Dampers to suppress wind-induced oscillations of tall flexible structures
Viscous dampers for suppressing wind-induced oscillations of large flexible structures, antenna arrays, and Saturn 5 launch vehicle
Duncan, R. L.↗
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Algorithm development for the control design of flexible structures
The critical problems associated with the control of highly damped flexible structures are outlined. The practical problems include: high performance; assembly in space, configuration changes; on-line controller software design; and lack of test data. Underlying all of these problems is the central problem of modeling errors. To justify the expense of a space structure, the performance requirements will necessarily be very severe. On the other hand, the absence of economical tests precludes the availability of reliable data before flight. A design algorithm is offered which: (1) provides damping for a larger number of modes than the optimal attitude controller controls; (2) coordinates the rate of feedback design with the attitude control design by use of a similar cost function; and (3) provides model reduction and controller reduction decisions which are systematically connected to the mathematical statement of the control objectives and the disturbance models.
Skelton, R. E.↗
On identifiability of flexible structure parameters
This report investigates the identifiability of modal parameters of flexible structures. Expressions are derived for Cramer-Rao lower bounds for the modal parameters, that is, frequencies, damping ratios and mode shapes or slopes. The optimal initial state, which maximizes the trace of the Fisher information matrix in the absence of persistent input, is obtained. The concepts discussed are applied to a finite-element model of the 122 meter hoop/column antenna. The numerical results show that the identifiability of the structural frequencies is excellent, followed by that of the damping ratios and the mode-slopes.
Joshi, S. M.↗
Modeling and control of flexible structures
This monograph presents integrated modeling and controller design methods for flexible structures. The controllers, or compensators, developed are optimal in the linear-quadratic-Gaussian sense. The performance objectives, sensor and actuator locations and external disturbances influence both the construction of the model and the design of the finite dimensional compensator. The modeling and controller design procedures are carried out in parallel to ensure compatibility of these two aspects of the design problem. Model reduction techniques are introduced to keep both the model order and the controller order as small as possible. A linear distributed, or infinite dimensional, model is the theoretical basis for most of the text, but finite dimensional models arising from both lumped-mass and finite element approximations also play an important role. A central purpose of the approach here is to approximate an optimal infinite dimensional controller with an implementable finite dimensional compensator. Both convergence theory and numerical approximation methods are given. Simple examples are used to illustrate the theory.
Gibson, J. S.↗
Cost averaging techniques for robust control of flexible structural systems
Viewgraphs on cost averaging techniques for robust control of flexible structural systems are presented. Topics covered include: modeling of parameterized systems; average cost analysis; reduction of parameterized systems; and static and dynamic controller synthesis.
Hagood, Nesbitt W.↗
Experiments in control of flexible structures with noncolocated sensors and actuators
While the stable control of such flexible structures as limber spacecraft is easily achieved through the colocation of control actuators with sensors, noncolocation renders this extremely difficult. The most difficult case in point is that in which structural damping is low and spacecraft stiffness and inertia values are uncertain and changing. Attention is presently given to an apparatus in which each basic sensor/actuator noncolocation configuration is available, and inertias can be abruptly halved or doubled during control maneuvers. This feature can impose a sudden reversal in the plant's pole-zero sequence, which is a very difficult condition for the controller. Test results obtained to date demonstrate the inherent difficulty of achieving robustness in the case of noncolocation. It is noted that there may be very simple configurations in which there is no alternative to adaptive control.
Cannon, R. H., Jr.↗
System identification for modeling for control of flexible structures
The major components of a design and operational flight strategy for flexible structure control systems are presented. In this strategy an initial distributed parameter control design is developed and implemented from available ground test data and on-orbit identification using sophisticated modeling and synthesis techniques. The reliability of this high performance controller is directly linked to the accuracy of the parameters on which the design is based. Because uncertainties inevitably grow without system monitoring, maintaining the control system requires an active on-line system identification function to supply parameter updates and covariance information. Control laws can then be modified to improve performance when the error envelopes are decreased. In terms of system safety and stability the covariance information is of equal importance as the parameter values themselves. If the on-line system ID function detects an increase in parameter error covariances, then corresponding adjustments must be made in the control laws to increase robustness. If the error covariances exceed some threshold, an autonomous calibration sequence could be initiated to restore the error enveloped to an acceptable level.
Mettler, Edward↗
Low authority-threshold control for large flexible structures
An improved active control strategy for the vibration control of large flexible structures is presented. A minimum force, low authority-threshold controller is developed to bring a system with or without known external disturbances back into an 'allowable' state manifold over a finite time interval. The concept of a constrained, or allowable feedback form of the controller is introduced that reflects practical hardware implementation concerns. The robustness properties of the control strategy are then assessed. Finally, examples are presented which highlight the key points made within the paper.
