Coupling of tether lateral vibration and subsatellite attitude motion

Nonlinear Attitude Control of a Tether-Connected Multi-Satellite in Three-Dimensional Space

“…Like in LQR controllers state-space equations, such as (6) or (9), are needed to apply the SDRE controllers to the dynamic systems. Unlike LQR controllers which use a constant or time-varying dynamic model matrix (A and B or A(t) and B(t)), however, the SDRE controllers update the dynamic model matrix (A(x)) and the input coupling matrix (B(x)) in the state-space equation in every given time step.…”

“…From the state-space equations that are described as (9), the initial state values x c (t 0 ), x 1 (t 0 ), and x 2 (t 0 ) are given, and x c (t) 2 R n c , x 1 (t) 2 R n 1 , x 2 (t) 2 R n 2 , u c (t) 2 R m c , u 1 (t) 2 R m 1 , and u 2 (t) 2 R m 2 are assumed. The performance index to be minimized is…”

“…For tethered formation flying both the relative positions and the attitudes of the individual satellites need to be accurately controlled to point toward the same inertial target [7]. Attitude dynamics and control for tethered satellite systems have received considerable attention in many papers [8][9][10][11][12]. However these studies considered a gravity-gradient, Earth-orbiting tether, while the attitude control of tethered platforms in tether formations has not been studied.…”

Nonlinear Model Reduction and Decentralized Control of Tethered Formation Flight

“…The tether is assumed to be ideal, i.e., massless and inextensible; therefore, neither longitudinal nor transverse vibrations of tether are allowed. The zero mass assumption can be realized by rather strong thin material like Kevlar [21] to avoid a detrimental phenomenon such as the coupling between in-plane and out-plane oscillations of the massive tether and the spacecraft attitude [35]. Additionally, the array is assumed to always rotate at a certain angular rate so the tether is taut and straight at all times.…”

Nonlinear Model Reduction and Decentralized Control of Tethered Formation Flight by Oscillation Synchronization

“…The zero mass assumption can be realized by rather strong thin material like Kevlar 26 to avoid a detrimental phenomenon such as the coupling between in-plane and out-plane oscillations of the massive tether and the spacecraft attitude. 33 Additionally, the array is assumed to always rotate at a certain angular rate so the tether is taut and straight at all times. A nonzero angular rotation 32 is a realistic assumption since tethered interferometers will attempt to fill a full u-v coverage 1 by rotation.…”