Characteristics of the time-optimal control of flexible structures with damping

Abstract

The time-optimal control of flexible structures with d a m p ing is considered. We formulate the general time-optimal control problem for single-axis flexible structures, and an analytical result is given for a lower bound on the number of control switches for the one-bending-mode case. Numerical solutions and simulations are presented to show several interesting trends of the time-optimal control switch times as the frequencies and dampings of the flexible modes are varied.

A comparison of constant and variable amplitude command shaping techniques for vibration reduction

“…As the damping increases, for a fixed natural frequency w and maneuver size L , 2 of the impulses near mid-maneuver migrate towards the end of the maneuver. A similar impulse migration was noted in the ZV CAP shapers [8]. Thus, for highly damped systems, there is 1 impulse at mid-maneuver and 4 impulses near the end of the maneuver.…”

“…The problem of input shaping for constant-amplitude actuators is similar to generating the time-optimal control of flexible structures as discussed in [8,9,141. Recent studies [7,8,111 revealing interesting characteristics of the time-optimal control for flexible structures motivates our current study to compare variable-amplitude input shaping to time-optimal, bang-bang, shaped commands.…”

“…Recent studies [7,8,111 revealing interesting characteristics of the time-optimal control for flexible structures motivates our current study to compare variable-amplitude input shaping to time-optimal, bang-bang, shaped commands. In this paper we first investigate the characteristics of robus t t ime-op t imal cons t ant-amplitude (bang-bang) control and then we compare these time-optimal commands to some variable-amplitude command shaping methods.…”

“…The timing of the im put shapers has been properties [8]. Figure 3: The structure of the time-optimal ZV CAP input shaper for flexible systems with no damping.…”

Time-optimal rest-to-rest slewing of multi-mode flexible spacecraft using ZVD robustness constraints

“…The effect of damping on robust and non-robust time-optimal shaping for single-mode systems has been presented. 13,43 Characteristics of the solution space will be presented by varying one of the parameters r, x d , or FM. Basing our problem formulation of the model shown in Figure 2, we set the force-to-mass ratio by setting m i =1/3, and then equating u max =FM.…”