This paper addresses the problem of designing jerk limited time-optimal control profiles for rest-to-rest maneuvers of flexible structures. The variation of the structure of the jerk profile as a function of the permissible jerk is studied. An optimal control problem is formulated which includes constraints to cancel the poles corresponding to the rigid body and flexible modes of the system and to satisfy the boundary conditions of the rest-to-rest maneuver. The proposed technique is illustrated on the benchmark Floating Oscillator problem where the jerk profile is parameterized as a bang-off-bang or bang-bang profile.

1.
Junkins, J. L., Rahman, Z., and Bang, H., 1990, “Near-Minimum Time Maneuvers of Flexible Vehicles: A Liapunov Control Law Design Method,” Mechanics and Control of Large Flexible Structures, AIAA Publication, Washington, DC.
2.
Ballhaus, W. L., Rock, S. M., and Bryson, A. E., 1992, “Optimal Control of a Two-Link Flexible Robotic Manipulator Using Time-Varying Controller Gains,” Amer. Astronautics Soc. Paper No. 92-055.
3.
Bhat
,
S. P.
, and
Miu
,
D. K.
,
1991
, “
Minimum Power and Minimum Jerk Control and its Application in Computer Disk Drives
,”
IEEE Trans. Magn.
,
27
(
6
), pp.
4471
4475
.
4.
Singhose, W. E., Porter, L. J., and Seering, W. P., 1997, “Input Shaped Control of a Planar Gantry Crane with Hoisting,” 1997 American Control Conf., Albuquerque, NM.
5.
Smith, O. J. M., 1957, “Posicast Control of Damped Oscillatory Systems,” Proc. of IRE, pp. 1249–1255.
6.
Singer
,
N. C.
, and
Seering
,
W. P.
,
1990
, “
Preshaping Command Inputs to Reduce System Vibrations
,”
ASME J. Dyn. Syst., Meas., Control
,
115
, pp.
76
82
.
7.
Singh
,
T.
, and
Vadali
,
S. R.
,
1993
, “
Robust Time-Delay Control
,”
ASME J. Dyn. Syst., Meas., Control
,
115
(
2A
), pp.
303
306
.
8.
Liu
,
Q.
, and
Wie
,
B.
,
1992
, “
Robust Time-Optimal Control of Uncertain Flexible Spacecraft
,”
J. Guidance Control Dyn.
,
15
(
3
), pp.
597
604
.
9.
Singh
,
T.
, and
Vadali
,
S. R.
,
1994
, “
Robust Time-Optimal Control: Frequency Domain Approach
,”
J. Guidance Control Dyn.
,
17
(
2
), pp.
346
353
.
10.
Hermes, H., and Lasalle, J. P., 1969, Functional Analysis and Time Optimal Control, Academic Press, New York, NY.
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