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At least 937 records · Page 52

Robust control with structured perturbations

This semi-annual report describes continued progress on the research. Among several approaches in this area of research, our approach to the parametric uncertainties are being matured everyday. This approach deals with real parameter uncertainties which other techniques such as H (sup infinity) optimal control, micron analysis and synthesis, and l(sub 1) optimal control cannot deal. The primary assumption of this approach is that the mathematical models are well obtained so that the most of system uncertainties can be translated into parameter uncertainties of their linear system representations. These uncertainties may be due to modeling, nonlinearity of the physical system, some time-varying parameters, etc. In this report period of research, we are concentrating on implementing a computer aided analysis and design tool based on new results on parametric robust stability. This implementation will help us to reveal further details in this approach.

Keel, Leehyun↗

Controlling Flexible Manipulators, an Experimental Investigation

Lightweight, slender manipulators offer faster response and/or greater workspace range for the same size actuators than tradional manipulators. Lightweight construction of manipulator links results in increased structural flexibility. The increase flexibility must be considered in the design of control systems to properly account for the dynamic flexible vibrations and static deflections. Real time control of the flexible manipulator vibrations are experimentally investigated. Models intended for real-time control of distributed parameter system such as flexible manipulators rely on model approximation schemes. An linear model based on the application of Lagrangian dynamics to a rigid body mode and a series of separable flexible modes is examined with respect to model order requirements, and modal candidate selection. Balanced realizations are applied to the linear flexible model to obtain an estimate of appropriate order for a selected model. Describing the flexible deflections as a linear combination of modes results in measurements of beam state, which yield information about several modes. To realize the potential of linear systems theory, knowledge of each state must be available. State estimation is also accomplished by implementation of a Kalman Filter. State feedback control laws are implemented based upon linear quadratic regulator design.

Hastings, Gordon Greene↗

Pole placement and order reduction in two-time-scale control systems through Riccati iteration

A transformation of variables taken from singular perturbations may be applied to two-time-scale linear systems in state space form to reduce the system to block-diagonal form with slow and fast modes decoupled. The transformation is easily computed by applying the new Riccati iteration. The iteration yields a solution to the nonsymmetric algebraic Riccati equation obtained by partitioning the original system matrix A. The numerical procedure is initiated with the trivial iterate L(0) = 0, and is globally convergent to the desired unique time scale decoupling solution. After transformation, the decoupled system may be used in controller design to achieve exact closed loop pole placement in the slow subsystem without altering the poles of the fast subsystem. The decoupled form may also be used to reduce system order by wetting a small parameter to zero. Provided the fast subsystem is stable, the order reduction can be expected to yield a good approximation to the original system. These methods are demonstrated using the 16th order linear model of a turbofan engine.

Anderson, L. R.↗

Real Time Digital Control of a Magnetostrictive Actuator

The use of the magnetostrictive material Terfenol-D as a motion source in active vibration control (AVC) systems are being studied. Currently it is of limited use due to the nonlinear nature of the strain versus magnetization curve and the magnetic hysteresis in the Terfenol-D. One manifestation of these nonlinearities is waveform distortion in the output velocity of the transducer. For Terfenol-D to be used in ever greater numbers of AVC systems, these nonlinearities must be addressed. In this study the nonlinearities are treated as disturbances to a linear system. The acceleration output is used in simple analog and digital feedback control schemes to improve linearity of the transducer. In addition, the use of a Terfenol-D actuator in an AVC system is verified. Both analog and digital controllers are implemented and results compared. A cantilever beam system is considered for AVC applications. The second thrust of this presentation is the reduction of harmonic distortions. Two conclusions can be reached from this work. One, the linearization of Terfenol-D transducers is possible with the use of feedback controllers, both digital and analog. Second, Terfenol-D is a viable motion source in active vibration control systems utilizing either analog or digital controllers.

Zrostlik, Rick L.↗

Linear embedding of nonlinear dynamical systems and prospects for efficient quantum algorithms

The simulation of large nonlinear dynamical systems, including systems generated by discretization of hyperbolic partial differential equations, can be computationally demanding. Such systems are important in both fluid and kinetic computational plasma physics. This motivates exploring whether a future error-corrected quantum computer could perform these simulations more efficiently than any classical computer. In this work, we describe a method for mapping any finite nonlinear dynamical system to an infinite linear dynamical system (embedding) and detail three specific cases of this method that correspond to previously studied mappings. Then we explore an approach for approximating the resulting infinite linear system with finite linear systems (truncation). Using a number of qubits only logarithmic in the number of variables of the nonlinear system, a quantum computer could simulate truncated systems to approximate output quantities if the nonlinearity is sufficiently weak. Other aspects of the computational efficiency of the three detailed embedding strategies are also discussed.

