Stability Analysis Method Research Articles

Stability Analysis of Buck Converter Based on Passivity-Based Stability Criterion

Recently, the stability of DC microgrids has attracted increasing attention. The traditional stability analysis method cannot not meet the requirements for the complexity and bidirectional energy flow of the system. In this paper, a passivity-based stability criterion (PBSC) is proposed to analyze the stability of the cascade system. In order to realize the passivity of the system, an improved feedback control method based on the traditional double-loop control strategy is proposed, which will improve the stability region and guarantee the passivity of the system. Moreover, a Buck-CPL simulation model is established based on MATLAB/Simulink R2008, and the correctness of the theoretical analysis is verified by experiments.

A data‐driven identification method for impedance stability analysis of inverter‐based resources

AbstractObtaining inverter controller information may be a premise for seeking its dynamic behaviour. But accurate knowledge of such information would be unrealistic for real functioning inverter‐interfaced generators (IIGs), which hinders the stability analysis of the IIG. A new data‐driven impedance identification method is proposed for stability analysis, which involves an improved sparse identification algorithm as an ancillary function within the system identification framework. It contains mainly two design stages. First, the transform basis matrix (TBM) is devised systematically as a prior knowledge library to contain the possibly existing control structures. In the second stage, a sparse identification algorithm is reformulated in order to extract the relevant structures in TBM while obtaining controller parameters. The authors demonstrate that the sparse vector between the TBM and output signal is closely related to the controller structure. The effectiveness of the proposed method is verified on grid‐connected inverters based on droop control and virtual synchronous machine control.

An efficient and precise stability analysis method for milling process

An efficient and precise stability analysis method for milling process

ANALYSIS OF LIMESTONE QUARRY SLOPE STABILITY, NIMBOKRANG DISTRICT, JAYAPURA REGENCY, PAPUA, INDONESIA

Slope stability analysis generally uses the concept of factor of safety (FoS) value using several whole rock parameters. The slope stability analysis method that will be used in this research is the slope stability analysis method in open pit mines based on rock mass classification with the Rock Mass Rating (RMR) system and the Geological Strength Index (GSI) system and analyses the potential for landslides that can occur on slopes at that location with kinematics and limit equilibrium methods so that the type of landslide can be determined based on the intensity of the geological structure on the slope of the CV. Inti Jaya open pit limestone mine, in Wahab Village, Nimbokrang District, Jayapura Regency. This research aims to provide information on the current condition of the slope whether it is by safety standards, make slope engineering improvements and redesign safe slopes if unstable slope conditions are found. Research on the stability of limestone slopes begins with the collection of field data and rock samples. Furthermore, sample testing was carried out to obtain physical and mechanical properties and weighting of rock masses, which were then analysed to obtain the characteristics and quality of rock masses that would be applied using the finite element method with Slide 6 from Rocscience to determine the Factor of Safety (FK) and the design of safe slope geometry. The RMR value for slope 1 is 62, slope 2 is 61, and slope 3 is 62. So it can be concluded that the rock is included in rock mass class 2 with good quality. Based on the analysis of potential avalanche types, the three slopes have non-arc avalanche types. From the analysis carried out using Rocscience Slide 6.0 software, the FoS value for slopes in original, dry, and saturated conditions is obtained, where on slope 1: FoS in original conditions is 0.935, FoS in dry conditions is 1.619, and FoS in saturated conditions is 0.671. Then slope 2: FoS in original condition is 0.896, FoS in dry condition is 1.457, and FoS in saturated condition is 0.806. Slope 3: FoS in original condition is 3.490, FoS in dry condition is 4.199, and FoS in saturated condition is 3.368. So it can be concluded that slopes 1 and 2 are unsafe or unstable in original and saturated conditions so that landslides can occur. In the analysis of the FoS value of the actual condition of the slopes in the field using the Hoek & Brown method, the FoS value of slope 1 is 0.387, the FoS value of slope 2 is 0.579, and the FoS value of slope 3 is 1.272, it can be seen that the actual condition of the slopes in the field is slopes 1 and 2 in an unsafe or unstable state. Improvements must be made to the slope geometry to maintain the stability of the slope to remain safe or stable. The recommended improvement is to create a new working level for slopes 1 and 2, with steep height and large rock porphyry.

