp.
1005
–
1019
.
11.
Xu
,
J.-X.
, and
Cao
,
W.-J.
,
2000
, “
Synthesized Sliding Mode Control of a Single-Link Flexible Robot
,”
Int. J. Control
,
73
, No.
3
, pp.
197
–
209
.
12.
Xu, J.-X., and Cao, W.-J., 1999, “Active Vibration Control of a Single-Link Flexible Manipulator by Pole-Placement Approach,” IEEE Proceedings of 38th Conference on Decision and Control, Dec., pp. 3888–3893.
13.
Xu, J.-X., and Cao, W.-J., 2000, “A Direct Approach for Tip Position Regulation of a Single-Link Flexible Manipulator, (in press),” Int. J. Syst. Sci.
14.
Arimoto
,
S.
,
Kawamura
,
S.
, and
Miyazaki
,
F.
,
1984
, “
Bettering Operation of Robots by Learning
,”
J. Robot. Syst.
,
1
, No.
2
, pp.
123
–
140
.
15.
Yuh
,
J.
,
1987
, “
Application of Discrete-Time Model Reference Adaptive Control to a Flexible Single-Link Robot
,”
J. Robot. Syst.
,
4
, No.
5
, pp.
621
–
630
.
16.
Albert
,
A.
,
1969
, “
Conditions for Positive and Nonnegative Definiteness in Terms of Pseudoinverses
,”
SIAM (Soc. Ind. Appl. Math.) J. Appl. Math.
,
17
, pp.
434
–
440
.
17.
Chen, Y. P., 1989, “Sliding Mode Controller Design for Flexible Multi-Link Manipulators,” Ph.D. thesis of University of Texas at Arlington, University Microfilms International, Ann Arbor, MI.
18.
Bontsema
,
J.
, and
Curtain
,
R. F.
,
1988
, “
A Note on Spillover and Robustness for Flexible Systems
,”
IEEE Trans. Autom. Control
,
33
, No.
6
, pp.
567
–
569
.
19.
Ioannou, P. A., and Sun, J., 1996, Robust Adaptive Control, Prentice Hall, Englewood Cliffs, New Jersey, p. 71 and pp. 101–104.
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