Uniform damping control of spacecraft

Abstract

This paper introduces the uniform damping control of flexible spacecraft. The dynamic characteristics of spacecraft are reviewed and a criterion for dynamic performance is described by a uniform damping control ap- proach which exhibits three distinctly attractive features. It is shown that 1) the associated uniform damping control law is independent of the spacecraft stiffness, 2) the associated control forces are proportional to the spacecraft mass density, and 3) the uniform damping control law is decentralized. The uniform damping control solution is shown to represent a first-order approximation to a special globally optimal control problem. Also, the implementation of uniform damping control is considered using discrete (in space) actuation and sensing type devices. Robustness in the presence of errors due to implementing the control using discrete components is characterized. VER one hundred and fifty years ago, investigations into the behavior of beams and membrances in bending vibra- tion, rods and shafts in torsional vibration, and bars in longitudinal vibration were conducted. Over the past one hun- dred years, considerable effort has been directed toward extending these classical results to structures of arbitrary shape and under the combined effects of bending, torsion, and longi- tudinal vibration. The extension of these classical works to the so-called field problems together with the development of numerical methods of solution for field problems has brought about the modern field of structural dynamics. More recently, with assistance from classical variational methods and modern linear system concepts, the dual theories of linear optimal con- trol and estimation were formulated along with modern control methods and strategies. Based on these developments, the con- trol of flexible spacecraft has been set on a firm mathematical foundation. To bridge the gap between engineering design and the mathematical foundations upon which the control of space- craft rests, a variety of concepts have been introduced. The representation of the motion of a spacecraft (or any structure) as a series of natural motions together with the representation of the forces acting on a spacecraft as a series of natural forces led to the first methods of modal control.1>2 The phenomena of control spillover and observation spillover were introduced3'4 and the method of independent modal-space control (IMSC)5'7 was presented together with the new concept of simultaneous internal and external decoupling. A number of examinations of the robustness of modal control methods were then conducted,811 and, to improve implementation capabilities, decentralized controls were characterized.12'13