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his paper reviews modern geometrical dynamics and control of humanoid robots. This general Lagrangian and Hamiltonian formalism starts with a proper definition of humanoid's configuration manifold, which is a set of all robot's active joint angles. Based on the `covariant force law', the general humanoid's dynamics and control are developed. Autonomous Lagrangian dynamics is formulated on the associated `humanoid velocity phase space', while autonomous Hamiltonian dynamics is formulated on the associated `humanoid momentum phase space'. Neural-like hierarchical humanoid control naturally follows this geometrical prescription. This purely rotational and autonomous dynamics and control is then generalized into the framework of modern non-autonomous biomechanics, defining the Hamiltonian fitness function. The paper concludes with several simulation examples. Keywords: Humanoid robots, Lagrangian and Hamiltonian formalisms, neural-like humanoid control, time-dependent biodynamics

We describe the behavior of two coupled Bose-Einstein condensates in time-dependent (TD) trap potentials and TD Rabi (or tunneling) frequency, using the two-mode approach. Starting from Bloch states, we succeed to get analytical solutions for the TD Schroedinger equation and present a detailed analysis of the relative and geometric phases acquired by the wave function of the condensates, as well as their population imbalance. We also establish a connection between the geometric phases and constants of motion which characterize the dynamic of the system. Besides analyzing the affects of temporality on condensates that differs by hyperfine degrees of freedom (internal Josephson effect), we also do present a brief discussion of a one specie condensate in a double-well potential (external Josephson effect).

A case study of a spacecraft having flexible solar arrays is presented. A stationkeeping attitude control mode using both earth and rate gyro reference signals and a flexible vehicle dynamics modeling and implementation is discussed. The control system is designed to achieve both pointing accuracy and structural mode stability during stationkeeping maneuvers. Reduction of structural mode interactions over the entire mode duration is presented. The control mode using a discrete time observer structure is described to show the convergence of the spacecraft attitude transients during Delta-V thrusting maneuvers without preloading thrusting bias to the onboard control processor. The simulation performance using the three axis, body stabilized nonlinear dynamics is provided. The details of a five body dynamics model are discussed. The spacecraft is modeled as a central rigid body having cantilevered flexible antennas, a pair of flexible articulated solar arrays, and to gimballed momentum wheels. The vehicle is free to undergo unrestricted rotations and translations relative to inertial space. A direct implementation of the equations of motion is compared to an indirect implementation that uses a symbolic manipulation software to generate rigid body equations.

A large-angle, flexible, multibody, dynamic modeling capability has been developed to help validate numerical simulations of the dynamic motion and control forces which occur during berthing of Space Station Freedom to the Shuttle Orbiter in the early assembly flights. This paper outlines the dynamics and control of the station, the attached Shuttle Remote Manipulator System, and the orbiter. The simulation tool developed for the analysis is described and the results of two simulations are presented. The first is a simulated maneuver from a gravity-gradient attitude to a torque equilibrium attitude using the station reaction control jets. The second simulation is the berthing of the station to the orbiter with the station control moment gyros actively maintaining an estimated torque equilibrium attitude. The influence of the elastic dynamic behavior of the station and of the Remote Manipulator System on the attitude control of the station/orbiter system during each maneuver was investigated. The flexibility of the station and the arm were found to have only a minor influence on the attitude control of the system during the maneuvers.

A new approach for adaptive identification and control of structural dynamic systems by using least squares lattice filters thar are widely used in the signal processing area is presented. Testing procedures for interfacing the lattice filter identification methods and modal control method for stable closed loop adaptive control are presented. The methods are illustrated for a free-free beam and for a complex flexible grid, with the basic control objective being vibration suppression. The approach is validated by using both simulations and experimental facilities available at the Langley Research Center.

Attitude control techniques for the pointing and stabilization of very large, inherently flexible spacecraft systems were investigated. The attitude dynamics and control of a long, homogeneous flexible beam whose center of mass is assumed to follow a circular orbit was analyzed. First order effects of gravity gradient were included. A mathematical model which describes the system rotations and deflections within the orbital plane was developed by treating the beam as a number of discretized mass particles connected by massless, elastic structural elements. The uncontrolled dynamics of the system are simulated and, in addition, the effects of the control devices were considered. The concept of distributed modal control, which provides a means for controlling a system mode independently of all other modes, was examined. The effect of varying the number of modes in the model as well as the number and location of the control devices were also considered.