Research on a novel compliant mechanism applied in the vehicle side door latch and stability analysis via Lyapunov exponents

The functional reliability of the vehicle latch is very important and is determined by the internal mechanism’s motion stability. In this paper, a novel compliant mechanism constructed with a novel compliant joint is applied to the vehicle latch, and multiple mode motions of the mechanism realize the newly added electric power release function. The repeatability of mechanism trajectories and phase diagrams of several different periodic motions is creatively regarded as the stability of the compliant mechanism. In this compliant mechanism, the endpoint of the groove-coupler is chosen as a characteristic point and the compliant joint’s spring stiffness kT is taken as the key parameter to obtain trajectories and phase diagram. It is found that all cycle overlapping phase diagrams possess intuitively good repeatability, except in two locally specific regions. Then, Wolf’s numerical calculation method of Lyapunov exponents is utilized to analyze the motion stability of the compliant mechanism. An appropriate range (1.0–1.05 N mm/°) of the joint stiffness kT is obtained, satisfying the stability criterion. Finally, characteristic point trajectory and functional experiments with kT = 1 N mm/° are conducted to verify the motion stability of the compliant mechanism. The method of mechanism motion stability analysis by means of Lyapunov exponents can be applied to other under-actuated mechanisms.

Investigation of the stability of trajectories for three-dimensional nonlinear dynamic system using an accompanying coordinate reference

The development of methods of stability analysis and the study of various types of dynamic systems stability belongs to an urgent scientific direction. Among the problems solved in the framework of this direction, an important place is occupied by the problems of finding conditions for stability and stabilization in the sense of N.E. Zhukovsky of trajectories of dynamic systems modeled by systems of three nonlinear differential equations of the first order. The aim of the work is to study the stability in the Zhukovsky sense of the trajectories of a dynamic system described by three autonomous nonlinear first-order differential equations using a differential geometric method called the accompanying coordinate reference method. The formulation of the stability problem in the Zhukovsky sense of the trajectories of dynamic systems described by systems of three nonlinear differential equations of the first order is considered. The definitions of stability of trajectories of a three-dimensional nonlinear system are specified. Using the accompanying coordinate reference, the conditions of exponential stability and instability according to Zhukovsky are obtained. The results can be used in studying the stability of processes in systems of natural science and technology, as well as in solving theoretical and applied problems of mathematical modeling and qualitative research of trajectories of nonlinear dynamic systems.

Multiple Noncooperative Targets Encirclement by Relative Distance-Based Positioning and Neural Antisynchronization Control

From prehistoric encirclement for hunting to GPS orbiting the earth for positioning, target encirclement has numerous real world applications. However, encircling multiple non-cooperative targets in GPS-denied environments remains challenging. In this work, multiple targets encirclement by using a minimum of two tasking agents, is considered where the relative distance measurements between the agents and the targets can be obtained by using onboard sensors. Based on the measurements, the center of all the targets is estimated directly by a fuzzy wavelet neural network (FWNN) and the least squares fit method. Then, a new distributed anti-synchronization controller (DASC) is designed so that the two tasking agents are able to encircle all targets while staying opposite to each other. In particular, the radius of the desired encirclement trajectory can be dynamically determined to avoid potential collisions between the two agents and all targets. Based on the Lyapunov stability analysis method, the convergence proofs of the neural network prediction error, the target-center position estimation error, and the controller error are addressed respectively. Finally, both numerical simulations and UAV flight experiments are conducted to demonstrate the validity of the encirclement algorithms. The flight tests recorded video and other simulation results can be found in <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://youtu.be/B8uTorBNrl4</uri>

Nonlinear Analysis of an Extended Heterogeneous Lattice Hydrodynamic Model Considering on/off-Ramps

To study the impact of on/off-ramps on traffic stability in heterogeneous traffic flow, a novel lattice hydrodynamic model was presented. The new model’s stability condition was determined using the linear stability analysis method. The theoretical results reveal that traffic flow stability is influenced by the proportion of vehicles with different maximum speeds and safe headway, as well as the presence of on-ramps and off-ramps to a certain degree. Through the approximate perturbation method, the mKdV equation and the kink–antikink solution of the traffic density at the jam area are obtained. In order to verify the effectiveness and feasibility of the new model, numerical simulations were conducted to demonstrate on/off ramp effect and different proportions of vehicles which possess bigger maximum velocity or safe space headway affect the traffic stability. The numerical results indicate that in heterogeneous traffic flow scenarios, increasing the ratio of vehicles which possess bigger maximum velocity or bigger safe space headway can lead to a deterioration of traffic stability. The effect of on-ramp could cause traffic instability, while the effect of off-ramp is beneficial for easing traffic congestion.

Stability Analysis for High-Speed Boundary-Layer Flow with Cavities

This study uses direct numerical simulation and stability analysis methods to investigate the impact of wall cavity defects on the instability of boundary layers at Ma=5.92 and Ma=1.38. For flow at Ma=5.92, synchronization points with equal phase velocities in both fast and slow modes play a crucial role in controlling disturbance wave growth. When the inlet disturbance wave frequency (ω=0.98) approaches the synchronization point frequency, the impact of cavity size on the growth of the disturbance wave can be divided into three regions in the (L/δ99, D/δ99) plane, namely, region A, region B, and region C. Region A refers to small cavities with L/δ99<2, which have the weakest suppression effect. Region B includes large cavities with L/δ99>2 and D/δ99<1.5 and exhibits the best suppression effect. Finally, region C covers cavities with L/δ99>3 and D/δ99>1.5 and shows a non-monotonic control effect on the growth of disturbance wave as the cavity depth varies. For flow at Ma=1.38, cavities of different sizes always enhance the growth of disturbance waves. The widest and shallowest cavities (L/δ99>5, D/δ99<2) exhibit the most significant enhancement.

