Dynamics and Control of a Tethered Flight Vehicle

Certain types of the problems of dynamics and control of maneuverable tethered flight vehicles are dealt with in this paper. The numerically linearized equations of motion are used in a stability analysis and to design control laws that may be used in station keeping and maneuvering of the vehicle. For motion in which deviations from the equilibrium states are small in magnitude and the maneuver of the vehicle is confined to a neighboring region, the use of a linear quadratic regulator (LQR) for the station keeping and a linear terminal controller for the maneuver is investigated. For the model and conditions used, it is shown that aerodynamic control may be used successfully for station keeping and maneuvering, and the aerodynamic control yields results comparable to those obtained by using reaction control. HE dynamics and control of tethered satellite systems (TSSs)1 have inspired many researchers and matured to the point where one enjoys the ampleness of the pertinent literature. Typical opera- tion of aTSS involves the deployment and retrieval of the subsatellite and station keeping. Because of the inherent instability of the re- trieval process, efforts have been focused on the dynamic analysis and synthesis of control laws for TSSs during the deployment and retrieval phases.2'3 After the subsatellite is fully deployed, its exact final position is not of concern in most cases. However, if the subsatellite is lowered into the region where the effect of the atmosphere is significant, the uncontrolled motion of the fully deployed TSS configuration could be unstable due to the combined effects of the tether elasticity and the atmospheric density gradient.4'5 It has been shown that stabilization can be achieved by modulat- ing the tension in the cable or using the thrusters.6'7 Also, one may postulate the situation where the position of a deployed subsatellite needs to be corrected and the capability to maneuver the subsatellite is needed. This will be especially important if the main satellite is on an elliptic orbit with nonzero inclination and rotation of the atmo- sphere is considered. These examples illustrate the station keeping and maneuvering of the subsatellite of a TSS.1 Often, subsatellites of TSSs have been modeled as point masses with simplified aerodynamic characteristics, usually drag only. Fur- thermore, not much attention has been paid to their attitude motion. When the subsatellite is modeled as a rigid body, No and Cochran8 showed that the motion of the tether and the subsatellite's attitude motion are coupled even if there is no tether attachment point offset from the center of mass of the subsatellite. In the presence of at- mospheric effects, not only the tether swinging motion, but also the attitude motion of the subsatellite may become unstable in certain cases. Therefore, it is necessary to consider the motion of the tether and the subsatellite together in the design of control systems. In view of the above, this paper addresses two problems. First, the dynamics of the motion of a rather general tethered flight vehicle is investigated. The resulting rather complicated equations of motion are numerically linearized for stability analysis and control synthe- sis. Second, control strategies for station keeping and maneuvering of the tethered flight vehicle are developed by using well-established linear optimal control theory.