The effect of delay in the control system input on the stability of a continuously acting controller which is designed without considering the delay is studied. The stability analysis of a second order plant is studied analytically and verified numerically. For this example it is found that the system becomes unstable for a delay which is equivalent to only 16 percent of its natural period of motion. It is also observed that even a small amount of natural damping in the system can increase the amount of delay that can be tolerated before the onset of instability. The delay problem is formulated in the discrete time domain and an analysis procedure suggested. The maximum principle from optimal control theory is applied to minimize the time required for the slewing of a general rigid spacecraft. The slewing motion need not be restricted to a single axis maneuver. The minimum slewing time is calculated based on a quasi-linearization algorithm for the resulting two point boundary value problem. Numerical examples based on the rigidized in-orbit model of the SCOLE also include the more general reflector line-of-sight slewing maneuvers.

In this paper, we derive and analyse a model for the control of arboviral diseases which takes into account an imperfect vaccine combined with some other mechanisms of control already studied in the literature. We begin by analyse the basic model without controls. We prove the existence of two disease-free equilibrium points and the possible existence of up to two endemic equilibrium points (where the disease persists in the population). We show the existence of a transcritical bifurcation and a possible saddle-node bifurcation and explicitly derive threshold conditions for both, including defining the basic reproduction number, R 0 , which determines whether the disease can persist in the population or not. The epidemiological consequence of saddle-node bifurcation (backward bifurcation) is that the classical requirement of having the reproduction number less than unity, while necessary, is no longer sufficient for disease elimination from the population. It is further shown that in the absence of disease--induced death, the model does not exhibit this phenomenon. We perform the sensitivity analysis to determine the model robustness to parameter values. That is to help us to know the parameters that are most influential in determining disease dynamics. The model is extended by reformulating the model as an optimal control problem, with the use of five time dependent controls, to assess the impact of vaccination combined with treatment, individual protection and vector control strategies (killing adult vectors, reduction of eggs and larvae). By using optimal control theory, we establish optimal conditions under which the disease can be eradicated and we examine the impact of a possible combined control tools on the disease transmission. The Pontryagin's maximum principle is used to characterize the optimal control. Numerical simulations, efficiency analysis and cost effectiveness analysis show that, vaccination combined with other control mechanisms, would reduce the spread of the disease appreciably, and this at low cost.

Experiments were conducted in a Link GAT-2 to evaluate the effectiveness of a system providing direct control over aircraft maneuvering performance. Pilots performed complex navigational tasks involving the use of a computer-assisted area navigation system. Changing waypoint storage capacity of the simulated navigation system induced variable task loading on subjects. The experiment was replicated with and without a self-adaptive side task to determine levels of residual attention associated with the control modifications and the varying workload levels. The flight performance controller yielded greater precision of maneuvering control, fewer procedural blunders, and an increased level of residual pilot attention. The side task proved to be a reliable discriminator of changes in workload associated with small changes in system design and task complexity.

The unprecedented requirements for rapid retargeting and precision pointing for spaced-based directed energy weapon platforms is the prime driver behind the reported modeling and control study. The combination of such requirements demand a comprehensive dynamic model of the nonlinear multibody dynamics of typical space platforms for such weapon including the interaction platform structural flexure effecting principal weapon system effective Line-Of-Sight. This report describes the first year effort of a three year project which focuses on: (1) the development of comprehensive; generic nonlinear dynamical models for typical space-based plat forms, (2) the development of high performance, nonlinear control laws for rapid slewing and precesion pointing of primary weapon system payload apertures, and (3) the design of a series of laboratory experiments to verify and test the control laws developed. The validation of the analytical models and the required control theory for the resulting class of nonlinear system is described in this report. Simulation results are given for a simplified benchmark model of a space-based laser slewing control and consideration for compensation for structural flexure effecting optical LOS using optical steering mirrors is discussed.

There has been an increased experimental understanding of boundary layer structure and behavior particularly in the turbulent regime as well as significant improvements in our knowledge of the factors affecting the boundary-layer transition in arbitrary flow fields. This symposium was intended to bring together the practitioners of the various applications of boundary layer control with those interested in the underlying fluid mechanics. Contributions covered theoretical and experimental developments in the use of both traditional and non-traditional means of boundary layer control for external flow applications such as lift augmentation, drag reduction and improved effectiveness of controls, and for internal flow applications such as air intakes and exit configurations. Techniques included shaping (geometry) suction and blowing; transverse blowing; vortex generators; heating and cooling; and turbulent boundary layer manipulation. The special emphasis on high-lift systems included consideration of the techniques of boundary layer control on characteristics of wings and wing-body arrangements that involve flaps, slats and jets (blown flaps), and vortex flaps.

