Stability analysis of Apollo attitude control during service propulsion thrusting - Project Apollo
Stability analysis of Apollo attitude control during service propulsion thrusting
Marcantel, B.↗
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Shuttle wing panel stability analysis
The use of the NASTRAN program in the shuttle wing stability analysis is described, and details of the actual structure, the finite element idealization, and the NASTRAN results are given. A comparison of the NASTRAN results with those obtained with another computer program and with hand generated results indicates good agreement. An alternate approach for solving eigenvalue problems is illustrated and shows a considerable savings in computer time. Some emphasis is placed on the relationship of the NASTRAN analysis in the design process bringing out more clearly the contribution of the results and showing the importance of the mode plots. A deficiency in the NASTRAN plate elements when used to model structures made up of intersecting plates is discussed.
Balderes, T.↗
DAC-3 Pointing Stability Analysis Results for SAGE 3 and Other Users of the International Space Station (ISS) Payload Attachment Sites (PAS)
The purpose of this paper is to provide final results of a pointing stability analysis for external payload attachment sites (PAS) on the International Space Station (ISS). As a specific example, the pointing stability requirement of the SAGE III atmospheric science instrument was examined in this paper. The instrument requires 10 arcsec stability over 2 second periods. SAGE 3 will be mounted on the ISS starboard side at the lower, outboard FIAS. In this engineering analysis, an open-loop DAC-3 finite element model of ISS was used by the Microgravity Group at Johnson Space Flight Center to generate transient responses at PAS to a limited number of disturbances. The model included dynamics up to 50 Hz. Disturbance models considered included operation of the solar array rotary joints, thermal radiator rotary joints, and control moment gyros. Responses were filtered to model the anticipated vibration attenuation effects of active control systems on the solar and thermal radiator rotary joints. A pointing stability analysis was conducted by double integrating acceleration transient over a 2 second period. Results of the analysis are tabulated for ISS X, Y, and Z Axis rotations. These results indicate that the largest excursions in rotation during pointing occurred due to rapid slewing of the thermal radiator. Even without attenuation at the rotary joints, the resulting pointing error was limited to less than 1.6 arcsec. With vibration control at the joints, to a maximum 0.5 arcsec over a 2 second period. Based on this current level of model definition, it was concluded that between 0 - 50 Hz, the pointing stability requirement for SAGE 3 will not be exceeded by the disturbances evaluated in this study.
Woods-Vedeler, Jessica A.↗
Linear Stability Analysis of Gravitational Effects on a Low-Density Gas Jet Injected into a High-Density Medium
The objective of this study was to determine the effects of buoyancy on the absolute instability of low-density gas jets injected into high-density gas mediums. Most of the existing analyses of low-density gas jets injected into a high-density ambient have been carried out neglecting effects of gravity. In order to investigate the influence of gravity on the near-injector development of the flow, a spatio-temporal stability analysis of a low-density round jet injected into a high-density ambient gas was performed. The flow was assumed to be isothermal and locally parallel; viscous and diffusive effects were ignored. The variables were represented as the sum of the mean value and a normal-mode small disturbance. An ordinary differential equation governing the amplitude of the pressure disturbance was derived. The velocity and density profiles in the shear layer, and the Froude number (signifying the effects of gravity) were the three important parameters in this equation. Together with the boundary conditions, an eigenvalue problem was formulated. Assuming that the velocity and density profiles in the shear layer to be represented by hyperbolic tangent functions, the eigenvalue problem was solved for various values of Froude number. The Briggs-Bers criterion was combined with the spatio-temporal stability analysis to determine the nature of the absolute instability of the jet whether absolutely or convectively unstable. The roles of the density ratio, Froude number, Schmidt number, and the lateral shift between the density and velocity profiles on the absolute instability of the jet were determined. Comparisons of the results with previous experimental studies show good agreement when the effects of these variables are combined together. Thus, the combination of these variables determines how absolutely unstable the jet will be.
Lawson, Anthony L.↗
Nonlocal stability analysis of the MHD Kelvin-Helmholtz instability in a compressible plasma
A general stability analysis is given of the Kevin-Helmholtz instability, for the case of sheared MHD flow of finite thickness in a compressible plasma which allows for the arbitrary orientation of the magnetic field, velocity flow, and wave vector in the plane perpendicular to the velocity gradient. The stability problem is reduced to the solution of a single second-order differential equation including a gravitational term to represent the coupling between the Kelvin-Helmholtz mode and the interchange mode. Compressibility and a magnetic field component parallel to the flow are found to be stabilizing effects, with destabilization of only the fast magnetosonic mode in the transverse case, and the presence of both Alfven and slow magnetosonic components in the parallel case. Analysis results are used in a discussion of the stability of sheared plasma flow at the magnetopause boundary and in the solar wind.
