Adaptive Suppression of Linear Structural Vibration Using Control Moment Gyroscopes

Single-gimbal control moment gyros (CMGs) have many advantages over other actuators for attitude control of spacecraft. For instance, they act as torque amplifiers and, thus, are suitable for slew maneuvers. However, their use as torque actuators is hindered by the presence of singularities, that, when encountered, do not allow a CMG cluster to generate torques about arbitrary directions. One method to overcome this drawback is to use variable-speed single-gimbal control moment gyros (VSCMGs). Whereas the wheel speed of a conventional CMG is constant, VSCMGs are allowed to have variable wheel speed. Therefore, VSCMGs have extra degrees of freedom that can be used to achieve additional objectives, such as singularity avoidance and/or power tracking, as well as attitude control. The singularity problem of a VSCMGs cluster is studied in detail for the cases of attitude tracking, with and without a power tracking requirement. A null motion method to avoid singularities is presented, and a criterion is developed to determine the momentum region over which this method will successfully avoid singularities. This criterion can be used to size the wheels and develop appropriate momentum damping strategies tailored to the specific mission requirements. I. Introduction A CONTROL moment gyro (CMG) is a device used as an actuator for attitude control of spacecraft. It generates torques through angular momentum transfer to and from the main spacecraft body. This is achieved by changing the direction of the angular momentum vector of a gimballed flywheel. Because a CMG operates in a continuous manner, contrary to the gas jet’s on/off operation, it can achieve precise attitude control. Moreover, as with other momentum exchange devices, for example, reaction wheels, it does not consume any propellant, thus prolonging the operational life of the spacecraft. Single-gimbal CMGs essentially act as torque amplifiers. 1 This torque amplification property makes them especially advantageous as attitude control actuators for large space spacecraft and space structures, for example, a space station. In fact, single-gimbal and double-gimbal CMGs have been used for attitude control of the Skylab, the MIR and the International Space Station (ISS). An obstacle when using a CMG system in practice is the existence of singular gimbal angle states for which the CMGs cannot generate a torque along arbitrary directions. At each singular state, all admissible torque directions lie on a two-dimensional surface in the three-dimensional angular momentum space; therefore, the CMG system cannot generate a torque normal to this surface. The CMG singularities can be classified into two categories: 1) external or saturated singularities in which the total angular momentum sum of the CMGs lies on the maximum momentum envelope and 2) internal singularities in which the total momentum lies inside this envelope. The external singularities can be easily anticipated from the given CMG configuration and mission profile; therefore, they can be taken into account at the design step. A properly designed momentum management scheme can also relieve the external singularity problem. The internal CMG singularities, on the other hand, are in general difficult to anticipate. Avoiding such internal singularities has, thus, been a long-standing problem in the CMG

The robotic maneuvering of large space structures is key to a number of future orbital missions. In this paper a large space structure maneuver control algorithm, recently proposed, is extended and experimentally validated. The method uses space robots’ manipulators to control the vibration of the structures being maneuvered and their reaction jets perform the large motion maneuvers. The algorithm quickly damps out the vibrations and requires less fuel than reaction jet-based vibration control methods. The approach is called maneuver decoupled control. Its performance is demonstrated and quantitatively evaluated in simulation and experiments.

A feedforward control algorithm for flexible spacecraft rest-to-rest maneuvers with CMGs (control moment gyros) parallel gimbal configuration is presented. Single-gimbal CMG cluster in parallel gimbal arrangement has singularity problem and output torque vector is constrained in a 2-DOF plane normal to gimbal axis. This CMGs parallel gimbal configuration is suitable in case that spacecraft has 2-DOF pointing requirement like a Japanese satellite called Astro-G (‘space VLBI’ = radio telescope observation satellite). A CMG guidance law presented in this paper is designed particularly for single-axis rest-torest rotational maneuvers for a flexible spacecraft with 2-DOF pointing requirement. Generally spacecraft with large flexible structure has a lot of large-mass flexible-modes. Therefore, uncertainity of high-order flexible-modes needs to be taken into account for highaccuracy controller design. Most researcher propose input preshaping algorithms with finite target flexible-modes and limited frequency tolerances, so if we apply these algorithms into an actual large flexible satellite, control errors might be theoretically inevitable. The NME (Nil-Mode-Exciting) profiler shown in this paper includes an extra-insensitive preshaping profiler which overcomes above-mentioned difficulties. The NME profiler is a preshaping profiler constructed from a pair of sampling functions (also known as sinc function), consequently feedforward profile generated from this profiler has no frequency response above a certain designed frequency. Therefore residual vibration at the end-point of maneuver can be highly reduced with minimum loss of maneuver agility. Flexible spacecraft dynamics model of Astro-G including 4-CMGs and 4-RWs is used to evaluate the proposed algorithm.

