Input-shaped control of three-dimensional maneuvers of flexible spacecraft

This paper deals with the control of three-dimensional rotational maneuvers of flexible spacecraft. A spacecraft model with a cylindrical huh and four symmetric appendages is considered. The appendages are tong and flexible, leading to low-frequency vibration under any control action. To provide a comprehensive treatment of input-shaped controllers (time-delay filters), both open-loop and closed-loop maneuvers are considered. For the open-loop maneuver, a five-switch, near-minimum-time bang-bang controller is designed based on the rigid-body model. The design procedure accounts for the presence of the time-delay filter for determining the switch times. In addition, a combination of a Lyapunov controller with the time-delay control technique is proposed to take advantage of the simple feedback control strategy and augment it with a technique that can eliminate the vibratory motion of the flexible appendages more efficiently. I. Introduction N this paper the problem of reorientation of a hub-apI pendage structure is considered. Considerable work has been done on Lyapunov control of single-axis maneuvers of hub-appendage structures. Hablani5 provides a technique for the estimation of the switch times for a bang-bang profile for zero residual energy, single-axis slew of a flexible spacecraft. Techniques are provided to estimate switch times for a system with either damped or undamped modes. A weighted time-fuel optimal controller for the rest-to-rest slew with zero residual energy is designed using the principles of dynamics by Skaar et a1.6 An elegant input-shaping scheme proposed by Smith 7 and later modified by Singer and Seering* has been used by Wie and Liu9 to modify the flexible-body time optimal control profile to produce a robust control scheme, which has been applied to the control of a two-mass spring model. Here we consider the three-dimensional case, leading to a model that has kinematic and dynamic nonlinearities. The system under consideration consists of a cylindrical hub, with four cantilevered cylindrical appendages of equal dimensions (Fig. 1). In modeling this system, only those modes that will be excited by a hub torque are considered. These modes lead to displacements of the appendages (which are modeled as EulerBernoulli beams), which resemble a three-dimensional starfish. The equations of motion of the flexible appendages are arrived at using the Lagrangian approach, and the rigidbody equations are arrived at using the Newton-Euler technique. The assumed modes technique is used to transform the partial differential equations (representing the equations of motion of the flexible appendages) to ordinary differential equations. Two modes are used to represent the displacement of each of the flexible appendages in the simulation of the system. The first controller proposed in this study is based on the amalgamation of two powerful control techniques. First, the rigid-body controller is designed based on the Lyapunov sta