Study on the steady-oscillatory transition of three-dimensional (3D) natural convection via Hopf bifurcation

The transition from steady-state flow to periodic oscillatory flow for the natural convection by Hopf bifurcation is investigated in a three-dimensional (3D) cavity. The spectral collocation method (SCM) in combination with the artificial compressibility method (ACM), which is developed by ourselves as a numerical method SCM-ACM with high accuracy, is employed to solve the governing equations directly instead of linear stability analysis method that is commonly used for the research on flow instability. The results show that the amplitude decays exponentially with time and the decay rate is linear with the Grashof number (Gr). The critical Grashof number for steady-oscillatory transition is obtained as Grcr = 3.423 × 106. The dimensionless angular frequency ωcr = 0.24 is also determined by Fourier analysis. In this work, we also examine the heat-momentum interactions within the boundary layers, visualize the periodic oscillations of temperature and velocity amplitudes, and analyze the origin of instability from multiple angles. The results show that large oscillations of velocity and temperature are observed near the isothermal walls. The oscillation is enhanced by the increase of thermal boundary layer thickness and flow velocity at both ends of isothermal walls. The maximum velocity and temperature amplitudes appear at the lower left and upper right corners of the mid-plane (Z = 0.5), where are the origin of instability, and the spanwise walls are almost independent of oscillations. The oscillatory flow of natural convection in three-dimensional cavity originates from the continuously increasing buoyancy force, and its transition occurs by Hopf bifurcation. Moreover, the temperature amplitude exhibits a wavy distribution on the mid-plane (X = 0.5) and strongly depends on the depth Z. These results provide benchmark data for future numerical studies and engineering application.

Numerical analysis of the SIS infectious disease model with spatial heterogeneity

PurposeThe susceptible-infectious-susceptible (SIS) infectious disease models without spatial heterogeneity have limited applications, and the numerical simulation without considering models’ global existence and uniqueness of classical solutions might converge to an impractical solution. This paper aims to develop a robust and reliable numerical approach to the SIS epidemic model with spatial heterogeneity, which characterizes the horizontal and vertical transmission of the disease.Design/methodology/approachThis study used stability analysis methods from nonlinear dynamics to evaluate the stability of SIS epidemic models. Additionally, the authors applied numerical solution methods from diffusion equations and heat conduction equations in fluid mechanics to infectious disease transmission models with spatial heterogeneity, which can guarantee a robustly stable and highly reliable numerical process. The findings revealed that this interdisciplinary approach not only provides a more comprehensive understanding of the propagation patterns of infectious diseases across various spatial environments but also offers new application directions in the fields of fluid mechanics and heat flow. The results of this study are highly significant for developing effective control strategies against infectious diseases while offering new ideas and methods for related fields of research.FindingsThrough theoretical analysis and numerical simulation, the distribution of infected persons in heterogeneous environments is closely related to the location parameters. The finding is suitable for clinical use.Originality/valueThe theoretical analysis of the stability theorem and the threshold dynamics guarantee robust stability and fast convergence of the numerical solution. It opens up a new window for a robust and reliable numerical study.

The seizure classification of focal epilepsy based on the network motif analysis

Due to the complexity of focal epilepsy and its risk for transiting to the generalized epilepsy, the development of reliable classification methods to accurately predict and classify focal and generalized seizures is critical for the clinical management of patients with epilepsy. In order to holistically understand the seizure propagation behavior of focal epilepsy, we propose a three-node motif reduced network by respectively simplifying the focal region, surrounding healthy region and their critical regions as the single node. Because three-node motif can richly characterize information evolutions, the motif analysis method could comprehensively investigate the seizure behavior of focal epilepsy. Firstly, we define a new seizure propagation marker value to capture the seizure onsets and intensity. Based on the three-node motif analysis, it is shown that the focal seizure and spreading can be categorized as inhibitory seizure, focal seizure, focal-critical seizure and generalized seizures, respectively. The four types of seizures correspond to specific modal types respectively, reflecting the strong correlation between seizure behavior and information flow evolution. In addition, it is found that the intensity difference of outflow and inflow information from the critical node (connection heterogeneity) and the excitability of the critical node significantly affected the distribution and transition of the four seizure types. In particular, the method of local linear stability analysis also verifies the effectiveness of four types of seizures classification. In sum, this paper computationally confirms the complex dynamic behavior of focal seizures, and the study of criticality is helpful to propose novel seizure control strategies.

