Xj. Liu et J. Onoda, 2-STAGE STRATEGY FOR SIMULTANEOUS SLEWING AND VIBRATION SUPPRESSION OF FLEXIBLE STRUCTURES, Computer methods in applied mechanics and engineering, 147(3-4), 1997, pp. 357-367
This paper presents an open loop near-minimum-time solution for simult
aneous slewing and vibration suppression of flexible structures. The p
roblem is formulated as an open-loop, minimum-system energy and/or con
trol effort optimal control problem in modal space. With parametric co
ntrol law, a two-level problem-solving strategy is presented. In the f
irst stage, a sequence of rigid mode-based time-optimal control proble
ms is solved and the minimum maneuver time is found by gradually reduc
ing the maneuver time until the solution converges. In the second stag
e, the optimal parameters of the control law are evaluated using nonli
near programming with prescribed performance index as its objective fu
nction. The proposed strategy, through time-optimal control of the rig
id mode combined with the parametric quadratic control of the elastic
modes, determines the control profiles which give both minimum maneuve
r time and desired value of performance index. As an example, the opti
mal control of a slewing flexible beam is presented, and high performa
nce slewing maneuver is achieved.