Tension Control Law Research Articles

Feedback tether deployment and retrieval

Introduction S tethers have been proposed for many important applications such as the study of planetary atmosphere, micro and variable-^ experiments, space construction, and energy transmission. One of the primary issues in tether utilization is fast deployment/retrieval of attached payloads. Much work has been done on developing models for studying tether dynamics during deployment and retrieval. These models include tether flexibility, atmospheric effects, orbital eccentricity, and planetary oblateness effects. Two basic methods for controlling tether deployment/retrieval have emerged to date: 1) tension control' (reeling in or out) and 2) crawler mechanism. The second method has been proposed due to concerns of slow retrieval rates in the terminal phases and violent tether oscillations during tension controlled retrieval. The disadvantage of this method is that if the tether is not retrieved it may have to be jettisoned. A comparison of the two aforementioned control schemes has been conducted by Glickman and Rybak. Overall, much physical insight can be obtained by using simple mathematical models. A Lyapunov (mission function) approach has been used for tether deployment and retrieval by Fujii and Ishijima. The proposed nonlinear tension control law has been designed for controlling deployment and retrieval in the orbital plane. It performs well, but terminal oscillations of the tether length and tension are encountered during deployment. Furthermore, the pitch angle seems to remain constant during the terminal phase of retrieval indicating that it cannot be controllable to the origin. In this Note, we consider a modified Lyapunov control law to eliminate the terminal oscillations observed by Fujii and Ishijima and show that rapid retrieval is possible if moderate pitch angle excursion of the tether is allowed during the intermediate phase of retrieval. In all cases, the pitch angle can be controlled to the desired equilibrium point.

Stabilization of tethered satellites during station keeping

After deriving a set of dynamic equations governing the dynamics of a tethered satellite system (TSS), stabilizing tension-control laws are derived in feedback form. The tether is assumed to be rigid and massless, and the equations of motion are derived using the system Lagrangian. It is observed that, to stabilize the system, tools from stability analysis of critical nonlinear systems must be applied. Tools related to the Hopf bifurcation theorem are used in the construction of the stabilizing control laws, which may be taken purely linear. Simulations illustrate the nature of the conclusions and show that nonlinear terms in the feedback can be used to significantly improve the transient response.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Stability of a ring of connected satellites

The motion of a large number of artificial satellites connected in a ring one after another by tethers of variable length is considered. Every satellite is supposed to have a control system programmed according to some tether tension law as a function of the distance between tethered satellites. The effect of the tension control law on the stability of stationary rotation of this ring is investigated. The final stability condition includes two requirements: 1) the nominal tether tension should be less than a definite limit equal, up to numerical coefficient, to one satellite weight divided by the number of satellites; 2) tether tension should decrease (or remain constant) with the increase of the distance between tethered satellites. In dynamics the artificial rings of this kind are much like their natural prototype—meteor rings. On the other hand, the investigation of the artificial rings contributes to developing an unexpected view upon meteor rings, suggesting a model of an imaginary equivalent string.

On Control of Tethered Satellite Systems

The dynamics of tethered satellite systems is rather complex and consists of various rotational and vibrational degrees of freedom. While designing its control system, some of these degrees of freedom may be modeled while the others are likely to be left unmodeled to reduce complexity and cost. This paper examines the effectiveness of control procedures based on lower order dynamical models, when applied to higher order models. It appears that if a tension control law or its derivative is to be used to control the tether dynamics, a reasonably higher order model including the transverse vibrations must be considered to synthesize the control system.