Identification and control of structures in space

Work during the period July 1 - December 31, 1985, has concentrated on the application of the equations derived in the preceding period to the maneuvering and vibration suppression of the Spacecraft Control Laboratory Experiment (SCOLE) model. Two different situations have been considered: (1) a space environment and (2) a laboratory environment. This report covers the first case and consists of a paper entitled Maneuvering and Vibration Control of Flexible Spacecraft, presented at the Workshop on Structural Dynamics and Control Interaction of Flexible Structures, Marshall Space flight Center, Huntsville, AL, April 22 to 24, 1986. The second case will be covered in the report for the next period

Identification and control of structures in space

Work during the period January 1 to June 30, 1985 has concentrated on the completion of the derivation of the equations of motion for the Spacecraft Control Laboratory Experiment (SCOLE) as well on the development of a control scheme for the maneuvering of the spacecraft. The report consists of a paper presented at the Fifth Symposium on Dynamics and Control of Large Structures, June 12 to 14, 1985 at Blacksburg, VA

The stability of motion of satellites with flexible appendages Semiannual technical progress report, 1 Apr. - 30 Sep. 1970

Stability of motion of satellites with flexible appendage

A Rayleigh-Ritz approach to the synthesis of large structures with rotating flexible components

The equations of motion for large structures with rotating flexible components are derived by regarding the structure as an assemblage of substructures. Based on a stationarity principle for rotating structures, it is shown that each continuous or discrete substructure can be simulated by a suitable set of admissible functions or admissible vectors. This substructure synthesis approach provides a rational basis for truncating the number of degrees of freedom both of each substructure and of the assembled structure

Control of large flexible spacecraft by the independent modal-space control method

The problem of control of a large-order flexible structure in the form of a plate-like lattice by the Independent Modal-Space Control (IMSC) method is presented. The equations of motion are first transformed to the modal space, thus obtaining internal (plant) decoupling of the system. Then, the control laws are designed in the modal space for each mode separately, so that the modal equations of motion are rendered externally (controller) decoupled. This complete decoupling applies both to rigid-body modes and elastic modes. The application of linear optimal control, in conjunction with a quadratic performance index, is first reviewed. A solution for high-order systems is proposed here by the IMSC method, whereby the problem is reduced to a number of modal minimum-fuel problems for the controlled modes

Dynamic analysis of the long-term zonal earth energy budget experiment (LZEEBE) spacecraft

The motions of the flexible LZEEBE spacecraft after injection into a circular orbit were analyzed. The spacecraft consists of three spherical balloons connected to a central hub by three long flexible booms which lie in a plane such that the angle between any pair of booms is 120 degrees. The major torques acting on the spacecraft are gravity-gradient torques and torques due to solar radiation pressure acting on the balloons which have different reflective properties. A development of the equations of motion is presented. Computer simulations indicate that the spacecraft will have random motion, provided the injection into orbit does not create conditions favorable to gravity-gradient capture

Dynamic characteristics of a variable-mass flexible missile: Dynamics of a two-stage variable-mass flexible rocket

The dynamic characteristics of two-stage slender elastic body were investigated. The first stage, containing a solid-fuel rocket, possesses variable mass while the second stage, envisioned as a flexible case, contains packaged instruments of constant mass. The mathematical formulation was in terms of vector equations of motion transformed by a variational principle into sets of scalar differential equations in terms of generalized coordinates. Solutions to the complete equations were obtained numerically by means of finite difference techniques. The problem has been programmed in the FORTRAN 4 language and solved on an IBM 360/50 computer. Results for limited cases are presented showing the nature of the solutions

Dynamic characteristics of a two-stage variable-mass flexible missile with internal flow

A general formulation of the dynamical problems associated with powered flight of a two stage flexible, variable-mass missile with internal flow, discrete masses, and aerodynamic forces is presented. The formulation comprises six ordinary differential equations for the rigid body motion, 3n ordinary differential equations for the n discrete masses and three partial differential equations with the appropriate boundary conditions for the elastic motion. This set of equations is modified to represent a single stage flexible, variable-mass missile with internal flow and aerodynamic forces. The rigid-body motion consists then of three translations and three rotations, whereas the elastic motion is defined by one longitudinal and two flexural displacements, the latter about two orthogonal transverse axes. The differential equations are nonlinear and, in addition, they possess time-dependent coefficients due to the mass variation

Structural Dynamics, Stability, and Control of Helicopters

The dynamic synthesis of gyroscopic structures consisting of point-connected substructures is investigated. The objective is to develop a mathematical model capable of an adequate simulation of the modal characteristics of a helicopter using a minimum number of degrees of freedom. The basic approach is to regard the helicopter structure as an assemblage of flexible substructures. The variational equations for the perturbed motion about certain equilibrium solutions are derived. The discretized variational equations can be conveniently exhibited in matrix form, and a great deal of information about the system modal characteristics can be extracted from the coefficient matrices. The derivation of the variational equations requires a monumental amount of algebraic operations. To automate this task a symbolic manipulation program on a digital computer is developed

Dynamic characteristics of a variable-mass flexible missile

The general motion of a variable mass flexible missile with internal flow and aerodynamic forces is considered. The resulting formulation comprises six ordinary differential equations for rigid body motion and three partial differential equations for elastic motion. The simultaneous differential equations are nonlinear and possess time-dependent coefficients. The differential equations are solved by a semi-analytical method leading to a set of purely ordinary differential equations which are then solved numerically. A computer program was developed for the numerical solution and results are presented for a given set of initial conditions