Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Linear stability analysis”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 469 records · Page 26

High-Speed Linear Raman Spectroscopy for Instability Analysis of a Bluff Body Flame

We report a high-speed laser diagnostics technique based on point-wise linear Raman spectroscopy for measuring the frequency content of a CH4-air premixed flame stabilized behind a circular bluff body. The technique, which primarily employs a Nd:YLF pulsed laser and a fast image-intensified CCD camera, successfully measures the time evolution of scalar parameters (N2, O2, CH4, and H2O) in the vortex-induced flame instability at a data rate of 1 kHz. Oscillation of the V-shaped flame front is quantified through frequency analysis of the combustion species data and their correlations. This technique promises to be a useful diagnostics tool for combustion instability studies.

Kojima, Jun↗

Subharmonic Route to Boundary-Layer Transition - Critical Layer Nonlinearity

The linear and nonlinear dynamics of a triad of initially linear stability waves comprising a single plane wave at fundamental frequency and two symmetric oblique waves with half the frequency and streamwise wave number of the plane wave are presented. Analysis is performed for the initial nonlinear development of the waves where the order of the oblique waves' amplitude is equal to or less than that of the plane wave. Results show that the fundamental basically follows the linear theory, while the subharmonic follows an exponential-of-an-exponential growth.

Mankbadi, Reda R.↗

CFD Based Computations of Flexible Helicopter Blades for Stability Analysis

As a collaborative effort among government aerospace research laboratories an advanced version of a widely used computational fluid dynamics code, OVERFLOW, was recently released. This latest version includes additions to model flexible rotating multiple blades. In this paper, the OVERFLOW code is applied to improve the accuracy of airload computations from the linear lifting line theory that uses displacements from beam model. Data transfers required at every revolution are managed through a Unix based script that runs jobs on large super-cluster computers. Results are demonstrated for the 4-bladed UH-60A helicopter. Deviations of computed data from flight data are evaluated. Fourier analysis post-processing that is suitable for aeroelastic stability computations are performed.

Guruswamy, Guru P.↗

Estimation and Analysis of Nonlinear Stochastic Systems

The algebraic and geometric structures of certain classes of nonlinear stochastic systems were exploited in order to obtain useful stability and estimation results. The class of bilinear stochastic systems (or linear systems with multiplicative noise) was discussed. The stochastic stability of bilinear systems driven by colored noise was considered. Approximate methods for obtaining sufficient conditions for the stochastic stability of bilinear systems evolving on general Lie groups were discussed. Two classes of estimation problems involving bilinear systems were considered. It was proved that, for systems described by certain types of Volterra series expansions or by certain bilinear equations evolving on nilpotent or solvable Lie groups, the optimal conditional mean estimator consists of a finite dimensional nonlinear set of equations. The theory of harmonic analysis was used to derive suboptimal estimators for bilinear systems driven by white noise which evolve on compact Lie groups or homogeneous spaces.

Marcus, S. I.↗

Lie theoretic aspects of the Riccati equation

Various features of the application of Lie theory to matrix Riccati equations, of basic importance in control and system theories, are discussed. Particular consideration is given to centralizer foliation, the Cartan decomposition, matrix Riccati equations as Lie systems on Grassmanians, local analysis near a zero point of a vector field, linearization in homogeneous space, the tangent bundle in terms of partitioned matrices, and stability properties of fixed points of Riccati vector fields.

Hermann, R.↗

Feedback maximization

Consideration is given to synthesis methods for feedback systems with nonlinear dynamic compensation, which permits increased feedback while preserving robustness, global stability, good transient responses, and stability of the output processes. Material needed for the realization of design goals from the areas of linear systems, nonlinear oscillation, and stability of nonlinear systems is covered. The three main parts of the book are: (1) linear feedback systems, (2) nonlinear feedback system analysis, and (3) synthesis methods for globally stable Nyquist-stable feedback systems with increased feedback.

Lurie, B. J.↗

The effects of suction on the nonlinear stability of the three-dimensional boundary layer above a rotating disc

There exist two types of stationary instability of the flow over a rotating disc corresponding to the upper branch, inviscid mode and the lower branch mode, which has a triple deck structure, of the neutral stability curve. A theoretical study of the linear problem and an account of the weakly nonlinear properties of the lower branch modes have been undertaken by Hall and MacKerrell respectively. Motivated by recent reports of experimental sightings of the lower branch mode and an examination of the role of suction on the linear stability properties of the flow here, the effects are studied of suction on the nonlinear disturbance described by MacKerrell. The additional analysis required in order to incorporate suction is relatively straightforward and enables the derivation of an amplitude equation which describes the evolution of the mode. For each value of the suction, a threshold value of the disturbance amplitude is obtained; modes of size greater than this threshold grow without limit as they develop away from the point of neutral stability.

