Control and Stabilization of Rotating flexible structure

Cataloged from PDF version of article.We consider a flexible beam clamped to a rigid base at one end and free at the other end. We assume that the rigid base rotates with a constant angular velocity and that the motion of the flexible beam takes place on a plane. To suppress the beam vibrations, we propose dynamic control laws for boundary control force and torque, both applied to the free end of the beam. We show that, under some conditions, one of which is the strict positive realness of the actuator transfer functions which generate the boundary control force and torque, the beam vibrations asymptotically decay to zero if the rigid base angular frequency is sufficiently small. Moreover, if the transfer functions are proper but not strictly proper, we show that the decay is exponential. We also give a bound on the constant angular velocity above which the system becomes unstable

NASA Workshop on Distributed Parameter Modeling and Control of Flexible Aerospace Systems

Although significant advances have been made in modeling and controlling flexible systems, there remains a need for improvements in model accuracy and in control performance. The finite element models of flexible systems are unduly complex and are almost intractable to optimum parameter estimation for refinement using experimental data. Distributed parameter or continuum modeling offers some advantages and some challenges in both modeling and control. Continuum models often result in a significantly reduced number of model parameters, thereby enabling optimum parameter estimation. The dynamic equations of motion of continuum models provide the advantage of allowing the embedding of the control system dynamics, thus forming a complete set of system dynamics. There is also increased insight provided by the continuum model approach

Control of large space structures

The control of large space structures was studied to determine what, if any, limitations are imposed on the size of spacecraft which may be controlled using current control system design technology. Using a typical structure in the 35 to 70 meter size category, a control system design that used actuators that are currently available was designed. The amount of control power required to maintain the vehicle in a stabilized gravity gradient pointing orientation that also damped various structural motions was determined. The moment of inertia and mass properties of this structure were varied to verify that stability and performance were maintained. The study concludes that the structure's size is required to change by at least a factor of two before any stability problems arise. The stability margin that is lost is due to the scaling of the gravity gradient torques (the rigid body control) and as such can easily be corrected by changing the control gains associated with the rigid body control. A secondary conclusion from the study is that the control design that accommodates the structural motions (to damp them) is a little more sensitive than the design that works on attitude control of the rigid body only

Fourth NASA Workshop on Computational Control of Flexible Aerospace Systems, part 1

The proceedings of the workshop are presented. Some areas of discussion are as follows: modeling, systems identification, and control of flexible aircraft, spacecraft, and robotic systems

Rotorcraft aeroelastic stability

Theoretical and experimental developments in the aeroelastic and aeromechanical stability of helicopters and tilt-rotor aircraft are addressed. Included are the underlying nonlinear structural mechanics of slender rotating beams, necessary for accurate modeling of elastic cantilever rotor blades, and the development of dynamic inflow, an unsteady aerodynamic theory for low-frequency aeroelastic stability applications. Analytical treatment of isolated rotor stability in hover and forward flight, coupled rotor-fuselage stability in hover and forward flight, and analysis of tilt-rotor dynamic stability are considered. Results of parametric investigations of system behavior are presented, and correlation between theoretical results and experimental data from small and large scale wind tunnel and flight testing are discussed

Survey of Army/NASA rotorcraft aeroelastic stability research

Theoretical and experimental developments in the aeroelastic and aeromechanical stability of helicopters and tilt-rotor aircraft are addressed. Included are the underlying nonlinear structural mechanics of slender rotating beams, necessary for accurate modeling of elastic cantilever rotor blades, and the development of dynamic inflow, an unsteady aerodynamic theory for low frequency aeroelastic stability applications. Analytical treatment of isolated rotor stability in hover and forward flight, coupled rotor-fuselage stability are considered. Results of parametric investigations of system behavior are presented, and correlations between theoretical results and experimental data from small- and large-scale wind tunnel and flight testing are discussed

