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A users guide to the Sampled Data Stability Analysis Program (SADSAP) is provided. This program is a general purpose sampled data Stability Analysis Program capable of providing frequency response on root locus data.
The longitudinal static and dynamic stability of a Space Shuttle Vehicle-Orbiter (SSV Orbiter) model is analyzed using the FLEXSTAB computer program. Nonlinear effects are accounted for by application of a correction technique in the FLEXSTAB system; the technique incorporates experimental force and pressure data into the linear aerodynamic theory. A flexible Orbiter model is treated in the static stability analysis for the flight conditions of Mach number 0.9 for rectilinear flight (1 g) and for a pull-up maneuver (2.5 g) at an altitude of 15.24 km. Static stability parameters and structural deformations of the Orbiter are calculated at trim conditions for the dynamic stability analysis, and the characteristics of damping in pitch are investigated for a Mach number range of 0.3 to 1.2. The calculated results for both the static and dynamic stabilities are compared with the available experimental data.
Classical stability analysis consists of breaking the feedback loops one at a time and determining separately how much gain or phase variations would destabilize the stable nominal feedback system. For typical launch vehicle control design, classical control techniques are generally employed. In addition to stability margins, frequency domain Monte Carlo methods are used to evaluate the robustness of the design. However, such techniques were developed for Single-Input-Single-Output (SISO) systems and do not take into consideration the off-diagonal terms in the transfer function matrix of Multi-Input-Multi-Output (MIMO) systems. Robust stability analysis techniques such as H(sub infinity) and mu are applicable to MIMO systems but have not been adopted as standard practices within the launch vehicle controls community. This paper took advantage of a simple singular-value-based MIMO stability margin evaluation method based on work done by Mukhopadhyay and Newsom and applied it to the SLS high-fidelity dynamics model. The method computes a simultaneous multi-loop gain and phase margin that could be related back to classical margins. The results presented in this paper suggest that for the SLS system, traditional SISO stability margins are similar to the MIMO margins. This additional level of verification provides confidence in the robustness of the control design.
A barotropic stability model linearized about a zonally symmetric flow is used to examine the stability characteristics of horizontal zonal-mean flow profiles representative of the Southern Hemisphere middle stratosphere during winter and early spring, with emphasis on periods when planetary wave growth appears confined to the stratosphere. Unstable modes of eastward-travelling waves 2 and 3 are found to have period sand spatial structures, similar to observations. Wave-2 and wave-3 momentum fluxes are similar in observations and model results and are consistent with the transfer of kinetic energy from the zonal-mean flow to the wave. When a barotropic model with a zonally symmetric basic flow is used, wave 3 is usually most unstable. Including a stationary wave 1 in the basic flow destabilizes both wave 2 and wave 3, but has little effect on their periods or spatial structures. The similarity between observed fields and model results in a number of cases when wave 2 appears to grow within the stratosphere suggests that in situ instabilities play a role in the evolution of the eastward-traveling wave-2 characteristic of the Southern Hemisphere winter and early spring stratosphere.
Longitudinal dynamic stability derivatives required for design of aircraft are computed by using the state-of-the-art numerical methods for wing-body configurations. The flow is modeled using the Euler/Navier-Stokes equations with turbulence models and solved using an efficient finite-difference scheme suitable for patched structured grids. Computations are made at a flow regime that is beyond the limits of the current linear methods mostly used for computing stability derivatives. Flow conditions include shockwaves and viscous dominated vortical flows. Effect of Mach number and angle-of-attack on stability derivatives are demonstrated for a typical wing-body configuration. For the same configuration the effects of wing flexibility on the magnitude and phase angles of stability derivatives are also demonstrated.
Numerical methods are presented that exploit the polynomial properties of discretizations of the Euler equations. It is noted that most finite difference or finite volume discretizations of the steady-state Euler equations produce a polynomial system of equations to be solved. These equations are solved using classical polynomial elimination theory, with some innovative modifications. This paper also presents some preliminary results of a new non-linear stability analysis technique. This technique is applicable to determining the stability of polynomial iterative schemes. Results are presented for applying the elimination technique to a one-dimensional test case. For this test case, the exact solution is computed in three iterations. The non-linear stability analysis is applied to determine the optimal time step for solving Burgers' equation using the MacCormack scheme. The estimated optimal time step is very close to the time step that arises from a linear stability analysis.
This paper presents a transonic correction method for obtaining dynamic stability derivatives for flight dynamic stability analysis. The method provides a transonic correction to the Theodorsen's theory of unsteady aerodynamics using FUN3D CFD solver of unsteady Reynolds-averaged Navier-Stokes equations (RANS) for a series of wing sections of the Mach 0.745 Transonic Truss-Braced Wing in pitch and plunge oscillations. Unsteady lift and pitching moment coefficients are obtained and used to develop the correction terms in the Theodorsen's theory to account for transonic aerodynamics. The unsteady lift and pitching moment derivatives with respect to the unsteady angle of attack are obtained as frequency response functions of the reduced frequency. These frequency response functions are used to compute the dynamic stability derivatives of lift and pitching moment due to the angle of attack and pitch rate and the dynamic stability derivatives for the rolling moment and yawing moment with respect to the roll rate and yaw rate. A transonic correction is applied to steady-state stability derivatives computed by VSPAERO solver using transonic small disturbance code TSFOIL coupled to an integral boundary method. A dynamic stability analysis is conducted for longitudinal and lateral-directional motions. Without transonic corrections and dynamic stability derivatives, the analysis indicates an unstable phugoid mode. The transonic correction applied to the steady-state stability derivatives computed by VSPAERO shows a stable phugoid mode. This is due to the increase of the drag stability derivatives as a result of the additional wave drag contribution in transonic flow. The effect of the transonic dynamic stability derivatives is observed to be a significant contributor to the increase in the damping values of all the flight dynamic modes of the Mach 0.745 Transonic-Truss Braced Wing.
