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At least 199 records · Page 11

Precise Frequency Measurements Using a Superconducting Cavity Stabilized Oscillator

Many physics experiments call on improved resolution to better define the experimental results, thus improving tests of theories. Modern microwave technology combined with high-Q resonators can achieve frequency readout and control with resolutions up to a part in 10(exp 18). When the physical quantity in question in the experiment can be converted to a frequency or a change in frequency, a high-stability microwave oscillator can be applied to obtain state-of-the-art precision. In this work we describe the overall physical concepts and the required experimental procedures for optimizing a high-resolution frequency measurement system that employs a high-Q superconducting microwave cavity and a low-noise frequency synthesizer. The basic approach is to resolve the resonant frequencies of a high-Q (Q > 10(exp 10)) cavity to extremely high precision (one part in 10(exp 17)- 10(exp 18)). Techniques for locking the synthesizer frequency to a resonant frequency of the superconducting cavity to form an ultra-stable oscillator are described. We have recently set up an ultra-high-vacuum high-temperature annealing system to process superconducting niobium cavities, and have been able to consistently achieve Q > 10(exp 9). We have integrated high-Q superconducting cavities with a low-noise microwave synthesizer in a phase-locked-loop to verify the frequency stability of the system. Effects that disturb the cavity resonant frequency (such as the temperature fluctuations and mechanical vibrations) and methods to mitigate those effects are also considered. Applicability of these techniques to experiments will be discussed, and our latest experimental progress in achieving high-resolution frequency measurements using the superconducting-cavity-stabilized-oscillator will be presented.

Strayer, D. M.↗

The development of a pseudo-nyquist analysis technique for hybrid sampled-data control systems

The stability characteristics of a launch vehicle, as a function of gain and phase variations at the thrust vector controller, cannot be obtained using classical sampled-data control theory if the launch vehicle attitude control system contains both sampled-data and continuous feedback control loops. A method was developed which can be used to generate a sampled-data pseudo-Nyquist plot for gain and phase variations at the controller. This method was developed and used to determine the stability characteristics of the Saturn 1B launch vehicle in the backup guidance mode.

Burnitt, M. G.↗

Spacecraft Modeling, Attitude Determination, and Control: Quaternion-Based Approach

Spacecraft attitude determination and control is an important part of a spacecraft to achieve its designed mission. As of today, many spacecrafts have been successfully launched, and most of them have performed well as they were designed. Many research papers have been published to address the attitude determination and control design problems. Several text books are available for students to learn the technology and for engineers to use as references. The most popular spacecraft models for attitude determination algorithms and control design methods are the Euler angle models and the quaternion models . The Euler angle models have been proved very efficient as the linearized models are controllable, and all standard linear control system design methods are directly applicable. The drawbacks related to the Euler angle methods are (a) the designs based on linearized models may not globally stabilize the original nonlinear spacecraft, i.e., the design may not work when the attitude of the spacecraft is far away from the point where the linearization is performed; (b) the models depend on the rotational sequences, this can be error prone if several teams work on the same project and they use different rotational sequences; (c) for any rotational sequence, there is a singular point where the model is not applicable; and (d) since most attitude determination methods use quaternion to represent the spacecraft attitude, there is a need to transform quaternion into Euler angles. On the other hand, for quaternion models, people have found controllers that can globally stabilize nonlinear spacecraft systems; the models do not depend on rotational sequences and they have no singular point; and the quaternion is provided by attitude determination system and ready to use. The main problem with the quaternion model based control system design is that the linearized quaternion model is not controllable. Therefore, most published design methods heavily rely on Lyapunov functions for the nonlinear spacecraft system. But there is no systematic way to obtain a desired Lyapunov functions. Moreover, the Lyapunov function based designs focus on the closed-loop system stability but pay little attention to the closed-loop system performance. In a series of papers, the author proposed some reduced quaternion models which lead to some controllable linearized spacecraft models. Therefore, all standard linear system theory can be directly applied to analyze and design the spacecraft control systems. We showed that, in some cases, the designed control system is not only optimal for the linearized system, but also globally stabilize the original nonlinear system . Clearly, the reduced quaternion models do not depend on rotational sequences. Due to the special structure of the linearized spacecraft model, some most important design methods, such as LQR design and robust pole assignment design are very simple, enjoy the analytical solutions for some problems, have direct connection to the performance measures, such as settling time, rising time , and percentage of overshoot . All these features are attractive for high quality control system designs. The idea mentioned above is then extended to more spacecraft control problems using specific actuators such as magnetic torque bars and control momentum gyroscopes. These types of actuators may not provide exactly desired torques. Most existing methods use different conversions to get approximate solutions, meaning that these actuators may generate a torque close to but not equal to the desired one. Using the reduced quaternion models that incorporate the actuators into the system model, the control inputs are not torques but the operational parameters. The main benefit of this idea is that the control actions are not approximate but accurate. As all actuators have their operational limit, design with input constraints are also considered in this book by using recently developed interior-point optimization techniques. This book grows up from my research on the spacecraft attitude determination and control design methods in more than a decade which is focused on using reduced quaternion models because of their merits stated above. The book provides all necessary background materials on orbital dynamics, rotations and quaternion, frequently used reference frames, transformations between reference frames, space environment and disturbance torques, ephemeris astronomical vector calculations and measurement instruments, spacecraft control actuators and their models, so that the readers will get a global picture and can apply all these information into the spacecraft system modeling, attitude determination, and spacecraft control system designs, which is the main purpose of this book. This book is different from existing books in that we focus on quaternion based spacecraft control system designs and we consider only attitude control system design related problems, from spacecraft modeling, to attitude determination and estimation, to control system design method selection, to control algorithm development, and to the simulation of the control system designs. Moreover, this book addresses different attitude control tasks in the spacecraft life cycle, including spacecraft maneuver, orbit raising, attitude control, and rendezvous. Finally, this book emphasizes the state space design methods rather than the classical frequency design methods.