Journal of Guidance, Control, and Dynamics was a publication covering guidance and control in aeronautical and astronautical systems. It is published monthly by American Institute of Aeronautics and Astronautics, Inc. The journal focuses on the study of dynamics, guidance, control, navigation, optimization, electronics, and information processing within the field of aeronautics and astronautics. It welcomes contributions that explore theoretical advances, computational techniques, experimental investigations, and practical applications. Journal of Guidance, Control, and Dynamics can be found online at: https://arc.aiaa.org/loi/jgcd Publication History Journal of Guidance and Control 0162-3192 Formerly (until 1982) USA United States

A PDE-based feedback control method for thin cylindrical shells with surface-mounted piezoceramic actuators is presented. Donnell-Mushtari equations modified to incorporate both passive and active piezoceramic patch contributions are used to model the system dynamics. The well-posedness of this model and the associated LQR problem with an unbounded input operator are established through analytic semigroup theory. The model is discretized using a Galerkin expansion with basis functions constructed from Fourier polynomials tensored with cubic splines, and convergence criteria for the associated approximate LQR problem are established. The effectiveness of the method for attenuating the coupled longitudinal, circumferential and transverse shell displacements is illustrated through a set of numerical examples.

This paper discusses the application of robust control theory to evaluate robustness of the Ares-I control systems. Three techniques for estimating upper and lower bounds of uncertain parameters which yield stable closed-loop response are used here: (1) Monte Carlo analysis, (2) mu analysis, and (3) characteristic frequency response analysis. All three methods are used to evaluate stability envelopes of the Ares-I control systems with uncertain aerodynamics and flex dynamics. The results show that characteristic frequency response analysis is the most effective of these methods for assessing robustness.

We consider the problem of controlling an aerial robot connected to the ground by a passive cable or a passive rigid link. We provide a thorough characterization of this nonlinear dynamical robotic system in terms of fundamental properties such as differential flatness, controllability, and observability. We prove that the robotic system is differentially flat with respect to two output pairs: elevation of the link and attitude of the vehicle; elevation of the link and longitudinal link force (e.g., cable tension, or bar compression). We show the design of an almost globally convergent nonlinear observer of the full state that resorts only to an onboard accelerometer and a gyroscope. We also design two almost globally convergent nonlinear controllers to track any sufficiently smooth time-varying trajectory of the two output pairs. Finally we numerically test the robustness of the proposed method in several far-from-nominal conditions: nonlinear cross-coupling effects, parameter deviations, measurements noise and non ideal actuators.

We consider the problem of controlling an aerial robot connected to the ground by a passive cable or a passive rigid link. We provide a thorough characterization of this nonlinear dynamical robotic system in terms of fundamental properties such as differential flatness, controllability, and observability. We prove that the robotic system is differentially flat with respect to two output pairs: elevation of the link and attitude of the vehicle; elevation of the link and longitudinal link force (e.g., cable tension, or bar compression). We show the design of an almost globally convergent nonlinear observer of the full state that resorts only to an onboard accelerometer and a gyroscope. We also design two almost globally convergent nonlinear controllers to track any sufficiently smooth time-varying trajectory of the two output pairs. Finally we numerically test the robustness of the proposed method in several far-from-nominal conditions: nonlinear cross-coupling effects, parameter deviations, measurements noise and non ideal actuators.

COFS 3 is the third project within the Control of Flexible Structures (COFS) program. It deals with developing multibody dynamics and control technology for large space structures. It differs from COFS 1 and 2 in two respects. First, it addresses a more complex class of structure, and second it is basically a scale model ground test and analysis program while COFS 1 and 2 feature Shuttle flight experiments. The specific technology thrusts within COFS 3 are model sensitivities, test methods, analysis validation, systems identification, and vibration suppression. The COFS 3 project will develop the methods for using dynamically scaled models and analysis to predict the structural dynamics of large space structures. The project uses the space station as a focus because it is typical of the structures of interest and provides the first opportunity to obtain full-scale on-orbit dynamics data.

Bibliographical references: leaves 21-22

Bibliographical references: leaves 21-22

In a recent report, a robotic spacecraft mission is proposed for the purpose of collecting a small asteroid, or a small part of a large one, and transporting it to an orbit in the Earth-Moon system. Such an undertaking will require solutions to many of the engineering problems associated with deflection of an asteroid that poses a danger to Earth. In both cases, it may be necessary for a spacecraft to approach an asteroid from a nearby position, hover for some amount of time, move with the same angular velocity as the asteroid, descend, perhaps ascend, and finally arrest the angular velocity of the asteroid. Dynamics and control in each of these activities is analyzed in order to determine the velocity increments and control torque that must be provided by a reaction control system, and the mass of the propellant that will be consumed. Two attitude control algorithms are developed, one to deal with synchronizing the spacecraft s angular velocity with that of the asteroid, and the other to arrest the asteroid s angular velocity. A novel approach is proposed for saving fuel in the latter case.

