Moon K. Kwak

Convergence of the classical Rayleigh-Ritz method and the finite element method

It is demonstrated in this paper that convergence of the classical Rayleigh-Ritz method can be vastly improved by introducing a new class of admissible functions, called quasi-comparison functions

Dynamics and control of spacecraft with retargeting flexible antennas

This investigation is concerned with the dynamics and control of a spacecraft comprising a rigid platform and a given number Of retargeting flexible antennas. The mission consists of maneuvering the antennas so as to coincide with preselected lines of sight while stabilizing the platform in an inertial space and suppressing the elastic vibration of the antennas. The paper contains the derivation of the equations of motion by a Lagrangian approach using quasicoordinates, as well as a procedure for designing the feedback controls. A numerical example involving a spacecraft consisting of a rigid platform and a flexible antenna is presented.

Control of flexible spacecraft with time-varying configuration

This paper is concerned with the dynamics and control of systems with time-varying configuration, such as maneuvering articulated flexible spacecraft. The mathematical model consists of a rigid platform and a given number of retargeting flexible antennas. The mission consists of maneuvering the antennas so as to coincide with preselected lines of sight while stabilizing the platform in an inertial space and suppressing the elastic vibration of the antennas. A perturbation technique permits the derivation of a new control law for systems with time-varying configuration, in which the time-varying terms are relatively small. According to the proposed perturbation method, the control gains consist of zero-order time-invariant gains obtained from the solution of a matrix algebraic Riccati equation, which are valid both during and after the maneuver, and higher-order time-varying gains obtained from the solution of matrix differential Lyapunov equations, which are valid only during the maneuver. The approach is illustrated by means of a numerical example.

Inclusion principle for the Rayleigh-Ritz based substructure synthesis

According to this substructure synthesis, the motion of every substructure is modeled in terms of quasicomparison functions, which are linear combinations of admissible functions capable of satisfying all the boundary conditions.

Control of flexible aircraft executing time-dependent maneuvers

A new generation of aircraft, namely, unmanned aerial vehicles (UAVs), and, in particular, autonomous UAVs, are expected to carry out very critical maneuvers, well in excess of what pilots are able to tolerate. A newly developed theory for the dynamics and control of maneuvering flexible aircraft is ideally suited for the analysis and design of such aircraft. The state equations for maneuvering flexible aircraft are nonlinear and of high dimension. With due consideration to the way aircraft are flown, the problem can be separated into one for the generally large aircraft motions on a given flight path and another one for small perturbations from the flight path and elastic vibration, where the second problem receives inputs from the first. The case in which the flight path represents a time-dependent maneuver, so that the system of perturbation equations is time varying is studied. Several developments designed to facilitate the treatment of time-varying systems are provided. In particular, included are 1) an explicit derivation of the matrices defining the state equations, 2) a new approach to the control of the perturbations from the flight path and the elastic vibration, and 3) expressions for the implementation of the controls in discrete time. Computer solutions for the system response can be carried out conveniently by the use of MATLAB® and MATHEMATICA. A numerical example illustrates the approach for the case of a flexible aircraft executing a pitch maneuver.