97 MATHEMATICS AND COMPUTING↗

An inertia-free filter line-search algorithm for large-scale nonlinear programming

We present a filter line-search algorithm that does not require inertia information of the linear system. This feature enables the use of a wide range of linear algebra strategies and libraries, which is essential to tackle large-scale problems on modern computing architectures. The proposed approach performs curvature tests along the search step to detect negative curvature and to trigger convexification. We prove that the approach is globally convergent and we implement the approach within a parallel interior-point framework to solve large-scale and highly nonlinear problems. Our numerical tests demonstrate that the inertia-free approach is as efficient as inertia detection via symmetric indefinite factorizations. We also demonstrate that the inertia-free approach can lead to reductions in solution time because it reduces the amount of convexification needed.

Chiang, Nai-Yuan↗

Operational Characteristics of an Accelerator Driven Fissile Solution System

Operational characteristics represent the set of responses that a nuclear system exhibits during normal operation. Operators rely on this behavior to assess the status of the system and to predict the consequences of off-normal events. These characteristics largely refer to the relationship between power and system operating conditions. The static and dynamic behavior of a chain-reacting system, operating at sufficient power, is primarily governed by reactivity effects. The science of reactor physics has identified and evaluated a number of such effects, including Doppler broadening and shifts in the thermal neutron spectrum. Often these reactivity effects are quantified in the form of feedback coefficients that serve as coupling coefficients relating the neutron population and the physical mechanisms that drive reactivity effects, such as fissile material temperature and density changes. The operational characteristics of such nuclear systems usually manifest themselves when perturbations between system power (neutron population) and system operating conditions arise. Successful operation of such systems requires the establishment of steady equilibrium conditions. However, prior to obtaining the desired equilibrium (steady-state) conditions, an approach from zero-power (startup) must occur. This operational regime may possess certain limiting system conditions that must be maintained to achieve effective startup. Once steady-state is achieved, a key characteristic of this operational regime is the level of stability that the system possesses. Finally, a third operational regime, shutdown, may also possess limiting conditions of operation that must be maintained. This report documents the operational characteristics of a “generic” Accelerator Driven Fissile Solution (ADFS) system during the various operational regimes of startup, steady-state operation, and shutdown. Typical time-dependent behavior for each operational regime will be illustrated, and key system parameters, such as response times, will be quantified. A generalized linear systems analysis of steady-state operations will be performed to evaluate the level of stability of ADFS systems. This information should provide a basic understanding of typical ADFS system operational behavior, and facilitate the development of monitoring procedures and operator aids.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Identification evaluation methods

Methods for airplane parameter estimation, the equation error method, output error method, and two advanced methods are presented and their basic properties described. The advanced methods include the maximum likelihood and extended Kalman filter method. For a better understanding of the estimation techniques a first-order scalar differential equation is used as a model of the system under test. Application of the methods to a general multivariable linear system is briefly outlined. A note on the parameter estimation in the frequency domain is also presented. Numerical examples along with the comparison of results from various methods are given.

Klein, V.↗

A separated bias identification and state estimation algorithm for nonlinear systems

A computational algorithm for the identification of biases in discrete-time, nonlinear, stochastic systems is derived by extending the separate bias estimation results for linear systems to the extended Kalman filter formulation. The merits of the approach are illustrated by identifying instrument biases using a terminal configured vehicle simulation.

Caglayan, A. K.↗

A bias identification and state estimation methodology for nonlinear systems

A computational algorithm for the identification of input and output biases in discrete-time nonlinear stochastic systems is derived by extending the separate bias estimation results for linear systems to the extended Kalman filter formulation. The merits of the approach are illustrated by identifying instrument biases using a terminal configured vehicle simulation.

Caglayan, A. K.↗

Exact spacecraft detumbling and reorientation maneuvers with gimbaled thrusters and reaction wheels

The equations of rotational motion for a spacecraft equipped with external jets and internal reaction wheels are shown to be feedback-equivalent to those of a linear system in attitude parameter space. Reorientation maneuvers are thereby formulated as linear optimal control problems with least mean square acceleration in attitude parameter space, solved in closed form and implementable either with internal or external torque commands, the choice depending on power and throttling requirements. For prior detumbling, an alternative solution with least mean square torque by angular momentum feedback is also given, that is implementable with gimbaled pairs of thrusters at constant throttle. Such a detumbling maneuver may then be followed by an acceleration-commanded rest-to-rest maneuver by means of the reaction wheels.

Dwyer, T. A. W., III↗

The Kronecker indices of affine-nonlinear control systems

The Kronecker indices of smooth affine-nonlinear control systems presently defined are noted to determine the collection of controllable linear systems that are obtainable on the basis of local feedback equivalences and state-space reductions. Because attention is given to the invariants of systems under equivalences, and the behavior of these invariants under mappings that arise from state submersions, local representations of systems are used wherever possible to render cases more accessible.

