Admittance-Based Stability Analysis: Bode Plots, Nyquist Diagrams or Eigenvalue Analysis?
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An analysis of 34 selected flight test data cases from a NASA flight program incorporating a natural laminar flow airfoil into partial wing gloves on the F-111 TACT airplane is given. This analysis determined the measured location of transition from laminar to turbulent flow. The report also contains the results of a boundary layer stability analysis of 25 of the selected cases in which the crossflow (C-F) and Tollmien-Schlichting (T-S) disturbance amplification factors are correlated with the measured transition location. The chord Reynolds numbers for these cases ranges from about 23 million to 29 million, the Mach numbers ranged from 0.80 to 0.85, and the glove leading-edge sweep angles ranged from 9 deg to 25 deg. Results indicate that the maximum extent of laminar flow varies from 56% chord to 9-deg sweep on the upper surface, and from 51% chord at 16-deg sweep to 6% chord at 25-deg sweep on the lower. The results of the boundary layer stability analysis indicate that when both C-F and T-S disturbances are amplified, an interaction takes place which reduces the maximum amplification factor of either type of disturbance that can be tolerated without causing transition.
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Cobaltocenium derivatives are promising components of the anion exchange membranes due to their excellent thermal and alkaline stability under the operating conditions of a fuel cell. Here we present an efficient modeling approach of assessing the chemical stability of substituted cobaltocenium CoCp 2 + based on the computed electronic structure enhanced by machine learning techniques. Within the aqueous environment, the positive charge of the metal cation is balanced by the hydroxide anion through formation of the CoCp 2 + OH¯ complexes, whose dissociation is studied within the implicit solvent employing density functional theory. The data set of about 118 species based on 42 substituent groups characterized by a range of electron- donating (ED) and electron-withdrawing (EW) properties is constructed and analyzed. Given 12 carefully chosen chemistry-informed descriptors of the complexes and relevant fragments, the stability of the complexes is found to strongly correlate with the energies of the highest occupied and lowest unoccupied molecular orbitals, modulated by a switching function of the Hirshfeld charge. The latter is used as a measure of the electron withdrawing-donating character of the substituents. Based on this observation from the conventional regression analysis, two fully connected, feed-forward neural network (FNN) models with different unit structures, called the chemistry-informed (CINN) and the quadratic (QNN) neural networks, are developed. Both models predict the bond dissociation energies of the cobaltocenium complexes with mean relative errors less than 5.40% and average absolute errors less than 0.94 kcal/mol. The results show the potential of QNN to efficiently capture more complex relationships. Here, the concept of incorporating the domain (chemical) knowledge/insight into the neural network structure paves the way to applications of machine learning techniques with small data sets, ultimately leading to better predictive models compared to the conventional regression analysis.
The stability of new symplectic n-body maps is examined from the point of view of nonlinear dynamics. The resonances responsible for the principal artifacts are identified. These are resonances between the stepsize and the difference of mean motions between pairs of planets. For larger stepsizes resonant perturbations are evident in the variation of the energy of the system corresponding to these stepsize resonances. It is shown that the principal instability of the method can be predicted and corresponds to the overlap of the stepsize resonances. It is noted that the analysis suggests that other artifacts will occur. For example, the overlap of a stepsize resonance with a resonance of the actual system may also give a region of chaotic behavior that is an artifact. It is pointed out that the fact that the principal artifacts corresponds to a particular set of stepsize resonances suggests that it may be possible to perturbatively remove the effect when the stepsize resonances are nonoverlapping.
Rearrangement inequalities in stability analysis applied to difference equations governing nonlinear feedback loop
Stability analysis of magnetosphere whistler amplification, discussing energetic electron interaction with background plasma
Stability analysis of rigid frames and trusses, including effect of bending moments and shear forces before buckling
Several methods of transition prediction by linear stability analysis are compared. The spectral stability analysis code SALLY is used to analyze flows over laminar flow control wings. It is shown that transition by the envelope method and a new modified wave packet method are comparable in reliability but that the envelope method is more efficient computationally.
Hydrodynamic simulation of fluids in vessels is often based on the internal energy (U), volume (V), and the number of moles of all components ( re N = N 1 , N 2 , ..., N n ) as the working variables to determine the thermodynamic state by finding the global maximum of entropy. The procedure of finding the equilibrium state may be divided into two steps: stability analysis and phase-split computations. Stability analysis is performed first, and the phase-split computation proceeds if the system is unstable. Most of the past work on UVN space has been based on phase-split computations, while the stability analysis is barely investigated. Furthermore, previous studies for the stability analysis use only Newton's method to solve the non-linear algebraic equations. We present an efficient and robust approach for stability analysis where UVN is specified. The successive substitution iteration (SSI) is used to provide good initial guesses for Newton's method. The proposed approach results in a reduced number of unknowns and does not require a large number of iterations to achieve convergence in Newton's method. Overall, our proposed formulation is compatible with different equations of state and is applicable to both pure component and multi-components. The robustness and efficiency of the algorithm for stability analysis are demonstrated in various examples.
