Robust colocated control for large flexible space structures

An Overview of Modeling and Control of Large Flexible Space Structures

Approaches to uncertainty modeling for robust control of large flexible space structures (LFSSs) such as additive or multiplicative perturbations in /spl Hscr//sub /spl infin// do not work very well because of the special properties of LFSS dynamics. We propose the use of a left-coprime factorization (LCF) of LFSS dynamics in modal coordinates in order to get improved stability margins and performance in robust control design. The plant uncertainty is then described as stable perturbations of the coprime factors accounting for modal parameter uncertainty and unmodeled dynamics. Two multivariable /spl Hscr//sub /spl infin// designs based on LCFs of 46th-order collocated and noncollocated models of an LFSS experimental testbed are presented together with simulation and experimental results to illustrate the technique.

Active vibration control of large flexible space structure is a challenging topic in the system dynamics and control of spacecraft. This paper proposes a novel approach for vibration control on a large hoop truss structure, typically used as mesh satellite antenna. First, to suppress the first-order bending modal response of the hoop truss structure with an initial disturbance, a piezoelectric bending actuator with excellent bending actuation performance was carefully designed as a key component of an active vibration control system. Then, the actuating characteristics of the actuator and the dynamic equations of the active structure were analyzed and formulated based on a finite element method. In order to improve the vibration-attenuating effect of the control system, a Mamdani-type fuzzy logic algorithm was employed in a closed-loop control system. Finally, simulations and experiments were implemented to validate the effectiveness of the proposed active control approach and structure. The experimental results showed that the decay time of first-order bending modal response (around 0.34 Hz) of control system reduces by 75% compared with that of the uncontrolled system. The results demonstrate that the proposed active vibration control system has good application potential in controlling the bending modes of a large flexible spacecraft.

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.

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.

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.

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.

Recently, increasing interest has been shown in structural safety design us ing active and hybrid control systems. This interest is driven by the rapid development of intelligent control systems, advanced sensor technology, signal processing, and successful applications in the control of large flexible space structures.

Decentralized Control for Large Flexible Space Structures by Local Proper Controllers Using Displacement Output

A smart structure involves distributed actuators and sensors, and one or more microprocessors that analyze the responses from the sensors and use distributed-parameter control theory to command the actuators to apply localized strains to minimize system response. A smart structure has the capability to respond to a changing external environment (such as loads or shape change) as well as to a changing internal environment (such as damage or failure). It incorporates smart actuators that allow the alteration of system characteristics (such as stiffness or damping) as well as of system response (such as strain or shape) in a controlled manner. Many types of actuators and sensors are being considered, such as piezoelectric materials, shape memory alloys, electrostrictive materials, magnetostrictive materials, electro- rheological fluids and fiber optics. These can be integrated with main load-carrying structures by surface bonding or embedding without causing any significant changes in the mass or structural stiffness of the system. Numerous applications of smart structures technology to various physical systems are evolving to actively control vibration, noise, aeroelastic stability, damping, shape and stress distribution. Applications range from space systems, fixed-wing and rotary-wing aircraft, automotive, civil structures and machine tools. Much of the early development of smart structures methodology was driven by space applications such as vibration and shape control of large flexible space structures, but now wider applications are envisaged for aeronautical and other systems. Embedded or surface-bonded smart actuators on an airplane wing or helicopter blade will induce alteration of twist/camber of airfoil (shape change), that in turn will cause variation of lift distribution and may help to control static and dynamic aeroelastic problems. Applications of smart structures technology to aerospace and other systems are expanding rapidly. Major barriers are: actuator stroke, reliable data base of smart material characteristics, non-availability of robust distributed parameter control strategies, and non-existent mathematical modeling of smart systems. The objective of this paper is to review the state-of-the-art of smart actuators and sensors and integrated systems and point out the needs for future research.© (1996) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Large Flexible Structure Control Technology Experiment and Facility Design

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.

: The research documented in this report addresses several major technical issues in vibration controller design methodologies that are of fundamental importance to control of large flexible space structures. Fundamentally important analytical and numerical results, as well as useful new insights, have been obtained on: optimality of fixed-form reduced-order compensators; full-order closed-loop stability and robustness with reduced-order controllers; prevention of control and observation spillover; active augmentation of damping, stiffness, and stability, stabilizability by output feedback control; large-angle maneuver with simultaneous vibration suppression; and possibilities for improving current controller design methodologies.

The design of dissipative linear-quadratic-Gaussian-type compensators for positive real plants is considered. It is shown that if the noise covariance matrices (used as weighting matrices) satisfy certain conditions, the compensator has a strictly positive real transfer function matrix. The stability of the resulting closed-loop system is guaranteed regardless of modeling errors as long as the plant remains positive real. In view of this property, the controller is expected to be useful for vibration suppression in large flexible space structures. >