Flexible space vehicle attitude control simulation procedures analysed for engineering specificity and computer applicability

We study experimentally a system comprised of linear chains of spin-1/2 nuclei that provides a test-bed for multi-body dynamics and quantum information processing. This system is a paradigm for a new class of quantum information devices that can perform particular tasks even without universal control of the whole quantum system. We investigate the extent of control achievable on the system with current experimental apparatus and methods to gain information on the system state, when full tomography is not possible and in any case highly inefficient.

The attitude stabilization of a charged rigid spacecraft in Low Earth Orbit (LEO) using torques due to Lorentz force in pitch and roll directions is considered. A spacecraft that generates an electrostatic charge on its surface in the Earth magnetic field will be subject to perturbations from Lorentz force. The Lorentz force acting on an electrostatically charged spacecraft may provide a useful thrust for controlling a spacecraft's orientation. We assume that the spacecraft is moving in the Earth's magnetic field in an elliptical orbit under the effects of the gravitational, geomagnetic and Lorentz torques. The magnetic field of the Earth is modeled as a non-tilted dipole. A model incorporating all Lorentz torques as a function of orbital elements has been developed on the basis of electric and magnetic fields. The stability of the spacecraft orientation is investigated both analytically and numerically. The existence and stability of equilibrium positions is investigated for different values of the charge to mass ratio ($\alpha^*$). Stable orbits are identified for various values of $\alpha^*$. The main parameters for stabilization of the spacecraft are $\alpha^*$ and the difference between the components of the moment of inertia of spacecraft.

The attitude stabilization of a charged rigid spacecraft in Low Earth Orbit (LEO) using torques due to Lorentz force in pitch and roll directions is considered. A spacecraft that generates an electrostatic charge on its surface in the Earth magnetic field will be subject to perturbations from Lorentz force. The Lorentz force acting on an electrostatically charged spacecraft may provide a useful thrust for controlling a spacecraft's orientation. We assume that the spacecraft is moving in the Earth's magnetic field in an elliptical orbit under the effects of the gravitational, geomagnetic and Lorentz torques. The magnetic field of the Earth is modeled as a non-tilted dipole. A model incorporating all Lorentz torques as a function of orbital elements has been developed on the basis of electric and magnetic fields. The stability of the spacecraft orientation is investigated both analytically and numerically. The existence and stability of equilibrium positions is investigated for different values of the charge to mass ratio ($\alpha^*$). Stable orbits are identified for various values of $\alpha^*$. The main parameters for stabilization of the spacecraft are $\alpha^*$ and the difference between the components of the moment of inertia of spacecraft.

The attitude stabilization of a charged rigid spacecraft in Low Earth Orbit (LEO) using torques due to Lorentz force in pitch and roll directions is considered. A spacecraft that generates an electrostatic charge on its surface in the Earth magnetic field will be subject to perturbations from Lorentz force. The Lorentz force acting on an electrostatically charged spacecraft may provide a useful thrust for controlling a spacecraft's orientation. We assume that the spacecraft is moving in the Earth's magnetic field in an elliptical orbit under the effects of the gravitational, geomagnetic and Lorentz torques. The magnetic field of the Earth is modeled as a non-tilted dipole. A model incorporating all Lorentz torques as a function of orbital elements has been developed on the basis of electric and magnetic fields. The stability of the spacecraft orientation is investigated both analytically and numerically. The existence and stability of equilibrium positions is investigated for different values of the charge to mass ratio ($\alpha^*$). Stable orbits are identified for various values of $\alpha^*$. The main parameters for stabilization of the spacecraft are $\alpha^*$ and the difference between the components of the moment of inertia of spacecraft.

This thesis presents the design and construction of a test-bed suitable for test and evaluation (T&E) of the Attitude Determination and Control System (ADCS) for a nanosatellite. This work briefly reviews the Navy's use of satellites and considers the role of nanosatellites within that context. A survey of threeaxis simulators precedes the development of an adaptive mass-balancing algorithm capable of effectively eliminating gravitational torques on a three-axis simulator without momentum exchange devices. This is followed by the design and construction of a test-bed for validation of the mass-balancing algorithm. Although primarily designed for integration within the NPS TINYSCOPE project, this test-bed's application reaches beyond TINYSCOPE to any payload onboard a nanosat requiring attitude control. The test-bed, based on the Cubesat standard, is modular and allows any ADCS, containable within a 1U (10 cm cube) space, to go through T&E prior to launch including, but not limited to, stability, pointing accuracy, and nadir tracking.

This report summarizes the main results obtained in the ARO funded research project performed at the University of Illinois at Chicago. The objectives of this research project were to provide a comprehensive study and to develop new computational methodologies in the area of mechanics, and control of constrained deformable bodies as applied to large scale flexible mechanical systems. In this research project, a new finite element procedure, the absolute nodal coordinate formulation, was developed. This new procedure can be used for the large deformation and rotation analysis of flexible multibody systems. It leads to exact modeling of the rigid body dynamics, and to a constant mass matrix for the finite elements in two- and three-dimensional applications. As a consequence, the vector of Coriolis and centrifugal forces is identically equal to zero. The new formulation captures the effect of the geometric centrifugal stiffness and accounts for the effect of the elastic nonlinearities. Several large deformation multibody problems were examined, and the results obtained using the new procedure were compared with the results obtained using existing finite element formulations. The results obtained in this research project are documented in several publications listed in this report.