Zimmerman, D. C.↗
Substructure-based control of flexible structures
A decentralized procedure is presented for the design of controllers for flexible structures. Spatially significant components are created which approximate the response of a specific part of the complete structure. For each component, the controller and observer gain matrices which are used in a controller for the complete structure. The proposed method is illustrated on a model of NASA Langley's CSI testbed structure.
Babuska, Vit↗
Modeling and tachometer feedback in the control of an experimental single link flexible structure
In this work a formulation for the modeling of a single link flexible structure will be introduced that includes the effects of dynamic interaction between the actuator and structure. These effects are the rotational modal participation factors for the structure's vibratory motion that occurs at the slewing axis. It will be shown, both theoretically and experimentally, that this dynamic interaction can be advantageous for vibration suppression of the flexible modes of the system during slewing positioning maneuvers.
Garcia, Ephrahim↗
Integration of mechanism and control for large-angle slew maneuvers of flexible structures
A rolling contact noncircular gear system is applied to assist a desired controller in the slewing of a flexible space structure. The varying gear ratio in cooperation with the controller results in lower feedback gains at the controller, as well as considerably reducing flexural vibrations of the space structure. The noncircular gears consist of a pair of convex noncircular cylinders with specially designed profiles that are synthesized in conjunction with the optimal controller gains for minimizing the flexural vibrations of flexible structure during a slew maneuver. Convexity of the cylindrical profiles for this noncircular gear device must be ensured to maintain rolling contact between the two cylinders. Simulations of slewing control tasks for two kinds of flexible space structures, such as a planar flexible beam and the planar articulated flexible beams, are presented.
Chew, Meng-Sang↗
Decentralized model reference adaptive control of large flexible structures
A decentralized model reference adaptive control (DMRAC) method is developed for large flexible structures (LFS). The development follows that of a centralized model reference adaptive control for LFS that have been shown to be feasible. The proposed method is illustrated using a simply supported beam with collocated actuators and sensors. Results show that the DMRAC can achieve either output regulation or output tracking with adequate convergence, provided the reference model inputs and their time derivatives are integrable, bounded, and approach zero as t approaches infinity.
Lee, Fu-Ming↗
Control of Shock Loading from a Jet in the Presence of a Flexible Structure
The control of shock noise or screech from a jet near a flexible structure is discussed. The pressure from the supersonic jet consists of a shock with spiral and flapping nonaxisymmetric modes superimposed on broadband response. This shock induces a nonlinear-nonstationary loading problem associated with acoustic wave generation and propagation coupled with structural vibration. Control of the shock is achieved by placing a ring at the nozzle lip oscillating at the shock fundamental frequency. The ring prevents the shock characteristics originating in the column of the shear layer from sustaining connection with the out-of-phase surface vibration. Shock-free flow is maintained over a large pressure ratio. The peak power pressure level is reduced by 40 dB.
Maestrello, Lucio↗
Modeling and Simulation of Variable Mass, Flexible Structures
The advent of the new Ares I launch vehicle has highlighted the need for advanced dynamic analysis tools for variable mass, flexible structures. This system is composed of interconnected flexible stages or components undergoing rapid mass depletion through the consumption of solid or liquid propellant. In addition to large rigid body configuration changes, the system simultaneously experiences elastic deformations. In most applications, the elastic deformations are compatible with linear strain-displacement relationships and are typically modeled using the assumed modes technique. The deformation of the system is approximated through the linear combination of the products of spatial shape functions and generalized time coordinates. Spatial shape functions are traditionally composed of normal mode shapes of the system or even constraint modes and static deformations derived from finite element models of the system. Equations of motion for systems undergoing coupled large rigid body motion and elastic deformation have previously been derived through a number of techniques [1]. However, in these derivations, the mode shapes or spatial shape functions of the system components were considered constant. But with the Ares I vehicle, the structural characteristics of the system are changing with the mass of the system. Previous approaches to solving this problem involve periodic updates to the spatial shape functions or interpolation between shape functions based on system mass or elapsed mission time. These solutions often introduce misleading or even unstable numerical transients into the system. Plus, interpolation on a shape function is not intuitive. This paper presents an approach in which the shape functions are held constant and operate on the changing mass and stiffness matrices of the vehicle components. Each vehicle stage or component finite element model is broken into dry structure and propellant models. A library of propellant models is used to describe the distribution of mass in the fuel tank or Solid Rocket Booster (SRB) case for various propellant levels. Based on the mass consumed by the liquid engine or SRB, the appropriate propellant model is coupled with the dry structure model for the stage. Then using vehicle configuration data, the integrated vehicle model is assembled and operated on by the constant system shape functions. The system mode shapes and frequencies can then be computed from the resulting generalized mass and stiffness matrices for that mass configuration. The rigid