Attitude determination and control↗

Frequency domain stability criteria. i.

Frequency domain stability of loop containing single nonlinearity, using Liapunov theory to give frequency domain stability criteria

FEEDBACK CONTROL SYSTEM↗

Digital robust control law synthesis using constrained optimization

Development of digital robust control laws for active control of high performance flexible aircraft and large space structures is a research area of significant practical importance. The flexible system is typically modeled by a large order state space system of equations in order to accurately represent the dynamics. The active control law must satisy multiple conflicting design requirements and maintain certain stability margins, yet should be simple enough to be implementable on an onboard digital computer. Described here is an application of a generic digital control law synthesis procedure for such a system, using optimal control theory and constrained optimization technique. A linear quadratic Gaussian type cost function is minimized by updating the free parameters of the digital control law, while trying to satisfy a set of constraints on the design loads, responses and stability margins. Analytical expressions for the gradients of the cost function and the constraints with respect to the control law design variables are used to facilitate rapid numerical convergence. These gradients can be used for sensitivity study and may be integrated into a simultaneous structure and control optimization scheme.

Mukhopadhyay, Vivekananda↗

The Theory of Pulsating Flow in Conical Nozzles

A knowledge of the dynamic characteristics of nozzles and orifices is important in many control and stability analyses of engineering devices. It is usual to assume that the instantaneous flow-rate, for a given set of inlet conditions and outlet pressure, is the same as the nontransient value for the same operating conditions. Recently, in connection with the stability analysis of an externally pressurized thrust bearing, the validity of this assumption was questioned. The analysis presented in this paper was undertaken to provide an answer. The present analysis applies to any fluid, liquid, or gas flowing into a simple conical nozzle. The amplitude and phase of the mass-flux response to a sinusoidally time-varying pressure fluctuation at the nozzle exit are determined. An approximate formula is given for these quantities in terms of the nozzle throat area, the solid angle subtended by the cone, the velocity of the fluid at the nozzle throat, the acoustic velocity at the throat, and the frequency of the pressure fluctuation.

Elrod, H. G., Jr.↗

Lyapunov-based control designs for flexible-link manipulators

A feedback controller for the stabilization of closed-loop systems is proposed which is based on the Liapunov stability criterion. A feedback control law is first generated for the linear portion of the system equation using linear control theory. A feedback control is then designed for the nonlinear portion of the system equation by making negative the time derivative of a positive definite Liapunov function.

