Near-minimum time, closed-loop slewing of flexible spacecraft

The near-minimum time single-axis slewing of a flexible spacecraft with simultaneous suppression of vibration of elastic modes is considered. The hyperbolic tangent (tahh) function is used as a smooth approximation to the discontinuous sgn function occurring in the rigid body bang-bang control. Variable structure control concepts are used to identify the necessary characteristics of the control switching line. Simulations of the rest-to-rest and tracking maneuvers indicate that the elastic energy can be reduced by several orders of magnitude with only a modest increase in the maneuver time. Introduction M ANY future large space structures, due to mass con- traints, will be flexible. For the purpose of analysis these systems can be modeled with a large number of modes of vibration. For certain applications, it will be desirable that such a spacecraft be able to slew as rapidly as possible, within the operating limits of the control actuators. The problem of control design for rotational maneuver and vibration suppres- sion of flexible spacecraft has been addressed extensively.1'10 Optimal control theory can be applied to enforce quiescent terminal conditions on the flexible modes, usually by applying a quadratic cost function that weights the control rates and the states. The order of the system model grows rapidly as the number of flexible modes to be controlled is increased, mak- ing it impractical to attempt to control more than a few flexible modes. Furthermore, there is no rigorous means by which control magnitude constraints may be enforced. Al- though a feedback method such as the linear quadratic regula- tor (LQR) with terminal constraints911 is attractive because it can enforce quiescent conditions oh the elastic modes, its computational complexity is burdensome. The optimal control solution to the minimum time, single- axis, rotational maneuver problem for a rigid body gives a control scheme characterized by saturation of the control throughout the maneuver with at most one control switch that is instantaneous (bang-bang). Although not exactly achiev- able in physical systems, and even though the trajectories are extremely sensitive to variations in spacecraft parameters, this control law has wide application for rigid systems using on-off thrusters. When rigorously applied to flexible systems, how- ever, the result is typically multiple control switches and excessive excitation of the flexible modes of vibration. Previ- ous investigations of the near-time optimal maneuver for flexible systems7'8 are open-loop designs requiring extensive computational effort. An alternative is to compute the re- quired parameters for a number of initial conditions off-line and use table lookup and interpolation for a particular ma- neuver. This may involve excessive storage. We start with the assumption that the minimum time solution for a rigid space- craft can serve as an initial approximation to the near-mini- mum time solution for a flexible structure. In other words, we