Yinghong Jia

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.

Recursive Dynamics Algorithm for Multibody Systems with Variable-Speed Control Moment Gyroscopes

This paper presents a comprehensive recursive formulation of dynamic equations for multibody systems with variable-speed control moment gyroscopes. It permits any rigid or flexible body in the system to have a cluster of variable-speed control moment gyroscopes in a generic configuration as actuators. The detailed dynamics of the actuators is taken into consideration to capture its interactions with the flexibilities of the structures. The recursive algorithm is obtained through analyzing the kinematics and dynamics between two adjacent bodies, both of which can be rigid or flexible, or one of which is rigid and the other is flexible. The orthonormal complement of the projection matrix of the joint is adopted to express the constraint equations for structural loops uniformly. Numerical results of an illustrative example are presented to show the accuracy and efficiency of the proposed method by comparing it with a nonrecursive formulation.

Optimal Placement of Sensors and Actuators for Gyroelastic Body Using Genetic Algorithms

A flexible body with a distribution of stored angular momentum is viewed as a gyroelastic body. The flexible structure may require active vibration suppression, which can be controlled using a collection of control moment gyroscopes. This study investigates the optimal placement of collocated angular rate sensors and control moment gyroscope actuators for a constrained gyroelastic body based on genetic algorithms. First, the dynamics and modal analysis of the constrained gyroelastic body are presented. The state-space model is adopted that contains the distribution of actuators and sensors. Based on the concept of the controllability and the observability of the gyroelastic system, the objective functions are proposed aiming at the maximization of the controllability and observability of the constrained gyroelastic system. For situations with a fixed number of actuators and sensors, an exhaustive enumeration method and genetic algorithms are used to determine the locations of actuators and sensors. For a ...

Simple Adaptive Control for Vibration Suppression of Space Structures Using Control Moment Gyroscopes as Actuators

This paper presents an adaptive control strategy for vibration suppression of cantilevered flexible space structures with collocated control moment gyroscopes and angular rate sensors. Equations of motion capturing the detailed dynamics of the control moment gyroscopes and their interactions with the small-scale flexible motion of the structures are linearized to a state-space form. Modal analysis is then performed based on the linearized equations to transform the dynamic model into a bicoupled form. It shows that the skew-symmetric gyricity terms produced by using control moment gyroscopes as actuators make the dynamic characteristics of the structures much different from those of the traditional structures. The strictly positive realness of the system, which could guarantee the stability of the proposed adaptive controller, is proved both in the frequency-domain condition and the time-domain condition. It is found that any small damping could make the system strictly positive real. An adaptive controller is designed, and then its Lyapunov stability is analyzed. The controller is synthesized only by using the angular rates of the locations where the actuators are mounted. Numerical examples of cantilevered gyroelastic beam and plate structures demonstrate the efficacy of the proposed method.

Recursive Dynamics Algorithm for Multibody Systems with Variable-Speed Control Moment Gyroscopes as Actuators

This paper presents a comprehensive recursive formulation of dynamic equations for multibody systems with variable-speed control moment gyroscopes (VS-CMGs). It permits any rigid or flexible body in the system to have a cluster of VS-CMGs in a generic configuration as actuators. The detailed dynamics of the VS-CMGs is taken into consideration to capture the interactions between the VS-CMGs and the flexibilities of the structures. The equations of motion of a flexible body with n VS-CMGs are developed by the Kane’s method. The recursive algorithm is obtained through analyzing the kinematics and dynamics between two adjacent bodies, both of which can be rigid or flexible, or one of which is rigid and the other is flexible. The orthonormal complement of the projection matrix of the joint is adopted to express the constraint equations for the structural loops uniformly. Numerical results of an illustrative example are presented to show the accuracy and efficiency of the proposed method by comparing it with a nonrecursive formulation. Nomenclature j B = flexible or rigid body numbered j j h = hinge numbered j

Direct Dynamics of a Space Robot Actuated by Control Moment Gyros

This paper presents a direct formulation of dynamical equations for a space robot actuated by control moment gyros (CMGs). The space robot consists of a service satellite and a robotic manipulator comprising an arbitrary number of rigid links connected by spherical joints. A cluster of CMGs is mounted on the base and on each link. The static and dynamic imbalances of the gimbals and the rotors are both considered. Dynamical equations for the robotic system level are derived using Kane’s equations. The nominal output torques of the CMGs and the disturbance torques caused by the imbalances are separated, with each having explicit expressions. A feedback controller based on the nominal model is also proposed for system trajectory tracking control. Simulation comparisons based on different imbalance parameters show that the controller works, but the imbalances may cause both high-frequency and low-frequency disturbance torques, which may distinctly decrease system-control accuracy.