Juang, Jer-Nan↗

(abstract) Ulysses Orbit Determination at High Declinations

The trajectory of the Ulysses spacecraft carries it over the South polar region of the Sun in mid-1994, albeit at a great distance from the Sun itself. During this time the South Solar latitude of Ulysses' orbit reaches a maximum value of 80.2 degrees, and the geocentric declination reaches a magnitude of over 75 degrees. As a result, a number of unique and interesting events occur, not the least of which being that Ulysses never sets over the Canberra tracking station of the DSN for more than two months. A less obvious aspect of the Sun-spacecraft-Earth geometry during this time is the return of solar-induced nutation to the spin-stabilized Ulysses spacecraft, and the consequent use of active nutation control. Both of these events have significant implications for theory and practice of Ulysses' orbit determination during this period, which is the subject of the proposed paper.

orbit↗

Robust Control Design for Uncertain Nonlinear Dynamic Systems

Robustness to parametric uncertainty is fundamental to successful control system design and as such it has been at the core of many design methods developed over the decades. Despite its prominence, most of the work on robust control design has focused on linear models and uncertainties that are non-probabilistic in nature. Recently, researchers have acknowledged this disparity and have been developing theory to address a broader class of uncertainties. This paper presents an experimental application of robust control design for a hybrid class of probabilistic and non-probabilistic parametric uncertainties. The experimental apparatus is based upon the classic inverted pendulum on a cart. The physical uncertainty is realized by a known additional lumped mass at an unknown location on the pendulum. This unknown location has the effect of substantially altering the nominal frequency and controllability of the nonlinear system, and in the limit has the capability to make the system neutrally stable and uncontrollable. Another uncertainty to be considered is a direct current motor parameter. The control design objective is to design a controller that satisfies stability, tracking error, control power, and transient behavior requirements for the largest range of parametric uncertainties. This paper presents an overview of the theory behind the robust control design methodology and the experimental results.

Kenny, Sean P.↗

Stability and control of hypersonic waveriders

The longitudinal and lateral stability derivatives of caret-wing waveriders flying on-design are calculated using linear piston theory. The experimental work of Kipke is used to validate the lift and pitch stiffness coefficients. Comparison is also made to the analytical work done by Hui. The calculations are extended to off-design conditions with an attached shock wave using tangent wedge theory. The stability derivatives of a Mach 6 waverider are computed and conclusions about its stability are drawn.

Tarpley, Christopher↗

Stability analysis for laminar flow control, part 2

Topics covered include: (1) optimization of the numerics of the SALLY stability analysis code; (2) relation between temporal and spatial stability theory; (3) compressible flow stability calculations; (4) spectral methods for the boundary layer equations; and (5) numerical study of nonlinear, nonparallel stability of incompressible flows.

Orszag, S. A.↗

Application of transonic codes to aeroelastic modeling of airfoils including active controls

A study is performed using aeroelastic modeling to investigate the stability behavior of airfoils in small-disturbance transonic flow. Two conventional airfoils, NACA 64.A006 and NACA 64A010, and a supercritical airfoil, MBB A-3, are considered. Three sets of unsteady aerodynamic data are computed using three different transonic codes (LTRAN2-NLR, LTRAN2-HI, and USTS) for comparison purposes. Stability results obtained using a constant matrix, state-space, aeroelastic model are presented in a root-locus format. Use of the state-space model is demonstrated through application to flutter suppression using active controls. Aeroelastic effects due to simple, constant gain, partial feedback, control laws that utilize displacement, velocity, and acceleration sensing are studied using a variety of control gains. Calculations are also performed using linear subsonic aerodynamic theory to reveal the differences between including and not including transonic effects in the aeroelastic model. Aeroelastic stability behavior of these airfoils is physically interpreted and discussed in detail.

