Peter M. Bainum

Breakwell memorial lecture: Review of Astrodynamics, 1958 – 2001 - a personal perspective

Abstract A review of Astrodynamics during the 43 year career of the author is presented. The following projects/programs are reviewed: (1) launch vehicles-as launchers of small satellites and also the use of advanced robust reduced order techniques for autopilot control of contemporary flexible, expendable systems; (2) the use of the Clohessy-Wiltshire equations for the Gemini mission rendezvous, and recently in constellation formation flying station keeping; (3) lessons learned from the design of attitude control system for gravity-gradient and dual-spin spacecraft; (4) design of attitude control systems for large, flexible space platforms and antenna systems; (5) participation in the original Tethered-Shuttle-Subsatllite system and other proposed orbiting tethered systems; and (6) integrated structural/control optimization of large (articulated) structures in low Earth orbit. This review will emphasize lessons learned as well as advances in astrodynamics techniques/concepts.

The dynamics and control of the orbiting spacecraft control laboratory experiment (SCOLE) during station keeping

A mathematical model is developed to predict the dynamics of the proposed orbiting Spacecraft Control Laboratory Experiment during the station keeping phase. The Shuttle as well as the reflector are assumed to be rigid, the mast is flexible and is assumed to undergo elastic displacements very small as compared with its length. The equations of motion are derived using a Newton-Euler formulation. The model includes the effects of gravity, flexibility, and orbital dynamics. The control is assumed to be provided to the system through the Shuttles three torquers, and through six actuators located by pairs at two points on the mast and at the mass center of the reflector. At each of the locations, an actuator acts parallel to the roll axis while the other one acts parallel to the pitch axis. It is seen that, in the presence of gravity-gradient torques in the system dynamics, the system assumes a new equilibrium position about which the equations must be linearized, primarily due to the offset in the mast attachment point to the reflector. The linear regulator theory is used to derive control laws for the linear model of the SCOLE including the first four flexible modes. Numerical results confirm the robustness of this control strategy for station keeping with maximum control efforts significantly below saturation levels.

On the accuracy of modelling the dynamics of large space structures

Abstract Recently new space missions which require large-scale, light weight space based structural systems have been proposed. Because of the inherent size of these structures, system dynamic performance must be accurately predicted prior to launch and assembly, usually by mathematical modelling and simulation. Santini has developed a mathematical formulation for predicting the motion of a general orbiting flexible body using a continuum approach, different from the finite element techniques which model structures as a system of lumped masses connected by a series of (restoring) springs. When finite element techniques are used to model a system, the coupling terms between the rigid and flexible modes and between different flexible modes are usually neglected. In this paper a computational algorithm is developed to evaluate the coefficients of the various coupling terms in the equations of motion as applied to the finite element model of the 122 m diameter Hoop/Column system. It is seen that when deflections are of the order of meters (still within small amplitude assumptions) the coupling between the flexible and rigid modes should be included in the rigid rotational modal equations of the mathematical model.

Development of lyapunov functions for freely spinning dual-spin spacecraft

Abstract Lyapunov functions for linear multivariable time-invariant systems are developed by use of construction techniques which are based on Lyapunovs second method. Two methods of construction are studied. In the first method (direct method) the Lyapunov function is obtained by directly solving the Lyapunov matrix equation while in the second method (indirect method) it is generated by reducing the system matrix by two successive similarity transformations to the Schwarz canonical form. The conditions of stability on the resulting matrix from Lyapunovs second method are the same as the Routh-Hurwitz conditions. Both construction techniques are applied to a freely-spinning dual-spin system, with viscous rate damping assumed about both principal transverse axes. It is seen that when the rotor is spinning relative to the main part, damping about only one of the principal transverse axes is required for stability. The Lyapunov functions constructed are quadratic forms whose different coefficients, collectively, involve all of the system parameters including the damping coefficients.

On the Development of Control Laws for an Orbiting Tethered Antenna / Reflector System Test Scale Model

Tethered systems can be used to change the geometry and inertial characteristics of space structural systems to meet the gravity gradient stability requirements. The control law design for an orbiting shallow spherical shell (antenna/reflector) system connected by a massive and flexible tether to a subsatellite is investigated in this article. The subsatellite is nominally deployed below the antenna along the yaw axis at a sufficient distance to provide a favorable composite moment of inertia ratio for gravitational stabilization. It is assumed that the tether would be deployed through the end of a rigid boom attached to the shell apex. The tension control strategy is used for stationkeeping and deployment and the control gains are obtained based on the structural data for a future proposed real space antenna/reflector. In order to prove the feasibility of this concept, a test scale model for an in-orbit experiment is also studied. The scale model should be small enough so that it could be accommodated within the volume and size limitations of the space shuttle cargo bay. Since the or bital angular velocity (determined by the orbital altitude of the space shuttle), tether diameter, etc. may not be directly scaled, the control gains will be adjusted to fit the requirements for the scale model. Furthermore, during the deployment, the real control gains will be adjusted to the change of the length of the tether and the deployed tether mass. Therefore, the control law gains for the pro posed in-orbit experiment scale model would be synthesized in a piece-wise adaptive manner. Nu merical results are presented both for the real antenna as well as for the proposed in-orbit (test) scale model.