Lewis, J. H.↗

An approximate loop transfer recovery method for designing fixed-order compensators

A method for designing fixed-order dynamic compensators for multivariable time invariant linear systems is presented which is based on the minimization of a linear quadratic performance index. The present formulation is performed in an output feedback setting which uses an observer cononical form to represent the compensator dynamics. Techniques for penalizing the plant and compensator states and for selecting the distribution on initial conditions such that the loop transfer matrix approximates that of a full-state feedback design have been developed. The effectiveness of the method is demonstrated using the examples of the pointing of a flexible structure and a helicopter flight control problem.

Calise, Anthony J.↗

Attitude determination and calibration using a recursive maximum likelihood-based adaptive Kalman filter

An adaptive Kalman filter design that utilizes recursive maximum likelihood parameter identification is discussed. At the center of this design is the Kalman filter itself, which has the responsibility for attitude determination. At the same time, the identification algorithm is continually identifying the system parameters. The approach is applicable to nonlinear, as well as linear systems. This adaptive Kalman filter design has much potential for real time implementation, especially considering the fast clock speeds, cache memory and internal RAM available today. The recursive maximum likelihood algorithm is discussed in detail, with special attention directed towards its unique matrix formulation. The procedure for using the algorithm is described along with comments on how this algorithm interacts with the Kalman filter.

Kelly, D. A.↗

Analysis of lightning field changes produced by Florida thunderstorms

A new method is introduced for inferring the charges deposited in a lightning flash. Lightning-caused field changes (delta E's) are described by a more general volume charge distribution than is defined on a large cartesian grid system centered above the measuring networks. It is shown that a linear system of equations can be used to relate delta E's at the ground to the values of charge on this grid. It is possible to apply more general physical constraints to the charge solutions, and it is possible to access the information content of the delta E data. Computer-simulated delta E inversions show that the location and symmetry of the charge retrievals are usually consistent with the known test sources.

Koshak, William John↗

Discretized energy minimization in a wave guide with point sources

An anti-noise problem on a finite time interval is solved by minimization of a quadratic functional on the Hilbert space of square integrable controls. To this end, the one-dimensional wave equation with point sources and pointwise reflecting boundary conditions is decomposed into a system for the two propagating components of waves. Wellposedness of this system is proved for a class of data that includes piecewise linear initial conditions and piecewise constant forcing functions. It is shown that for such data the optimal piecewise constant control is the solution of a sparse linear system. Methods for its computational treatment are presented as well as examples of their applicability. The convergence of discrete approximations to the general optimization problem is demonstrated by finite element methods.

Propst, G.↗

Planetary Defence Activities Beyond NASA and ESA

The collision of a significant asteroid or comet with Earth represents a singular natural disaster for a myriad of reasons, including: its extraterrestrial origin; the fact that it is perhaps the only natural disaster that is preventable in many cases, given sufficient preparation and warning; its scope, which ranges from damaging a city to an extinction-level event; and the duality of asteroids and comets themselves---they are grave potential threats, but are also tantalising scientific clues to our ancient past and resources with which we may one day build a prosperous spacefaring future. Accordingly, the problems of developing the means to interact with asteroids and comets for purposes of defence, scientific study, exploration, and resource utilisation have grown in importance over the past several decades. Since the 1980s, more and more asteroids and comets (especially the former) have been discovered, radically changing our picture of the solar system. At the beginning of the year 1980, approximately 9,000 asteroids were known to exist. By the beginning of 2001, that number had risen to approximately 125,000 thanks to the Earth-based telescopic survey efforts of the era, particularly the emergence of modern automated telescopic search systems, pioneered by the Massachusetts Institute of Technology’s (MIT’s) LINEAR system in the mid-to-late 1990s. Today, in late 2019, about 840,000 asteroids have been discovered, with more and more being found every week, month, and year. Of those, approximately 21,400 are categorised as near-Earth asteroids (NEAs), 2,000 of which are categorised as Potentially Hazardous Asteroids (PHAs) and 2,749 of which are categorised as potentially accessible. The hazards posed to us by asteroids affect people everywhere around the world. As well, the opportunities presented by asteroids may benefit our entire species. Thus, with such a large number of currently known asteroids and so many yet to be discovered, it is not surprising that individuals, organisations, institutions, and governments all around the world have become interested in the study of asteroids. Indeed, a variety of government space agencies, private organisations, and individuals have worked on developing the means by which to observe, study, and even interact with asteroids and comets for purposes including science, exploration, pioneering, commerce, and planetary defence. This includes significant individual contributions by amateur asteroid astronomers all over the world. International cooperation in planetary defence within the contexts of the United Nations and the International Asteroid Warning Network (IAWN) are discussed in Chapter 2, and the activities undertaken by the world’s larger space agencies, ESA and NASA, are discussed in Chapters 3 and 4. But, what of the other agencies and institutions around the world who are also working on the problem of defence against hazardous asteroids and comets, or related topics? In this chapter we provide an overview, in alphabetical order, of some of the planetary defence related efforts that have been undertaken around the world beyond the activities at the United Nations, NASA, and ESA.

Barbee, Brent W.↗