Batina, J. T.↗

Dynamics and Control of Articulated Anisotropic Timoshenko Beams

The paper illustrates the use of continuum models in control design for stabilizing flexible structures. A 6-DOF anisotropic Timoshenko beam with discrete nodes where lumped masses or actuators are located provides a sufficiently rich model to be of interest for mathematical theory as well as practical application. We develop concepts and tools to help answer engineering questions without having to resort to ad hoc heuristic ("physical") arguments or faith. In this sense the paper is more mathematically oriented than engineering papers and vice versa at the same time. For instance we make precise time-domain solutions using the theory of semigroups of operators rather than formal "inverse Laplace transforms." We show that the modes arise as eigenvalues of the generator of the semigroup, which are then related to the eigenvalues of the stiffness operator. With the feedback control, the modes are no longer orthogonal and the question naturally arises as to whether there is still a modal expansion. Here we prove that the eigenfunctions yield a biorthogonal Riesz basis and indicate the corresponding expansion. We prove mathematically that the number of eigenvalues is nonfinite, based on the theory of zeros of entire functions. We make precise the notion of asymptotic modes and indicate how to calculate them. Although limited by space, we do consider the root locus problem and show for instance that the damping at first increases as the control gain increases but starts to decrease at a critical value, and goes to zero as the gain increases without bound. The undamped oscillatory modes remain oscillatory and the rigid-body modes go over into deadbeat modes. The Timoshenko model dynamics are translated into a canonical wave equation in a Hilbert space. The solution is shown to require the use of an "energy" norm which is no more than the total energy: potential plus kinetic. We show that, under an appropriate extension of the notion of controllability, rate feedback with a collocated sensor can stabilize the structure in the sense that all modes are damped and the energy decays to zero. An example, non-numeric, is worked out in some detail illustrating the concepts and theory developed.

Balakrishnan, A. V.↗

Flap-lag-torsion aeroelastic stability of a circulation control rotor in forward flight

The aeroelastic stability of a circulation control rotor blade undergoing three degrees of motion (flap, lag, and torsion) is investigated in forward flight. Quasi-steady strip theory is used to evaluate the aerodynamics forces; and the airfoil characteristics are from data tables. The propulsive and the auxiliary power trims are calculated from vehicle and rotor equilibrium equations through the numerical integration of element forces in azimuth as well as in radial directions. The nonlinear time dependent periodic blade response is calculated using an iterative procedure based on Floquet theory. The periodic perturbation equations are solved for stability using Floquet transition matrix theory. The effects of several parameters on blade stability are examined, including advance ratio, collective pitch, thrust level, shaft tilt, structural stiffnesses variation, and propulsive and auxiliary power trims.

Chopra, Inderjit↗

Wind Tunnel Investigation of the Effect of Jet-Motor Operation Stability

The effects of jet-motor operation on the stability and control characteristics of two fighter-type airplanes as determined by wind-tunnel tests of 1/5-scale models are presented. It is shown that the action of the jets is to cause a small loss in stick-fixed stability which is predictable from known theories.

WIND TUNNEL TESTS↗

Development of a simple, self-contained flight test data acquisition system

This paper describes a simple, self-contained flight test data acquisition system. The system makes use of the latest sensor and microprocessor technology available, to reduce overall system costs. Coupled with this is the use of modern control theory techniques allowing minimization of data requirements, as well as flight time requirements. Capability of the system includes primarily stability and performance analysis of general aviation airplanes, although system versatility has been designed into the package. Presented are details of the prototype system constructed, as well as details of the data reduction technique utilized. Preliminary results of the flight test program have also been included which demonstrate the capability of this system.

Renz, R. R. L.↗

An Integrated Approach to Damage Accommodation in Flight Control

In this paper we present an integrated approach to in-flight damage accommodation in flight control. The approach is based on Multiple Models, Switching and Tuning (MMST), and consists of three steps: In the first step the main objective is to acquire a realistic aircraft damage model. Modeling of in-flight damage is a highly complex problem since there is a large number of issues that need to be addressed. One of the most important one is that there is strong coupling between structural dynamics, aerodynamics, and flight control. These effects cannot be studied separately due to this coupling. Once a realistic damage model is available, in the second step a large number of models corresponding to different damage cases are generated. One possibility is to generate many linear models and interpolate between them to cover a large portion of the flight envelope. Once these models have been generated, we will implement a recently developed-Model Set Reduction (MSR) technique. The technique is based on parameterizing damage in terms of uncertain parameters, and uses concepts from robust control theory to arrive at a small number of "centered" models such that the controllers corresponding to these models assure desired stability and robustness properties over a subset in the parametric space. By devising a suitable model placement strategy, the entire parametric set is covered with a relatively small number of models and controllers. The third step consists of designing a Multiple Models, Switching and Tuning (MMST) strategy for estimating the current operating regime (damage case) of the aircraft, and switching to the corresponding controller to achieve effective damage accommodation and the desired performance. In the paper present a comprehensive approach to damage accommodation using Model Set Design,MMST, and Variable Structure compensation for coupling nonlinearities. The approach was evaluated on a model of F/A-18 aircraft dynamics under control effector damage, augmented by nonlinear cross-coupling terms and a structural dynamics model. The proposed approach achieved excellent performance under severe damage effects.

Boskovic, Jovan D.↗