We have developed a new global eigenvalue code, Multiscale Analysis for plasma Stabilities (MAS), for studying plasma problems with wave toroidal mode number (n) and frequency (ω) in a broad range of interest in general tokamak geometry, based on a five-field Landau-fluid description of thermal plasmas. Beyond keeping the necessary plasma fluid response, we further retain the important kinetic effects including diamagnetic drift, ion finite Larmor radius, finite parallel electric field (E||), ion and electron Landau resonances in a self-consistent and non-perturbative manner without sacrificing the attractive efficiency in computation. The physical capabilities of the code are evaluated and examined in the aspects of both theory and simulation. In theory, the comprehensive Landau-fluid model implemented in MAS can be reduced to the well-known ideal MHD model, electrostatic ion-fluid model, and drift-kinetic model in various limits, which clearly delineates the physics validity regime. In simulation, MAS has been well benchmarked with theory and other gyrokinetic and kinetic-MHD hybrid codes in a manner of adopting the unified physical and numerical framework, which covers the kinetic Alfv\'en wave (KAW), ion sound wave (ISW), low-n kink, high-n ion temperature gradient mode (ITG) and kinetic ballooning mode (KBM). Moreover, MAS is successfully applied to model the Alfv\'en eigenmode (AE) activities in DIII-D discharge #159243, which faithfully captures the frequency sweeping of reversed shear Alfv\'en eigenmode (RSAE), the tunneling damping of toroidal Alfv\'en eigenmode (TAE), as well as the polarization characteristics of kinetic beta-induced Alfv\'en eigenmode (KBAE) and beta-induced Alfv\'en-acoustic eigenmode (BAAE) being consistent with former gyrokinetic theory and simulation. With respect to the key progress contributed to the community, MAS has the advantage of combining rich physics ingredients, realistic global geometry and high computation efficiency together for plasma stability analysis in linear regime.
Eigenvalue analysis is a well-established tool for stability analysis of dynamical systems. However, there are situations where eigenvalues miss some important features of physical models. For example, in models of incompressible fluid dynamics, there are examples where linear stability analysis predicts stability but transient simulations exhibit significant growth of infinitesimal perturbations. This behavior can be predicted by pseudospectral analysis. In this study, we show that an approach similar to pseudospectral analysis can be performed inexpensively using stochastic collocation methods and the results can be used to provide quantitative information about instability.In addition, we demonstrate that the results of the perturbation analysis provide insight into the behavior of unsteady flow simulations.
The paper compares several methods of transition prediction of linear stability analysis. The spectral stability analysis code SALLY is used to analyze flows over laminar flow control wings. It is shown that transition prediction by the envelope method and a new modified wave packet method are comparable in reliability, but that the envelope method is more efficient computationally. This is based on the results which show that the wave packet method provides N factors which are at best as consistent as those of the envelope method; since the wave packet method is at least 3 times as expensive as the envelope method, the latter is recommended for engineering design calculations.
This paper presents the application of Bounded Linear Stability Analysis (BLSA) method for metrics-driven adaptive control. The bounded linear stability analysis method is used for analyzing stability of adaptive control models, without linearizing the adaptive laws. Metrics-driven adaptive control introduces a notion that adaptation should be driven by some stability metrics to achieve robustness. By the application of bounded linear stability analysis method the adaptive gain is adjusted during the adaptation in order to meet certain phase margin requirements. Analysis of metrics-driven adaptive control is evaluated for a second order system that represents a pitch attitude control of a generic transport aircraft. The analysis shows that the system with the metrics-conforming variable adaptive gain becomes more robust to unmodeled dynamics or time delay. The effect of analysis time-window for BLSA is also evaluated in order to meet the stability margin criteria.
This paper presents a small-signal stability analysis tool for large-scale power systems with high penetration of inverter-based resources (IBRs). Firstly, a network transfer function matrix (NTFM), which represents the information of the system topology, transmission lines, loads, IBRs locations, etc., is derived to model the entire power system network. Secondly, small-signal perturbation method is applied to obtain the sequence impedance/admittance models of the block-box IBRs considering the frequency cross-coupling effects. With the obtained NTFM as well as IBR models, a multi-input, multi-output (MIMO) feedback system is constructed, and the generalized Nyquist criterion (GNC)-based stability method is employed to analyze the stability of the entire power system. Furthermore, based on the developed stability analysis method, sensitivity analysis is conducted on an unstable case to identify which parameter has a high impact on the system stability. As a result, different test cases based on a modified IEEE 14- bus system as well as a reduced 240-bus WECC system are studied to verify the proposed stability analysis tool.
This paper presents the application of Bounded Linear Stability Analysis (BLSA) method for metrics driven adaptive control. The bounded linear stability analysis method is used for analyzing stability of adaptive control models, without linearizing the adaptive laws. Metrics-driven adaptive control introduces a notion that adaptation should be driven by some stability metrics to achieve robustness. By the application of bounded linear stability analysis method the adaptive gain is adjusted during the adaptation in order to meet certain phase margin requirements. Analysis of metrics-driven adaptive control is evaluated for a linear damaged twin-engine generic transport model of aircraft. The analysis shows that the system with the adjusted adaptive gain becomes more robust to unmodeled dynamics or time delay.
This paper presents a new modeling and analysis approach to address the small-signal stability issues among interconnected grid-forming (GFM) inverters. A novel phasor domain “power impedance” model is developed to capture the terminal characteristics of GFM inverters. Based on the developed models, a sum-type impedance stability criterion is proposed to analyze the power oscillations between GFM Inverters. The developed models are validated with EMT simulations and the stability analysis results using the proposed stability criterion can match both EMT simulations and eigenvalue analysis. In addition, the application of the developed model can be extended to the stability analysis of large-scale power system with high penetration of GFM inverters.