Adaptive Suppression of Linear Structural Vibration Using Control Moment Gyroscopes

L ARGE space structures (LSS) have been extensively used in space engineering.Because of the large size, low rigidity, and low natural damping, active vibration suppression of LSS is required to achieve the desired system pointing accuracy and acceptable vibration levels. In recent years, mounting control moment gyroscopes (CMGs) on space structures for active vibration suppression began to draw much attention. It provides an attractive option for vibration control because the CMG is an efficient mean of generating continuous and precise torques without expending the propellant. The concept of mounting angular momentum devices, such as CMGs and flywheels (FWs), on structures was proposed by D’Eleuterio and Hughes [1,2]. They assumed that an infinitesimal angular momentum device was embedded in each volume element of a structure. The distribution of the angular momentum on the structure forms a continuous function. Such system is referred to as a gyroelastic body, whereas the stored angular momentum embedded in the structure is named “gyricity.” They found that the gyricity can shift frequency, couple modes, and add controllable damping to the system. These attributes have been experimentally validated by Peck in [3]. Then, Damaren and D’Eleuterio investigated the system controllability and observability and the optimal control of the gyroelastic body [4,5]. The optimal control law requires measuring the modal rates, which are difficult in practical engineering, thus restricting its application. In the subsequent studies, Yang et al. adopted a scissored pair of CMGs to maneuver and suppress the vibration of a flexible truss [6]; Shi and Damaren mounted a CMG and a collocated angular velocity sensor at the end of a cantilevered beam to damp the vibration [7]. These two studies are both easy to implement; however, they only aim at specific systems. It is desirable to establish a general and practical methodology for active vibration suppression of the flexible structures by CMGs. Simple adaptive control (SAC) method is particularly attractive because it does not require explicitly identifying the structure parameters, measuring the modal coordinates, or considering the number of the relevant flexible modes. The SACwas first introduced by Sobel et al. [8]. It can force the error between the plant and the reference model to approach zero. It is formulated by use of the command generator tracker theory and Lyapunov stability analysis. Barkana et al. [9], Balas [10], and Barkana and Ben-Asher have further developed the technique. It has been successfully implemented on large flexible structures. Application of SAC requires the controlled system to be strictly passive (SP), or at least almost strictly passive. In other words, the transfer function of the system should be strictly positive real (SPR), or at least almost strictly positive real. Those properties of traditional flexible space structures have been well studied [9,11–13]. However, the SP, SPR, and the application of SAC for the flexible structureswithCMGshave not been discussed in the open literature. The contribution of the present Note can be summarized as a comprehensive SAC strategy for vibration suppression of cantilevered LSS using CMGs as actuators. The formulation consists of two building blocks. First, modal analysis is performed based on the linearized equations of motion to obtain the system dynamics model in a bicoupled form. Then, the SP of the system and the SPR of its transfer function are proved, based on which a SAC strategy is designed and the proof of stability is given.