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 comprehensive optimization of the number and locations of actuator–sensor pairs, genetic algorithms are used to avoid calculating all possible combinations, increasing factorially in the enumeration method. The optimized results are verified by the responses of the constrained gyroelastic body. Numerical simulations are presented for a cantilevered plate.

Based on the theory of modified constrained modal methods, in which the constraints can be defined on arbitrary points of the system or subsystems, a simplified method for free–free modal analysis is presented in this paper. Using this method, the rigid–body motion of structures can be eliminated by an arbitrary selection of the constraints. The constrained structures then become either statically determinate or indeterminate. Therefore, the inverse of the stiffness matrix of the constrained system exists. The modelling of the finite–element method can be verified or corrected via numerical or experimental results involving statically constrained and normal modes of the constrained system. Hence, the modal analysis of the free–free system can be easily performed using modal information from numerical or experimental results. The traditional modal experimental method of hanging with flexible strings can be changed, and the effective experimental methods can be chosen in accordance with the real condition of the test structure and site. To verify the effectiveness of this approach, several examples of a free–free rocket are presented. From the results, it can be clearly seen that the presented method is practical for modal analysis. Additionally, it is suitable for large space structures, especially those involving the assemblage of large flexible space structures. For such a system, generally, the components can be tested on–ground but the assemblage cannot, as it can only be deployed in space.

The mutual impacts between adjacent buildings caused large-scale damage during past major earthquakes sparking interest in examining the reliability and effectiveness of various control devices for alleviating the seismic responses of adjacent buildings. In this study, seismic response attenuation of multi-story adjacent buildings connected with MR dampers is examined using the Simple Adaptive Control (SAC) method. The use of the adaptive controller is advantageous as it can cope with the structural characteristics change during the severe events such as earthquakes. The simple Bouc-Wen model is considered in the analysis to model the highly nonlinear behavior of the MR damper. The Linear Quadratic Regulator (LQR) is used to design the reference model with desired trajectories. The change in the structural characteristics is reflected as a reduction in the plant's mass and stiffness as a result of the damage in the structural system. The efficacy of the simple adaptive controller is investigated in the presence of damage and in case where the system still undamaged. The results show that connecting adjacent buildings with MR dampers driven by the Simple Adaptive Control method is quite effective in mitigating the seismic responses.

Feasible angular momentum of spacecraft installed with control moment gyros

This paper considers the control problem of nonlinear uncertain systems arising from flexible aerospace structures. We begin by addressing the tracking problem of a class of nonlinear dynamic systems with modeling uncertainties and external disturbances. New control algorithms against modeling uncertainties are proposed. It is shown that these algorithms not only guarantee system stability, but also achieve certain bounded performance index, and they are readily applicable in vibration suppression of large flexible space structures. Numerical verification of the proposed strategy is demonstrated via the lumped mass model of a hypersonic aerospace flight vehicle structure.

This paper presents a method of continuous-time simple-adaptive control (SAC) for multi-input multi-output (MIMO) nonlinear systems using multifraction neural networks. The control input is given by the sum of the output of the simple adaptive controller and the output of the multifraction neural network is used to compensate the nonlinearity of plant dynamics that is not taken into consideration in the usual SAC. The role of the multifraction neural network is to construct a linearized model by minimizing the output error caused by nonlinearities in the control systems.

Control moment gyroscopes (CMGs) offer a unique approach to address power consumption issues that currently limit the design of prosthetic limbs. CMGs generate large output torques while requiring less power than conventional actuators. This advance is possible because CMGs conserve angular momentum without increasing the kinetic energy of the system, providing high-agility, low-power movements. We have designed a novel, three degree-of-freedom prosthetic arm actuated with small-scale CMGs. Each of the three segments contains one CMG scissored pair, which allows precise control over joint torques and accelerations. The prototype arm will have a workspace of 360 degrees of rotation about each joint axis, although it will be limited to physiological standards. The motions replicate elbow flexion/extension, wrist flexion/extension, and forearm supination/pronation. We will implement real-time, myoelectric control using electromyographic (EMG) signals recorded from the biceps brachii for the elbow joint, brachioradialis for the forearm, and the flexor carpi radialis and extensor digitorum communis for the wrist. The control system will correlate the EMG signals with output force of the arm and produce corresponding movements that mimic those produced by humans during voluntary contractions. Ultimately, our arm will serve as a prototype for future designs that utilize the unique characteristics of CMGs to enable upper-limb amputees to return to normal function.

The decentralized robust servomechanism problem (DRSP) for large flexible space structures (LFSS) under sensor and actuator failures is considered. Failure conditions are modelled by failure matrices. This permits a unified treatment of sensor and actuator failures. For colocated LFSS, stabilization, tracking of constant set points, and regulating constant disturbances can be simultaneously handled using a decentralized tuning PID output-feedback controller. Necessary and sufficient conditions for solvability of the DRSP for colocated LFSS under sensor and actuator failures are derived. Two detailed examples demonstrate the effectiveness of the controller.