Miura, A.↗
Absolute stability analysis of attitude control systems for large boosters.
A method for performing an absolute stability analysis of attitude control systems for large launch vehicles is presented. Absolute stability of these systems is shown to be of a limited extent. The regions of absolute stability are computed by using a quadratic Liapunov function. The function is chosen to provide additional information about the exponential property of absolute stability. A system model is used to illustrate the method.
Siljak, D. D.↗
A Quasi-Steady Flexible Launch Vehicle Stability Analysis Using Steady CFD with Unsteady Aerodynamic Enhancement
Launch vehicles frequently experience a reduced stability margin through the transonic Mach number range. This reduced stability margin is caused by an undamping of the aerodynamics in one of the lower frequency flexible or rigid body modes. Analysis of the behavior of a flexible vehicle is routinely performed with quasi-steady aerodynamic lineloads derived from steady rigid computational fluid dynamics (CFD). However, a quasi-steady aeroelastic stability analysis can be unconservative at the critical Mach numbers where experiment or unsteady computational aeroelastic (CAE) analysis show a reduced or even negative aerodynamic damping. This paper will present a method of enhancing the quasi-steady aeroelastic stability analysis of a launch vehicle with unsteady aerodynamics. The enhanced formulation uses unsteady CFD to compute the response of selected lower frequency modes. The response is contained in a time history of the vehicle lineloads. A proper orthogonal decomposition of the unsteady aerodynamic lineload response is used to reduce the scale of data volume and system identification is used to derive the aerodynamic stiffness, damping and mass matrices. The results of the enhanced quasi-static aeroelastic stability analysis are compared with the damping and frequency computed from unsteady CAE analysis and from a quasi-steady analysis. The results show that incorporating unsteady aerodynamics in this way brings the enhanced quasi-steady aeroelastic stability analysis into close agreement with the unsteady CAE analysis.
Bartels, Robert E.↗
Region-Based Stability Analysis of Resilient Distribution Systems with Hybrid Grid-Forming and Grid-Following Inverters
In this paper, distribution system stability considering mixed grid-forming (GFM) and grid-following (GFL) inverters is discussed. A holistic small-signal model of the distribution feeder accommodating both GFM and GFL inverters is derived. In contrast to conventional point-by-point stability analysis, a region-based stability assessment approach is proposed and implemented to evaluate small-signal system stability with both GFM and GFL controls. Furthermore, to enhance the computational efficiency, an Artificial Intelligence (AI) assisted Kernel Ridge Regression (KRR) approach is developed to obtain the stability region boundary. Therefore, with the derived stability region, the impact of critical parameters on system stability is intuitively shown, and more importantly, the relationship between the maximum penetration level and the corresponding feasible range of the selected control parameters can be quantified. The proposed approach has been validated using MATLAB/Simulink.
grid-following↗
Incompressible boundary-layer stability analysis of LFC experimental data for sub-critical Mach numbers
An incompressible boundary-layer stability analysis of Laminar Flow Control (LFC) experimental data was completed and the results are presented. This analysis was undertaken for three reasons: to study laminar boundary-layer stability on a modern swept LFC airfoil; to calculate incompressible design limits of linear stability theory as applied to a modern airfoil at high subsonic speeds; and to verify the use of linear stability theory as a design tool. The experimental data were taken from the slotted LFC experiment recently completed in the NASA Langley 8-Foot Transonic Pressure Tunnel. Linear stability theory was applied and the results were compared with transition data to arrive at correlated n-factors. Results of the analysis showed that for the configuration and cases studied, Tollmien-Schlichting (TS) amplification was the dominating disturbance influencing transition. For these cases, incompressible linear stability theory correlated with an n-factor for TS waves of approximately 10 at transition. The n-factor method correlated rather consistently to this value despite a number of non-ideal conditions which indicates the method is useful as a design tool for advanced laminar flow airfoils.
Berry, S. A.↗
Liapunov functions from auxiliary exact difference equations for nonlinear difference equation stability analysis
Liapunov functions from auxiliary exact difference equations for nonlinear difference equation stability analysis
Kinnen, E.↗
On the validity of the modified equation approach to the stability analysis of finite-difference methods
The validity of the modified equation stability analysis introduced by Warming and Hyett was investigated. It is shown that the procedure used in the derivation of the modified equation is flawed and generally leads to invalid results. Moreover, the interpretation of the modified equation as the exact partial differential equation solved by a finite-difference method generally cannot be justified even if spatial periodicity is assumed. For a two-level scheme, due to a series of mathematical quirks, the connection between the modified equation approach and the von Neuman method established by Warming and Hyett turns out to be correct despite its questionable original derivation. However, this connection is only partially valid for a scheme involving more than two time levels. In the von Neumann analysis, the complex error multiplication factor associated with a wave number generally has (L-1) roots for an L-level scheme. It is shown that the modified equation provides information about only one of these roots.
