Spillover stabilization of large space structures

An Overview of Modeling and Control of Large Flexible Space Structures

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 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.

A special output feedback control design technique for flexible large space structures is proposed in this paper to achieve: (a) increase in both the damping and frequency of selected modes for more effective control, (b) integrated control of elastic and rigid-body modes, and, in particular, (c) closed-loop system stability and its robustness to modal truncation and to parameter variation. This technique represents an improvement over previous work concerning large space structures output feedback control.

A Survey of Automatic Control Techniques for Large 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.

Closed-loop performance properties of a large flexible space structure with colocated actuators and sensors are examined. It is shown that when an output feedback gain matrix is chosen as symmetric negative-definite, a linear quadratic optimization (LQ) problem can be stated and solved in closed form via an inverse optimal control formulation. The known properties of this LQ problem guarantees the stability of the closed-loop system. It is further shown that the closed-loop system remains stable in the presence of certain parameter variations. These robustness properties include also the effect of truncated modes on stability. The understanding of the specific output feedback controller, offered through the inverse optimal control solution, lends itself to a design procedure that selects the output feedback gain matrix in an iterative manner.

Sliding mode control of a large flexible space structure

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.

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.

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.

No AccessEngineering NoteAdaptive Suppression of Linear Structural Vibration Using Control Moment GyroscopesQuan Hu, Yinghong Jia and Shijie XuQuan HuSchool of Astronautics, Beihang University, 100191 Beijing, People's Republic of China, Yinghong JiaSchool of Astronautics, Beihang University, 100191 Beijing, People's Republic of China and Shijie XuSchool of Astronautics, Beihang University, 100191 Beijing, People's Republic of ChinaPublished Online:25 Apr 2014https://doi.org/10.2514/1.62267SectionsRead Now ToolsAdd to favoritesDownload citationTrack citations About References [1] D'Eleuterio G. M. T. and Hughes P. C., "Dynamics of Gyroelastic Continua," Journal of Applied Mechanics, Vol. 51, No. 2, June 1984, pp. 412–422. JAMCAV 0021-8936 Google Scholar[2] D'Eleuterio G. M. T. and Hughes P. C., "Dynamics of Gyroelastic Spacecraft," Journal of Guidance, Control, and Dynamics, Vol. 10, No. 4, 1987, pp. 401–405. doi:https://doi.org/10.2514/3.20231 JGCDDT 0162-3192 LinkGoogle Scholar[3] Peck M., "Practicable Gyroelastic Technology," 27th Annual AAS Guidance and Control Conference, AAS Paper 2004-023, Feb. 2004. Google Scholar[4] Damaren C. J. and D'Eleuterio G. M. T., "Controllability and Observability of Gyroelastic Vehicles," Journal of Guidance, Control, and Dynamics, Vol. 14, No. 5, 1991, pp. 886–894. doi:https://doi.org/10.2514/3.20728 JGCDDT 0162-3192 LinkGoogle Scholar[5] Damaren C. J. and D'Eleuterio G. M. T., "Optimal Control of Large Space Structures Using Distributed Gyricity," Journal of Guidance, Control, and Dynamics, Vol. 12, No. 5, 1989, pp. 723–731. JGCDDT 0162-3192 LinkGoogle Scholar[6] Yang L. F., Mikulas M. M. and Park K. C., "Slewing Maneuvers and Vibration Control of Space Structures by Feedforward/Feedback Moment-Gyro Controls," Journal of Dynamic Systems, Measurement, and Control, Vol. 117, No. 3, 1995, pp. 343–351. doi:https://doi.org/10.1115/1.2799125 JDSMAA 0022-0434 CrossrefGoogle Scholar[7] Shi J. F. and Damaren C. J., "Control Law for Active Structural Damping Using a Control Moment Gyro," Journal of Guidance, Control, and Dynamics, Vol. 28, No. 3, 2005, pp. 550–553. doi:https://doi.org/10.2514/1.11269 JGCDDT 0162-3192 LinkGoogle Scholar[8] Sobel K., Kaufman H. and Mabus L., "Adaptive Control for a Class of MIMO Systems," IEEE Transactions on Aerospace, Vol. 18, No. 2, 1982, pp. 576–590. CrossrefGoogle Scholar[9] Barkana I., Kaufman H. and Balas M., "Model Reference Adaptive Control of Large Structural Systems," Journal of Guidance, Control, and Dynamics, Vol. 6, No. 2, 1983, pp. 112–118. JGCDDT 0162-3192 LinkGoogle Scholar[10] Balas M., "Direct Model Reference Adaptive Control in Infinite-Dimensional Linear Spaces," Journal of Mathematical Analysis and Applications, Vol. 196, No. 1, 1995, pp. 153–171. doi:https://doi.org/10.1006/jmaa.1995.1403 JMANAK 0022-247X CrossrefGoogle Scholar[11] Barkana I. and Ben-Asher J. Z., "Simple Adaptive Control Applications to Large Flexible Structures," Journal of Guidance, Control, and Dynamics, Vol. 34, No. 6, 2011, pp. 1929–1932. doi:https://doi.org/10.2514/1.54217 JGCDDT 0162-3192 LinkGoogle Scholar[12] Livneh R. and Slater G. L., "Some Conditions for Strictly Positive Real and Almost Strictly Positive Real Structures," IEEE International Conference on Systems Engineering, Vol. 1, IEEE Publications, Piscataway, NJ, 1990, pp. 81–85. Google Scholar[13] Mehiel E. A. and Balas M. J., "Determining Strictly Positive Realness from System Modal Characteristics," Journal of Guidance, Control, and Dynamics, Vol. 30, No. 5, 2007, pp. 1539–1542. doi:https://doi.org/10.2514/1.28240 JGCDDT 0162-3192 LinkGoogle Scholar[14] Hu Q., Jia Y. and Xu S., "Recursive Dynamics Algorithm for Multibody Systems with Variable-Speed Control Moment Gyroscopes" Journal of Guidance, Control, and Dynamics, Vol. 35, No. 5, 2013, pp. 1388–1398. JGCDDT 0162-3192 LinkGoogle Scholar[15] Damaren C. J., "Optimal Control Formulation for Lightly Damped, Gyroelastic Continua," M.S. Thesis, Inst. for Aerospace Studies, Univ. of Toronto, Downsview, ON, Canada, 1987. Google Scholar[16] Wen J. T., "Time Domain and Frequency Domain Conditions for Strict Positive Realness," IEEE Transactions on Automatic Control, Vol. 33, No. 10, 1988, pp. 988–992. doi:https://doi.org/10.1109/9.7263 IETAA9 0018-9286 CrossrefGoogle Scholar[17] Anderson B. D. O. and Vongpanitlerd S., Network Analysis and Synthesis, Prentice–Hall, Englewood Cliffs, NJ, 1973, pp. 215–220. Google Scholar[18] Broussard J. R. and O'Brien M. J., "Feedforward Control to Track the Output of a Forced Model," IEEE Transactions on Automatic Control, Vol. 25, No. 4, 1980, pp. 851–853. doi:https://doi.org/10.1109/TAC.1980.1102409 IETAA9 0018-9286 CrossrefGoogle Scholar Previous article Next article

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.