An Overview of Modeling and Control of Large Flexible Space Structures

A secondary controller which uses a number of Annular Momentum Control Devices (AMCD's) for enhancement of structural damping in large flexible space structures is investigated. The closed-loop secondary controller is shown to be equivalent to a certain closed-loop optimal linear regulator, and the necessary and sufficient conditions for asymptotic stability are obtained. Sufficient conditions for asymptotic stability are also obtained which are much less restrictive than those obtained in an earlier paper. Design of a robust stable primary controller is also discussed.

The reduction of the large order models of complex systems into a sufficiently low dimensional order in such a way that important dynamic characteristics of the real system are preserved, is a nontrivial task. The motivations for such a model order reduction are either to reduce computations for analysis and practical control design or to simplify the control system structure. In the present article, major techniques in model order reduction are briefly discussed. The characteristic similarities and differences are highlighted, their advantages and disadvantages are underlined, and further research requirements and trends are commented upon. Introduction and Perspective One of the central issues in the active control of complex systems such as large flexible space structures (LFSS) is the derivation of a correct mathematical model for both the controlled and the uncontrolled dynamical systems. Theoretically, there are infinitely many elastic modes or degrees of freedom (DOF) in the distributed parameter (DP) models of LFSS, usually with very low natural damping. Moreover, the flexible modes contribute to the actual deformation of the structure.' The truly infinite dimensional character of LFSS models has to be approximated by some fidelity finite (but usually very large) dimensional model. The normal approach taken by engineers to achieve this end is via modal models with a large number of modes that provide a reasonable representation of the spacecraft dynamic characteristics. However, a difficult problem still remains to be the development of a model of lowenough dimensional order that it can be utilized by the onboard controller, yet high enough dimensional order that it preserves the dynamic characteristics of the real system represented and controlled. The motivations for such a reduction are either to reduce computations for analysis and practical control design or to simplify the control system structure. Discretization procedures will not be discussed herein and it will be assumed that a large finite dimensional model has been generated somehow and for implementation and other practical considerations, the model needs to be further reduced. *This work was-supported, in part, by the Air Force Wright Aeronautical, Air Force Systems Command, Flight Dynamics Lab, Structures and Dynamics Division, while the author was employed with HR-Textron, Valencia, California. There are various approaches to model order reduction; some are or pseudo-optimal and others are ad-hoc methods based on practical considerations and engineering experience and judgment. These techniques are known by different names such as reduction, condensation, economization, aggregation, optimal projection, and other combinations thereof. It has often been pointed out that such techniques generally constitute application of Rayleigh-Ritz/Galerkin optimization, and matrix transformation methods to the eigenvalue/eigenvector formulation for structural dynamic problems. The reduction or the condensation methods are based on transformations of the coordinates in the equations of motion that essentially maintain the invariance of the quadratic forms of the potential and kinetic energies. An important feature of these methods is that the reduced order model often loses the basic characteristics of the original system. Considerable progress was made by Likins, Ohkami, and wong5 in this respect. However, they failed to develop a general enough criterion that could reduce the system model in an sense without significantly affecting the eigenvalues of the original model. The optimization or the mathematical reduction procedure, on the other hand, is based on the reduction of the eigenvalue problem to a smaller size based on some optimality criterion (usually quadratic). In these techniques, the reductions are carried out without actually resorting to approximations, i .e. , without truncatiag any coordinates or states of the original system. Balanced model reduction of linear timeinvariant dynamical systems is essentially based on the controllability and observability relations of the states of the system. Subsystem models are obtained by deleting those states that contribute the least to the controllability and observability (or the impulse response) of the original system7 and thus are only in this sense. A more recent approach to model reduction is proposed in Skelton's work,* where each state of the system model is assigned a relative to a given basis, via a quadratic criterion, and the states with the least cost are deleted in a systematic manner. The resulting reduced model is a function of the state-space basis, and thus there is no guarantee for optimality for all choices. The latest development in model order reduction techniques is the work by Hyland and erns stein.^ Herein first order necessary conditions for reduced order modeling of linear time-invariant systems are derived via a pair of modified Lyapunov equations coupled by a nonorthogonal projection. This approach reveals the possibility of multiple extrema forsome of the abovementioned methods. Copyright @ 1988 by the American Institute of Aeronautics and Astronautics. Inc. All Rights Reserved.

Active control of large flexible space structures is typically implemented to control only a few known elastic modes. This paper considers the stabilization of the neglected dynamics of the higher modes of vibration. An attempt is made to design modal controllers with improved spillover stability properties. Two formulations for designing the observer to improve spillover stability with minimum performance loss are proposed. One optimizes the noise statistics used in the design of the Kalman-Bucy Filter (KBF), while the other directly optimizes the the gain matrix of the KBF.