body mass properties of the vehicle are derived from the integrated vehicle model. The coupling terms between the vehicle rigid body motion and elastic deformation are also updated from the constant system shape functions and the integrated vehicle model. This approach was first used to analyze variable mass spinning beams and then prototyped into a generic dynamics simulation engine. The resulting code was tested against Crew Launch Vehicle (CLV-)class problems worked in the TREETOPS simulation package and by Wilson [2]. The Ares I System Integration Laboratory (SIL) is currently being developed at the Marshall Space Flight Center (MSFC) to test vehicle avionics hardware and software in a hardware-in-the-loop (HWIL) environment and certify that the integrated system is prepared for flight. The Ares I SIL utilizes the Ares Real-Time Environment for Modeling, Integration, and Simulation (ARTEMIS) tool to simulate the launch vehicle and stimulate avionics hardware. Due to the presence of vehicle control system filters and the thrust oscillation suppression system, which are tuned to the structural characteristics of the vehicle, ARTEMIS must incorporate accurate structural models of the Ares I launch vehicle. The ARTEMIS core dynamics simulation models the highly coupled nature of the vehicle flexible body dynamics, propellant slosh, and vehicle nozzle inertia effects combined with mass and flexible body properties that vary significant with time during the flight. All forces that act on the vehicle during flight must be simulated, including deflected engine thrust force, spatially distributed aerodynamic forces, gravity, and reaction control jet thrust forces. These forces are used to excite an integrated flexible vehicle, slosh, and nozzle dynamics model for the vehicle stack that simulates large rigid body translations and rotations along with small elastic deformations. Highly effective matrix math operations on a distributed, threaded high-performance simulation node allow ARTEMIS to retain up to 30 modes of flex for real-time simulation. Stage elements that separate from the stack during flight are propagated as independent rigid six degrees of freedom (6DOF) bodies. This paper will present the formulation of the resulting equations of motion, solutions to example problems, and describe the resulting dynamics simulation engine within ARTEMIS.
Tobbe, Patrick A.↗
Natural modes of oscillation of rotating flexible structures about nontrivial equilibrium
This paper is concerned with the vibrational characteristics of rotating flexible structures in the neighborhood of steady rotation. It is assumed that the structure undergoes deformations during the steady rotation, so that the equilibrium is nontrivial. The object of the paper is to formulate the eigenvalue problem associated with small oscillations of the structure about the nontrivial equilibrium and to develop efficient methods to compute the system natural frequencies and modal vectors. A numerical example showing the procedure for the calculation of spacecraft modes is presented.
Meirovitch, L.↗
Static shape control for flexible structures
An integrated methodology is described for defining static shape control laws for large flexible structures. The techniques include modeling, identifying and estimating the control laws of distributed systems characterized in terms of infinite dimensional state and parameter spaces. The models are expressed as interconnected elliptic partial differential equations governing a range of static loads, with the capability of analyzing electromagnetic fields around antenna systems. A second-order analysis is carried out for statistical errors, and model parameters are determined by maximizing an appropriate defined likelihood functional which adjusts the model to observational data. The parameter estimates are derived from the conditional mean of the observational data, resulting in a least squares superposition of shape functions obtained from the structural model.
Rodriguez, G.↗
A distributed finite-element modeling and control approach for large flexible structures
An unconventional framework is described for the design of decentralized controllers for large flexible structures. In contrast to conventional control system design practice which begins with a model of the open loop plant, the controlled plant is assembled from controlled components in which the modeling phase and the control design phase are integrated at the component level. The developed framework is called controlled component synthesis (CCS) to reflect that it is motivated by the well developed Component Mode Synthesis (CMS) methods which were demonstrated to be effective for solving large complex structural analysis problems for almost three decades. The design philosophy behind CCS is also closely related to that of the subsystem decomposition approach in decentralized control.
Young, K. D.↗
Decentralized control of large flexible structures by joint decoupling
A decentralized control design method is presented for large complex flexible structures by using the idea of joint decoupling. The derivation is based on a coupled substructure state-space model, which is obtained from enforcing conditions of interface compatibility and equilibrium to the substructure state-space models. It is shown that by restricting the control law to be localized state feedback and by setting the joint actuator input commands to decouple joint 'degrees of freedom' (dof) from interior dof, the global structure control design problem can be decomposed into several substructure control design problems. The substructure control gains and substructure observers are designed based on modified substructure state-space models. The controllers produced by the proposed method can operate successfully at the individual substructure level as well as at the global structure level. Therefore, not only control design but also control implementation is decentralized. Stability and performance requirement of the closed-loop system can be achieved by using any existing state feedback control design method. A two-component mass-spring damper system and a three-truss structure are used as examples to demonstrate the proposed method.
Su, Tzu-Jeng↗