This study investigates how control discrepancy relates to anxiety symptoms in a multi‐wave longitudinal design. We will assess the stability of control discrepancy scores across waves, within‐wave concurrent associations between control discrepancy and anxiety symptoms, and within‐person change in control discrepancy and anxiety symptoms.

The goals of these research projects were to examine the nonlinear dynamics and control of flexible structures, some of which might be used for space applications. This project was a collaborative one involving structural, electrical and mechanical engineers. A major part of the research was on trusses/frames structures. Five different truss structures from three to ten meters in size were constructed, two with active controls. However, nonlinear dynamics of continuous beam type structures were also investigated. One of the principal themes was to explore what types of nonlinearities would result in chaotic and unpredictable vibrations. Loose joints in truss structures, friction, buckling and geometric nonlinearities were all found to lead to chaotic motions under certain periodic forcing conditions. Actuators and sensors for space truss active vibration suppression was investigated. New methods were developed for structural control using techniques for simulated annealing for actuator placement, nonlinear random vibrations of pin-jointed trusses, vibration analysis and new models to analyze chaotic dynamics in nonlinear structures with large deformations and friction forces. Finally, a major numerical effort resulted in new codes to predict large motions of structures under active control using parallel processing algorithms.

An aerodynamic model, for a minimally actuated flapping wing micro air vehicle (FWMAV), is derived from blade element theory. The vehicle considered in this work is similar to the Harvard RoboFly, except that it is equipped with independently actuated wings. A blade element-based approach is used to compute both instantaneous and cycle-averaged forces and moments for a specific type of wingbeat motion that enables nearly decoupled, multi-degree-of-freedom control of the aircraft. The wing positions are controlled using oscillators whose frequencies change once per wingbeat cycle. A technique is introduced, called Split-Cycle Constant-Period Frequency Modulation with Wing Bias, that provides a high level of control input decoupling for vehicles without active angle of attack control. This technique allows the frequencies of the upstroke and downstroke of each wing to differ such that non-zero cycleaveraged drag can be generated. Additionally, a wing bias term has been added to the wingbeat waveform and is utilized to provide pitching moment control. With this technique, it is possible to achieve five degree-of-freedom control using only two physical actuators. The present paper is concerned with the derivation of the instantaneous and cycle-averaged forces and moments for the Split- Cycle Constant-Period Frequency Modulation with Wing Bias technique. Implementation of the wing bias is discussed and modifications to the wingbeat forcing function, which are necessary to maintain a continuous wing position, are made.

The subject matter of this dissertation relates to the dynamics of non-smooth vehicle systems, and in particular, supercavitating vehicles. These high-speed underwater vehicles are designed to have sustained vaporous or ventilated gas cavities that form over the entire vehicle. In terms of the modeling, the system non-smoothness is caused by the interaction forces generated when the vehicle contacts the cavity. These planing interactions can cause stable and unstable dynamics, some of which could be limit-cycle dynamics. Here, planing forces are considered on the basis of non-cylindrical cavity shapes that include shifts induced by the cavitator angle of attack. Incorporating these realistic physical effects into a vehicle system model generates a unique hydrodynamic non-smoothness that is characterized by non-constant switching boundaries and non-constant switched dynamics. Nonlinear stability analyses are carried out, Hopf bifurcations of equilibrium solutions are identified and stabilizing control is investigated. Also considered is partially cavitating system dynamics, where active fin forces are used to support the vehicle. Non-steady planing is also considered, which accounts for vehicle motions into the cavity, and this planing provides a damping-like component in the planing force formulation. Modeled with non-steady planing is a physical time delay relating to the fact that the cavity, where planing occurs, is based on the previous cavitator position and orientation data. This delay is found to be stabilizing for certain values of speed. Maneuvering is considered by using inner-loop and outer-loop control schemes. A feedback inner-loop scheme helps reject fast planing instabilities, while a numeric optimal control approach is used to generate outer-loop commands to guide the vehicle through desired maneuvers.

