Experimental validation of a fuel-efficient robotic maneuver control algorithm for very large flexible space structures

An Overview of Modeling and Control of Large Flexible Space Structures

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.

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.

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 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.

Consideration is given to the selection of velocity feedback gains for individual dampers for the members of a structurally controlled large flexible space structure. The problem is formulated as an optimal output feedback regulator problem, and necessary conditions are derived for minimizing a quadratic performance function. The diagonal nature of the gain matrix is taken into account, along with knowledge of noise covariances. It is pointed out that the method presented offers a systematic approach to the design of a class of controllers for enhancing structural damping, which have significant potential if used in conjunction with a reduced-order optimal controller for rigid-body modes and selected structural modes.

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

Large Flexible Structure Control Technology Experiment and Facility Design

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.

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.

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 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.

In this study, a 'lump-parameter' model was formulated to represent a large flexible space structure (solar panel) controlled by bonded piezoceramic actuators. A control strategy based on fuzzy logic theory (FLC) was developed for vibration damping. A comparison of the performance of the proposed FLC with that obtained by applying LQR is presented.

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. >

The spacecraft with large flexible space structures may be subject to the thermally induced vibration (TIV) due to the rapidly changed solar heat flux when it enters and leaves the eclipse, which would lead to certain spacecraft failure. This paper reports a laboratory experiment that aims to study the impact of transient characteristics of heat flux on the ground experiment of TIV. In the experiments on the TIV of a slender thin-walled beam, two different methods of providing transient heat flux were considered, and the process of entering and leaving eclipse was simulated, respectively. The experimental results demonstrate that different transient characteristics of heat flux will have large impact on the TIV of the specimen, and the ideal theoretical estimation of thermal characteristic time has limitations in practical engineering. In addition, it is found that the traditional way of simulating solar heat flux by turning on/off infrared heat lamps is not suitable for the TIV ground experiment. Instead, a transient heat flux simulation method by moving the baffle is recommended.