Chang, Sin-Chung↗
Boundary-Layer Stability Analysis of the Mean Flows Obtained Using Unstructured Grids
Boundary-layer stability analyses of mean flows extracted from unstructured-grid Navier- Stokes solutions have been performed. A procedure has been developed to extract mean flow profiles from the FUN3D unstructured-grid solutions. Extensive code-to-code validations have been performed by comparing the extracted mean ows as well as the corresponding stability characteristics to the predictions based on structured-grid solutions. Comparisons are made on a range of problems from a simple at plate to a full aircraft configuration-a modified Gulfstream-III with a natural laminar flow glove. The future aim of the project is to extend the adjoint-based design capability in FUN3D to include natural laminar flow and laminar flow control by integrating it with boundary-layer stability analysis codes, such as LASTRAC.
Liao, Wei↗
Impedance Scan of Inverter-Based Resources and Diesel Generator for Stability Analysis: Preprint
Impedance-based methods are widely used for power system stability analysis with inverter-based resources (IBRs), e.g., assessing dynamic interactions between the power grid and an IBR, control interactions between multiple IBRs, and the sub-synchronous oscillation and damping phenomenon. Since it is difficult to get a numerical model 100% matching with the hardware IBR, using the hardware inverter directly to obtain its output impedance has become a prominent approach nowadays. Therefore, this article presents the impedance scan using hardware IBRs, and also a hardware diesel generator as it still stays with the grid before the grid completely goes to renewable. The devices under test (DuTs) for the impedance scan includes two 3-..phi.., 480 V, 60 Hz commercial grid-forming IBRs (one of 250 kVA and another of 125 kVA rating) in series with ..delta..-Y transformers, one 3-..phi.., 480 V, 60 Hz commercial grid-following IBR (of 125 kVA rating), and a 3-..phi.., 480 V, 60 Hz commercial diesel generator (of 187.5 kVA rating). Using voltage signals perturbed with sub-, inter-, and higher harmonic components, and measuring the current response, the positive-sequence impedances are computed via an offline- based post-analysis. Moreover, best-fit transfer functions are estimated that closely resemble the measured data points of the positive-sequence impedances. Based on the observations from various outcomes of the hardware experiments, this article also provides some fundamental insights on the equivalent positive- sequence impedance of a combination of multiple hardware components by comparing the estimated and the empirically computed impedances. A comparative insight on the damping capability of the DuTs using the positive-sequence impedances of the hardware is also discussed.
grid following inverter↗
Advanced stability analysis for laminar flow control
Five classes of problems are addressed: (1) the extension of the SALLY stability analysis code to the full eighth order compressible stability equations for three dimensional boundary layer; (2) a comparison of methods for prediction of transition using SALLY for incompressible flows; (3) a study of instability and transition in rotating disk flows in which the effects of Coriolis forces and streamline curvature are included; (4) a new linear three dimensional instability mechanism that predicts Reynolds numbers for transition to turbulence in planar shear flows in good agreement with experiment; and (5) a study of the stability of finite amplitude disturbances in axisymmetric pipe flow showing the stability of this flow to all nonlinear axisymmetric disturbances.
Orszag, S. A.↗
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.↗
Stability analysis of lumped-distributed feedback systems via open-loop Nyquist plots
Stability analysis of lumped-distributed feedback systems by open loop Nyquist plots
Reis, G. C.↗
Development of an algorithm for the stability analysis of a nonlinear precision attitude control system
Nonlinear precision attitude control system stability analysis algorithm based on quadratic Liapunov function
Chomas, A.↗
Passivity-based stability analysis of dynamic electricity pricing with power flow
This paper deals with passivity-based stability analysis of dynamic electricity pricing considering power flow. In the near future electricity market, power consumers and generators will participate in electricity market trading as market players. For such a market trading system, the dynamic pricing procedure is required to consider the intermittent participation of power consumers and generators. Then, this paper discusses the stability of the electricity market trading system including power flow using passivity analysis. This paper also shows that the optimal power demand, supply and electricity prices are asymptotically stable and these values are derived in a distributed manner through market trading.
Okawa, Yoshihiro↗