In this project, we used computational models to analyze how the intrinsic dynamical properties of neural and mechanical systems interact to produce stable, but adaptable locomotion. Animal locomotion is a rhythmic behavior that requires the effective coupling of multiple feedback loops, including mechanical coupling between the animal's body and the environment, coupling between muscular force production and body movement, and sensory feedback. Floquet theory, a branch of nonlinear dynamics, includes ways to analyze how such rhythmic systems respond to perturbations. We developed several robust ways of estimating the Floquet modes of a rhythmic system, which are canonical patterns of activity after a perturbation. We found that when a block of muscle is forced to change length sinusoidally and is cyclically activated, it is strongly self-stabilizing, even with no sensory feedback. When two muscles act antagonistically, as they do around most vertebrate joints, then the system is less stable naturally. However, with sensory feedback, the joint can be stabilized very easily. This research may be extended to analyze Floquet modes based on empirical data, to examine the stability properties of real muscle, and to study the stability of fish swimming and control potential of fish fins.

This technical report is the culmination of the SCI-053 Task Group Vehicle Dynamics System Identification Control and Handling Qualities. Over three years this group held a series of meetings between experts on tanks trucks aircraft, helicopters, ships, submarines and satellites. They addressed the various technical areas identified in the name of the task group, exploring the similarities and differences between their respective vehicles and striving to identify areas where collaboration between experts would be the most valuable.

The completed research includes significant accomplishments on such problems as the stabilization and control of serially connected beams, point actuators and sensors for second order systems, the boundary element numerical method for two dimensional linear quadratic elliptic problems, quasi-variational inequalities, analysis and design of dissipative joints in structures, a boundary element method based on Cauchy integrals for some linear quadratic elliptic problems, and the stabilization of nonlinear strings.

The purpose of this effort was to provide a method of developing a linear model of an elastic aircraft. The model provides the capability to analyze the coupling between the rigid and elastic motion of the aircraft. The method developed in this effort obtains stability derivatives directly from unsteady aerodynamic forces. This results in a state space model whose states are just the normal aircraft states and rates, the structural coordinates and rates, and the control surface positions and rates. Using a representation of the YF-17 wind tunnel flutter model, it was demonstrated that the methodology developed predicted the required dynamics to make this a viable method of modelling rigid body and flutter behavior of the model. Flutter control laws were designed for motion about an equilibrium condition represented by a velocity 20% above the flutter velocity. Both classical and modern techniques yielded acceptable control laws. The control laws were also analyzed at off design conditions to check robustness. Keywords: Aeroelasticity; Airplane models; Aerodynamic Stability; Flight; Controls Systems; Theses.

The problems associated with uneven forced response vibration amplitudes in bladed disk assemblies is considered in the report. It is established that uneven vibration amplitudes arise principally by the destruction of cyclic-symmetry by some small perturbations usually within the component manufacturing tolerances. Such perturbations first split some of the eigenvalue degeneracies inherent in all cyclic systems. This split in turn gives rise to the modal bifurcation phenomenon. Particular forms of the modal phenomenon give rise to the uneven vibration amplitudes and under some restricted conditions to the mode localization phenomenon. In this report, group theory, singularity theory and singular perturbation theory are combined to give a complete analysis of uneven amplitudes and mode localization; as a prelude to blade vibration control.

An integrated nutrient budget for Lake Conway, Florida, was developed that integrated physical, chemical, and biological relationships. A hydrologic budget was constructed from measurements of stormwater runoff, subsurface seepage flows, and existing precipitation and evaporation data. It was determined that major sources of external nitrogen and phosphorus loadings were from atmospheric loadings, urban runoff, and subsurface seepage. Based upon a simulation model of the phosphorus dynamics of Lake Conway, it was concluded that sedimentation of phosphorus was occurring at higher than predicted rates, nutrient release by submerged macrophytes was salient to phosphorus dynamics, and release of phosphorus by sediments was not a significant internal source of this nutrient. (Author)

An integrated nutrient budget for Lake Conway, Florida, was developed that integrated physical, chemical, and biological relationships. A hydrologic budget was constructed from measurements of stormwater runoff, subsurface seepage flows, and existing precipitation and evaporation data. It was determined that major sources of external nitrogen and phosphorus loadings were from atmospheric loadings, urban runoff, and subsurface seepage. Based upon a simulation model of the phosphorus dynamics of Lake Conway, it was concluded that sedimentation of phosphorus was occurring at higher than predicted rates, nutrient release by submerged macrophytes was salient to phosphorus dynamics, and release of phosphorus by sediments was not a significant internal source of this nutrient. (Author)

Geometric effects make evolution time vary for different evolution curves that connect the same two quantum states. Thus, it is important to be able to control along which path a quantum state evolve to achieve maximal speed in quantum calculations. In this paper we establish fundamental relations between Hamiltonian dynamics and Riemannian structures on the phase spaces of unitarily evolving finite-level quantum systems. In particular, we show that the Riemannian distance between two density operators equals the infimum of the energy dispersions of all possible evolution curves connecting the two density operators. This means, essentially, that the evolution time is a controllable quantity. The paper also contains two applied sections. First, we give a geometric derivation of the Mandelstam-Tamm estimate for the evolution time between two distinguishable mixed states. Secondly, we show how to equip the Hamiltonians acting on systems whose states are represented by invertible density operators with control parameters, and we formulate conditions for these that, when met, makes the Hamiltonians transport density operators along geodesics.