Vibration, Control and Stability of Dynamical Systems

From Preface: This is the fourteenth time when the conference “Dynamical Systems: Theory and Applications” gathers a numerous group of outstanding scientists and engineers, who deal with widely understood problems of theoretical and applied dynamics. Organization of the conference would not have been possible without a great effort of the staff of the Department of Automation, Biomechanics and Mechatronics. The patronage over the conference has been taken by the Committee of Mechanics of the Polish Academy of Sciences and Ministry of Science and Higher Education of Poland. It is a great pleasure that our invitation has been accepted by recording in the history of our conference number of people, including good colleagues and friends as well as a large group of researchers and scientists, who decided to participate in the conference for the first time. With proud and satisfaction we welcomed over 180 persons from 31 countries all over the world. They decided to share the results of their research and many years experiences in a discipline of dynamical systems by submitting many very interesting papers. This year, the DSTA Conference Proceedings were split into three volumes entitled “Dynamical Systems” with respective subtitles: Vibration, Control and Stability of Dynamical Systems; Mathematical and Numerical Aspects of Dynamical System Analysis and Engineering Dynamics and Life Sciences. Additionally, there will be also published two volumes of Springer Proceedings in Mathematics and Statistics entitled “Dynamical Systems in Theoretical Perspective” and “Dynamical Systems in Applications”

Flat systems, equivalence and trajectory generation

Flat systems, an important subclass of nonlinear control systems introduced via differential-algebraic methods, are defined in a differential geometric framework. We utilize the infinite dimensional geometry developed by Vinogradov and coworkers: a control system is a diffiety, or more precisely, an ordinary diffiety, i.e. a smooth infinite-dimensional manifold equipped with a privileged vector field. After recalling the definition of a Lie-Backlund mapping, we say that two systems are equivalent if they are related by a Lie-Backlund isomorphism. Flat systems are those systems which are equivalent to a controllable linear one. The interest of such an abstract setting relies mainly on the fact that the above system equivalence is interpreted in terms of endogenous dynamic feedback. The presentation is as elementary as possible and illustrated by the VTOL aircraft

Orbiting Rainbows: Optical Manipulation of Aerosols and the Beginnings of Future Space Construction

Our objective is to investigate the conditions to manipulate and maintain the shape of an orbiting cloud of dust-like matter so that it can function as an ultra-lightweight surface with useful and adaptable electromagnetic characteristics, for instance, in the optical, RF, or microwave bands. Inspired by the light scattering and focusing properties of distributed optical assemblies in Nature, such as rainbows and aerosols, and by recent laboratory successes in optical trapping and manipulation, we propose a unique combination of space optics and autonomous robotic system technology, to enable a new vision of space system architecture with applications to ultra-lightweight space optics and, ultimately, in-situ space system fabrication. Typically, the cost of an optical system is driven by the size and mass of the primary aperture. The ideal system is a cloud of spatially disordered dust-like objects that can be optically manipulated: it is highly reconfigurable, fault-tolerant, and allows very large aperture sizes at low cost. See Figure 1 for a scenario of application of this concept. The solution that we propose is to construct an optical system in space in which the nonlinear optical properties of a cloud of micron-sized particles are shaped into a specific surface by light pressure, allowing it to form a very large and lightweight aperture of an optical system, hence reducing overall mass and cost. Other potential advantages offered by the cloud properties as optical system involve possible combination of properties (combined transmit/receive), variable focal length, combined refractive and reflective lens designs, and hyper-spectral imaging. A cloud of highly reflective particles of micron-size acting coherently in a specific electromagnetic band, just like an aerosol in suspension in the atmosphere, would reflect the Sun's light much like a rainbow. The only difference with an atmospheric or industrial aerosol is the absence of the supporting fluid medium. This new concept is based on recent understandings in the physics of optical manipulation of small particles in the laboratory and the engineering of distributed ensembles of spacecraft clouds to shape an orbiting cloud of micron-sized objects. In the same way that optical tweezers have revolutionized micro- and nano-manipulation of objects, our breakthrough concept will enable new large scale NASA mission applications and develop new technology in the areas of Astrophysical Imaging Systems and Remote Sensing because the cloud can operate as an adaptive optical imaging sensor. While achieving the feasibility of constructing one single aperture out of the cloud is the main topic of this work, it is clear that multiple orbiting aerosol lenses could also combine their power to synthesize a much larger aperture in space to enable challenging goals such as exoplanet detection. Furthermore, this effort could establish feasibility of key issues related to material properties, remote manipulation, and autonomy characteristics of cloud in orbit. There are several types of endeavors (science missions) that could be enabled by this type of approach, i.e. it can enable new astrophysical imaging systems, exoplanet search, large apertures allow for unprecedented high resolution to discern continents and important features of other planets, hyperspectral imaging, adaptive systems, spectroscopy imaging through limb, and stable optical systems from Lagrange-points. Future micro-miniaturization might hold promise of a further extension of our dust aperture concept to other more exciting smart dust concepts with other associated capabilities