The attitude stability of a class of spinning flexible spacecraft in a force-free environment is analyzed. The spacecraft is modeled as a rigid core having attached to it a flexible appendage idealized as a collection of elastically interconnected particles. Liapunov stability theorems are employed with the Hamiltonian of the system, constrained through the angular momentum integral so as to admit complete damping, used as a testing function. The Hamiltonian is written in terms of modal coordinates as interpreted by the hybrid coordinate formulation, thus allowing truncation to a level amenable to literal stability analysis. Testing functions are constructed for a spacecraft with an arbitrary (discretized) appendage, and closed form stability criteria are generated for the first mode of a restricted appendage model lying in a plane which contains the center of mass and is orthogonal to the spin axis. The criteria are (except for idealized cases on the stability boundary line in the parameter space) both necessary and sufficient for stability for any spacecraft characterized by the planar appendage model, such as a spacecraft containing solar panels and/or radial booms.
This paper presents steady and unsteady simulations of the Mach 0.8 and Mach 0.745Transonic Truss-Braced Wing (TTBW) aircrafts using the high-fidelity CFD solver FUN3D for the flight dynamic stability analysis. The steady-state stability derivatives with respect to the angle of attack, angle of sideslip, and airspeed are calculated with perturbations in the angle of attack, angle of sideslip, and Mach number, respectively. A series of unsteady CFD simulations conducted for the TTBW aircrafts in pitch oscillation at various reduced frequencies. The dynamic stability derivatives are estimated using a frequency domain estimation method. The results are then compared to the results obtained from the VSPAERO stability analysis.
Nonlinear nonconservative systems stability analysis by approximate method based on principle of energy conservation
For systems subject to unbalanced faults, analytical model building for stability assessment is a challenging task. This letter presents a straightforward modeling approach. A generalized dynamic circuit representation is achieved by use of the Laplacian transform variable s . Here, we translate the voltage and current relationship at the fault location into the relationship of three subsystems. The final circuit model is an interconnected sequence network with impedances in the Laplace domain. This circuit can be directly converted from a steady-state sequence network. This modeling procedure is illustrated by an example case of an induction motor served by a grid through a series compensated line. Electromagnetic transient simulation results demonstrate that sub-synchronous oscillations can be mitigated when a single-line to ground fault is applied at the motor terminal. Stability analysis results based on the dynamic circuit corroborate the simulation results. What's more, the derived circuit effortlessly reveals why unbalance can enhance stability.
Structural stability analysis and buckling modes of Apollo S-4B forward skirt, instrument unit, and spacecraft lunar module adapter /Apollo short stack/
Nonconservative problems motion stability analysis based on restricted admissible displacements, establishing two variational principles
A linear stability analysis of two Lorenz lasers coupled by their electric fields has been performed, and it is shown that the bad cavity condition becomes a function of coupling and that a good cavity instability may occur if the injected fields are inverted before injection. In addition, it is shown that the symmetrically coupled Lorenz system is isomorphic to the original Lorenz system with new parameters. The stability analysis also predicts a lowering of the second laser threshold with coupling for both the chaotic and self-pulsing regimes. Numerical integration of the equations is in agreement with these predictions and has revealed a coupling induced transition from self-pulsing to chaotic behavior. The classification of the behavior of the coupled system in the parameter space of the coupling constants has been investigated and shows that the results of symmetric coupling allow enough of a margin for an experimental test of the theory. This would allow experimentalists to observe the actual Lorenz instability at excitations as low as 4-5 times above threshold.
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.
We present a linear stability analysis of bow shocks created by the interaction of a spherical wind moving with respect to its surrounding medium. The bounding shocks are assumed isothermal and with Mach number M = infinity. Following Soker (1990) we study the evolution of short wavelength perturbations. We find that the motion is unstable in this limit. Moreover, the ratio of the wind velocity v(sub w) to the star velocity v(sub *) characterizes the stability properties. Bow shocks with fast winds for which v(sub *)/v(sub w)<<1 are more stable than bow sho with slow winds i.e. v(sub *)/v(sub w)>>1.
This paper presents aeroelastic simulation of the Mach 0.8 Transonic Truss-Braced Wing (TTBW) aeroelastic model using CFD solver FUN3D for the flight dynamic and control stability analysis. A jig twist optimization is performed to obtain a flight optimized jig twist for the flexible Mach 0.8 TTBW model. The developed aeroelastic model steady-state stability derivatives with respect to the angle of attack, angle of sideslip, and airspeed are calculated with perturbations in the angle of attack, angle of sideslip, and Mach number, respectively. A series of unsteady simulations is conducted for the developed aeroelastic model in pitch oscillation at various reduced frequencies. The dynamic stability derivatives are estimated using a frequency domain estimation method. The control derivatives of the elevator, rudder, and ailerons of the developed aeroelastic model are estimated for control stability analysis.
This report presents the system description, methods, and sample results of the in-flight stability analysis for the X-48B, Blended Wing Body Low-Speed Vehicle. The X-48B vehicle is a dynamically scaled, remotely piloted vehicle developed to investigate the low-speed control characteristics of a full-scale blended wing body. Initial envelope clearance was conducted by analyzing the stability margin estimation resulting from the rigid aircraft response during flight and comparing it to simulation data. Short duration multisine signals were commanded onboard to simultaneously excite the primary rigid body axes. In-flight stability analysis has proven to be a critical component of the initial envelope expansion.