Basic dynamics, sensor, control, and related artificial intelligence issues pertinent to smart robotic hands for the Extra Vehicular Activity (EVA) Retriever system are summarized and discussed. These smart hands are to be used as end effectors on arms attached to manned maneuvering units (MMU). The Retriever robotic systems comprised of MMU, arm and smart hands, are being developed to aid crewmen in the performance of routine EVA tasks including tool and object retrieval. The ultimate goal is to enhance the effectiveness of EVA crewmen.

Theoretical and applicable results concerning systems of nonlinear ordinary differential equations and control of partial differential equations are examined. Titles and abstracts of recent papers are presented.

This report is the final report of a six-month program with a six-month NCE comprising experimental work on problems arising with unsteady combustion of gases intended for use in propulsion systems. The experimental work comprises measurements providing the basis for inferring the local response function of a reacting mixture and is based on great extended equipment purchased before this program began, with a DURIP grant from AFOSR. The basic part of the facility is apparatus for PLIF (planar laser induced fluorescence) measurements of a combustion system exposed to a sinusoidally varying pressure field, p', with q', the local fluctuation of heat release, appropriate measurements allow inference of q'/p' proportional to the response function and q'p', the integral over volume is proportional to the Rayleigh factor. In principal knowledge of these two quantities permits deduction of all important dynamical properties of a dynamical system. The greatest part of work during this year has been directed to determining the effect of fluctuations in fuel mixture ratio, most of the experimental work has been based on the use of acetone PLIF.

The focus of this work was on the synthesis of control and optimization theory, numerical methods, and fluid mechanics. There are three primary thrusts in our study of model-based flow control: Optimization, Feedback, and Characterization of Fundamental Limitations. Work on this contract focused primarily on some delicate unsolved problems related to regularization in the first of these three areas, optimization, and how, by addressing these problems, some practical applications involving the adjoint analysis of complex turbulent flows (specifically, the mixing of cross-flow dilution jets in a jet engine combustor) could be tackled that could not formerly be considered using these approaches. Work on this problem led directly to significant advancements in the other two areas as well (that is, feedback and characterization of fundamental limitations in fluid systems).

This is a final report on the research project supported by the Air Force Office of Scientific Research under Grant F49620-87-C-0074, entitled Development of Nonlinear Transient Analysis Algorithms for Dynamics and Control of Large Space Structures, which covered the period of 01 October 1987 to 31 December 1990. The objectives of the research have been: (1) the development of improved dynamic modeling techniques that can capture essential response components encompassing an adequate frequency spectrum in large space structures including dynamic localizations, and (2) the development of efficient algorithms for solving the combined structural and control dynamics equations by taking advantage of computer hardware and software advances such as concurrent computers.

A ground-based simulation study was conducted on a large-scale motion simulator to study the effects in the vertical axis of engine response characteristics on handling qualities for a nap-of-the-earth (NOE) operating environment. This study concentrated specifically on the helicopter configuration with an rpm-governed gas-turbine engine and expands previous work by focusing on aspects peculiar to rotary-wing and NOE operations. A wide range of engine response time, vehicle damping and sensitivity, and excess power levels was studied. The data are compared with the existing handling-qualities specifications, MIL-F-83300 and AGARD 577, and in general show a need for higher minimums when performing such NOE maneuvers as a dolphin and bob-up task. (Author)

A high order rotorcraft mathematical model is developed and validated against the XV-15 and a Large Civil Tiltrotor (LCTR) concept. Separate modeling of each rotorcraft component in a multi-body like formulation allows for structural flexibility to be included, which is important when modeling large aircraft where structural modes affect the flight dynamics frequency ranges of interest. Details of the formulation of the mathematical model are given, including derivations of structural, aerodynamic, and inertial loads. Flexibility effects are evaluated by looking at the nature of the couplings between rigid-body modes and wing structural modes and vice versa. A proportional-integral feedback on the structural acceleration is used to improve damping and reduce the overall excitation of a structural mode. A model following control architecture is then implemented on full order flexible LCTR models. The impact of structural feedback investigated. A rigid aircraft model has optimistic performance characteristics, and a control system designed for a rigid aircraft could potentially destabilize a flexible one. The various control systems are flown in a fixed-base simulator. Pilot inputs and aircraft performance are recorded and analyzed.