Bassom, Andrew P.↗

Comments on the "Byzantine Self-Stabilizing Pulse Synchronization" Protocol: Counter-examples

Embedded distributed systems have become an integral part of many safety-critical applications. There have been many attempts to solve the self-stabilization problem of clocks across a distributed system. An analysis of one such protocol called the Byzantine Self-Stabilizing Pulse Synchronization (BSS-Pulse-Synch) protocol from a paper entitled "Linear Time Byzantine Self-Stabilizing Clock Synchronization" by Daliot, et al., is presented in this report. This report also includes a discussion of the complexity and pitfalls of designing self-stabilizing protocols and provides counter-examples for the claims of the above protocol.

Malekpour, Mahyar R.↗

The Analysis and Construction of Perfectly Matched Layers for the Linearized Euler Equations

We present a detailed analysis of a recently proposed perfectly matched layer (PML) method for the absorption of acoustic waves. The split set of equations is shown to be only weakly well-posed, and ill-posed under small low order perturbations. This analysis provides the explanation for the stability problems associated with the split field formulation and illustrates why applying a filter has a stabilizing effect. Utilizing recent results obtained within the context of electromagnetics, we develop strongly well-posed absorbing layers for the linearized Euler equations. The schemes are shown to be perfectly absorbing independent of frequency and angle of incidence of the wave in the case of a non-convecting mean flow. In the general case of a convecting mean flow, a number of techniques is combined to obtain a absorbing layers exhibiting PML-like behavior. The efficacy of the proposed absorbing layers is illustrated though computation of benchmark problems in aero-acoustics.

Hesthaven, J. S.↗

Attitude stability of a spinning spacecraft during appendage deployment/retraction

The work presented is motivated by the need for a national satellite rescue policy, not the ad hoc policy now in place. In studying different approaches for a national policy, the issue of capture and stabilization of a tumbling spacecraft must be addressed. For a rescue mission involving a tumbling spacecraft, it may be advantageous to have a rescue vehicle which is compact and 'rigid' during the rendezvous/capture phase. After capture, passive stabilization techniques could be utilized as an efficient means of detumbling the resulting system (i.e., both the rescue vehicle and captures spacecraft). Since the rescue vehicle is initially compact and 'rigid,' significant passive stabilization through energy dissipation can only be achieved through the deployment of flexible appendages. Once stabilization is accomplished, retraction of the appendages before maneuvering the system to its final destination may also prove advantageous. It is therefore of paramount interest that we study the effect of appendage deployment/retraction on the attitude stability of a spacecraft. Particular interest should be paid to appendage retraction, since if this process is destabilizing, passive stabilization as proposed may not be useful. Over the past three decades, it has been an 'on-again-off-again affair' with the problem of spacecraft appendage deployment. In most instances, these studies have been numerical simulations of specific spacecraft configurations for which there were specific concerns. The primary focus of these studies was the behavior of the appendage during deployment; the effects of appendage retraction was considered only in one of these studies. What is missing in the literature is a thorough study of the effects of appendage deployment/retraction on the attitude stability of a spacecraft. This paper presents a rigorous analysis of the stability of a spinning spacecraft during the deployment or the retraction of an appendage. The analysis is simplified such that meaningful insights into the problem can be inferred; it is not overly simplified such that critical dynamical behavior is neglected. The system is analyzed assuming that the spacecraft hub is rigid. The appendage deployment mechanism is modeled as a point mass on a massless rod whose length undergoes prescribed changes. Simplified flexibility effects of the appendage are included. The system is examined for stability by linearizing the equations in terms of small deviations from steady, noninterfering coning motion. Routh's procedure for analyzing small deviations from steady motion in dynamical systems is utilized in the analysis. The system of equations are nondimensionalized to facilitate parametric studies. The results are presented in terms of a reduced number of nondimensional parameters so that some general conclusions may be drawn. Verification of the linear analysis is presented through numerical simulations of the complete nonlinear, nonautonomous, coupled equations.

Fitz-Coy, Norman↗

Cooperative control theory and integrated flight and propulsion control

This report documents the activities and research results obtained under a grant (NAG3-998) from the NASA Lewis Research Center. The focus of the research was the investigation of dynamic interactions between airframe and engines for advanced ASTOVL aircraft configurations, and the analysis of the implications of these interactions on the stability and performance of the airframe and engine control systems. In addition, the need for integrated flight and propulsion control for such aircraft was addressed. The major contribution of this research was the exposition of the fact that airframe and engine interactions could be present, and their effects could include loss of stability and performance of the control systems. Also, the significance of two directional, as opposed to one-directional, coupling was identified and explained. A multi variable stability and performance analysis methodology was developed, and applied to several candidate aircraft configurations. Also exposed was the fact that with interactions present along with some integrated control approaches, the engine command/limiting logic (which represents an important non-linear component of the engine control system) can impact closed-loop airframe/engine system stability. Finally, a brief investigation of control-law synthesis techniques appropriate for the class of systems was pursued, and it was determined that multi variable techniques, included model-following formulations of LQG and/or H (infinity) methods showed promise. However, for practical reasons, decentralized control architectures are preferred, which is an architecture incompatible with these synthesis methods.