This Trident Project focuses on the development of a controller for the coordination of a swarm of Autonomous Surface Vessels (ASVs) under mission and environmental constraints. For this research project, we first improved an existing Four Degree of Freedom (4DOF) vessel model. The model of a 360 metric ton patrol contains nonlinear hydrodynamics for the vessel's surge, sway, roll, and yaw motions. This model was modified to take into account environmental conditions including wind, waves and currents. Additionally, the control inputs of the model (propeller thrust, and desired ruder angle) were adapted for easier integration with a swarm level controller and additional nonholonomic motion constraints were applied to increase model fidelity. We then integrated this model into a simulated swarm of ASVs. It is the intention that this model will more accurately depict nonlinear vessel dynamics than did models used in previous ASV swarm studies. Using a redundant robot manipulator formulation, the swarm controller enables ASVs to travel in a formation with the intent of protecting and escorting a hypothetical asset. To provide flexibility, the controller is capable of modifying its overall formation shape and mission parameters in response to varying environmental conditions. The Atlantic Center for the Innovative Design and Control of Small Ships, a research initiative sponsored by the Office of Naval Research, plans to apply techniques and methods developed in this study towards the construction and testing of a physical swarm of ASVs.

Equipment is needed to establish a Virtual Reality (VR) facility at the University of Maryland in College Park. The facility will enable engineers to Design, Simulate, Visualize and Test (DSVT) the dynamics, acoustics and controls of complex SMART structural systems in a virtual environment. With such facility, engineers will be immersed in an audio-visually coupled tele-operated environment whereby direct interaction with and control of the DSVT process can be achieved in real time. In this manner, the behavior of synthetic structural models can be monitored by literally walking through the structure and adjusting its design parameters as needed to ensure optimal performance while satisfying design and operational requirements. For example, engineers can move electronic wands to vary the number, size, type and location of sensors and actuators in a helicopter cabin, monitor the resulting closed-loop structural vibrations visually or by haptic feedback and simultaneously listen to the radiated sound pressure field. Such manipulations of the virtual smart objects in the scene are carried out while the engineer is navigating through the helicopter cabin to ensure that the vibration and sound levels, at any critical locations, are within the acceptable limits. The facility will serve also as a platform for virtual training of students and engineers on designing and operating complex smart structural controls on site as well as through collaborative efforts with other VR sites.

The objective of this research is to develop practical design procedures that can be used in conjunction with optimal digital controllers for future orbiting large space structural systems. In practice, the observational data used to verify the orientation and shape of large flexible systems will, in general, be collected on a sampled basis (discrete-time data system). The system is assumed to be completely observable and deterministic. Systems which will be designed to control both the overall orientation as well as the shape of some of the subsystems (such as antenna mesh form) must function in the discrete-time domain. The aim of this research is to develop methods that can be used to design linear quadratic regulator (LQR) controllers for orbiting large flexible systems. The digital control of an orbiting thin square plate system is analyzed in this volume of the final report.... Digital control, Large space structures, Observable deterministic system, Linear quadratic regulator technique.

During this research period we have made significant progress in the four proposed areas: (1) design of robust controllers via H infinity optimization; (2) design of robust controllers via mixed H2/H infinity optimization; (3) M-delta structure and robust stability analysis for structured uncertainties; and (4) a study on controllability and observability of perturbed plant. It is well known now that the two-Riccati-equation solution to the H infinity control problem can be used to characterize all possible stabilizing optimal or suboptimal H infinity controllers if the optimal H infinity norm or gamma, an upper bound of a suboptimal H infinity norm, is given. In this research, we discovered some useful properties of these H infinity Riccati solutions. Among them, the most prominent one is that the spectral radius of the product of these two Riccati solutions is a continuous, nonincreasing, convex function of gamma in the domain of interest. Based on these properties, quadratically convergent algorithms are developed to compute the optimal H infinity norm. We also set up a detailed procedure for applying the H infinity theory to robust control systems design. The desire to design controllers with H infinity robustness but H(exp 2) performance has recently resulted in mixed H(exp 2) and H infinity control problem formulation. The mixed H(exp 2)/H infinity problem have drawn the attention of many investigators. However, solution is only available for special cases of this problem. We formulated a relatively realistic control problem with H(exp 2) performance index and H infinity robustness constraint into a more general mixed H(exp 2)/H infinity problem. No optimal solution yet is available for this more general mixed H(exp 2)/H infinity problem. Although the optimal solution for this mixed H(exp 2)/H infinity control has not yet been found, we proposed a design approach which can be used through proper choice of the available design parameters to influence both robustness and performance. For a large class of linear time-invariant systems with real parametric perturbations, the coefficient vector of the characteristic polynomial is a multilinear function of the real parameter vector. Based on this multilinear mapping relationship together with the recent developments for polytopic polynomials and parameter domain partition technique, we proposed an iterative algorithm for coupling the real structured singular value.