Schmidt, David K.↗

A generalized method for the identification of aircraft stability and control derivatives from flight test data.

This paper discusses the application of a generalized identification method for flight test data analysis. The method is based on the maximum likelihood (ML) criterion and includes output error and equation error methods as special cases. Both the linear and nonlinear models with and without process noise are considered. The flight test data from lateral maneuvers of HL-10 and M2/F3 lifting bodies are processed to determine the lateral stability and control derivatives, instrumentation accuracies and biases. A comparison is made between the results of the output error method and the generalized ML method for M2/F3 data containing gusts. It is shown that better fits to time histories are obtained by using the generalized ML method.

Mehra, R. K.↗

Nonlinear stability of supersonic jets

The stability calculations made for a shock-free supersonic jet using the model based on parabolized stability equations are presented. In this analysis the large scale structures, which play a dominant role in the mixing as well as the noise radiated, are modeled as instability waves. This model takes into consideration non-parallel flow effects and also nonlinear interaction of the instability waves. The stability calculations have been performed for different frequencies and mode numbers over a range of jet operating temperatures. Comparisons are made, where appropriate, with the solutions to Rayleigh's equation (linear, inviscid analysis with the assumption of parallel flow). The comparison of the solutions obtained using the two approaches show very good agreement.

Tiwari, S. N.↗

Nonlinear Stability of Supersonic Jets

This paper presents stability calculations made for a shock-free supersonic jet using the model based on parabolized stability equations. In this analysis the large-scale structures, which play a dominant role in the mixing as well as the noise radiated, are modeled as instability waves. This model takes into consideration non-parallel flow effects and also nonlinear interaction of the instability waves. The stability calculations have been performed for different frequencies and mode numbers over a range of jet operating temperatures. Comparisons are made, where appropriate, with the solutions to Rayleigh's equation (linear, inviscid analysis with the assumption of parallel flow). The comparison of the solutions obtained using the two approaches show very good agreement.

Bhat, T. R. S.↗

Energy-like Liapunov functionals for linear elastic systems on a Hilbert space.

An approach is presented for generating energy-like functionals for linear elastic dynamic systems on a Hilbert space. The objective is to obtain a family of functionals which may be used for stability analysis of the equilibrium, i.e., Liapunov functionals. Although the energy functional, when one exists, is always a member of this family, the family is shown to exist even when an energy functional does not. Several discrete and distributed-parameter examples are presented, as are certain specific techniques for utilizing this approach.

Walker, J. A.↗

Stability and control of maneuvering high-performance aircraft

The stability and control of a high-performance aircraft was analyzed, and a design methodology for a departure prevention stability augmentation system (DPSAS) was developed. A general linear aircraft model was derived which includes maneuvering flight effects and trim calculation procedures for investigating highly dynamic trajectories. The stability and control analysis systematically explored the effects of flight condition and angular motion, as well as the stability of typical air combat trajectories. The effects of configuration variation also were examined.

Stengel, R. F.↗

Stochastic robustness synthesis for a benchmark problem

Stochastic robustness analysis guides the synthesis of robust linear quadratic Gaussian (LQG) regulators for a benchmark control problem. Probabilities of exceeding allowable design limits, including stability, setting time, and control usage, are estimated by Monte Carlo evaluation. Robust, low-gain compensators that fulfill objectives are designed by numerically minimizing quadratic functions of these probabilities. The method is straightforward and makes use of uncomplicated design principles.

Stengel, Robert F.↗

Longitudinal dynamic stability of a shuttle vehicle.

Analytical study of the longitudinal dynamic stability of a nonrolling, lifting vehicle gliding at hypersonic speeds. The analysis applies to shuttle vehicles designed for operating up to the rim of a planetary atmosphere. A general nondimensional time transformation is introduced to derive a unified second-order linear differential equation for the angle of attack, valid for all types of reentry of a general type of vehicle. The stability of motion is discussed for two fundamental regimes of flight that are based on widely different assumptions. For near ballistic entry along a straight line trajectory, the equation reduces to a confluent hypergeometric equation, the solution of which can be expressed in terms of Whittaker's function. Using a theorem in the theory of stability of differential equations, criteria for damped oscillations are derived. It is shown that the aerodynamic criteria for stability are the same as for the case of ballistic entry. In addition, for each vehicle configuration, and specified planetary atmosphere, there exists an altitude range where the angle of attack frequency is nearly equal to the orbital frequency causing instability in pitch. This resonance instability is due to the ellipticity of the orbit. Criteria for eccentricity instability are derived.

Vinh, N. X.↗