Construction of Big Data Analysis Platform for College Students’ Sports Training Driven by Wireless Communication Network

College students’ physical training is an important aspect of their studies and lives. In light of the existing issues with the accuracy of the physical training evaluation index for college students and other issues. Based on the theory of wireless communication networks, model definition and stability analysis methods are used to optimize the original model. The optimization model of a wireless communication network is obtained by considering the data output control theory, trained by college students. This model can analyze the big data of college students’ physical training and construct the corresponding data platform. Through calculations, the rules for data changes under different indicators can be obtained. Finally, the accuracy of the optimized model is verified by comparing it with the original model. Related studies show that the variable parameters in the control system include model parameters, network upper limit, and corresponding control system parameters. On the whole, the model parameters exhibit a consistent trend of change, while the upper limit of the network displays a characteristic three-stage linear pattern. The control system first increases rapidly and then exhibits a gradual decline in exponential function type. The control system and the switching system can be switched using model calculations. The two different change curves exhibit obvious symmetry characteristics when influenced by the output times. It shows that the two change systems have opposite effects on the model, and the overall volatility is relatively high. The wireless communication network model can analyze and build a platform for collecting college students’ sports training data. According to the model calculation, it can be seen that the changes in different indexes exhibit clear linear characteristics. Among them, the concepts of sports, personalized training, and basic training show linearly increasing changes. However, the training structure and content exhibit a typical linear decline. Finally, the advantages of the wireless communication network model are illustrated with the experimental data. This study can provide guidance and ideas for the construction of a data platform for college students’ physical training.

Stability analysis and evaluation of a highway slope in the high and cold mountain area and suggestions for prevention and control

In order to ensure the stability of a rocky slope on a highway in a high cold mountainous area, this paper evaluates the stability of the right high slope in the section from K155+320 to K155+460 using the Chi Ping projection method and the fuzzy evaluation method based on game theory-cloudified object model. Firstly, the geological, geomorphological, hydrological and other natural profile information of the slope is obtained through field investigation, and these indicators are transformed into evaluation indicators for qualitative evaluation using the Chi Ping projection method. Then, the fuzzy evaluation method based on game theory-cloudified object model is used to transform the qualitative evaluation results into quantitative data, taking into account the mutual influence between different factors. The results show that the results obtained by the two evaluation methods are consistent. Finally, based on the stability analysis and evaluation results, it is proposed to use the method of clearing the surface dangerous rocks and applying active protective nets to deal with the slope problem in that area. At the same time, the slope stability analysis and evaluation method and the prevention and control suggestions provide reference for the subsequent slope governance.

A constraint region of attraction-based large-signal stability analysis method for direct current microgrids

Large-signal stability of direct current (DC) microgrids (MGs) are required to be seriously considered when more power converters are penetrated. For DC MGs suffering from large disturbances, the power electronics at both source and load sides are operated within the voltage and current limits to ensure the stability and safety. However, no existing methods have been developed to address the non-conservative stability analysis of a DC MGs with physical variable constraints. To this end, a comprehensive is developed in this paper to analyze the large-signal stability of typical DC MGs with voltage/current and pulse-width modulation duty cycle constraints, with a low level of conservatism. First, the system-level model of a DC MG is established as the basis of stability analysis. Then, a workflow based on the Lyapunov theory and numerical integration is developed to evaluate the large signal stability with physical variable constraints. The developed stability analysis method has less conservatism than the existing methods with only one moderate computational cost. The effectiveness of the proposed strategy is validated by case studies based on a single-bus direct current microgrid.

Security sliding mode control for T-S fuzzy systems under attack probability-dependent dynamic round-robin protocol

In this paper, the security control problem for T-S fuzzy systems is investigated through the sliding mode control (SMC) strategy. Consider deception attacks occurring randomly, a multi-modes round-robin protocol is proposed on the sensor-to-controller channel. Under this protocol, the number of transmitted nodes can be dynamically adjusted according to attack probability and system state so as to balance the relationship between system performance and communication transmission. The fuzzy sliding mode controller depending on the scheduling signal is constructed, whose membership functions (MFs) are different from the ones of the controlled system. In addition, by using the membership-function-dependent (MFD) stability analysis method, appropriate sufficient conditions are derived to ensure both the stochastic stability and the reachability. Finally, simulation results are presented to prove the proposed SMC strategy.

Stability analysis of a loess landslide considering rainfall patterns and spatial variability of soil

Accurate analysis of the stability of rainfall-induced landslides is an important and urgent task. Under complex geological conditions, traditional stability analysis methods cannot meet stability evaluation requirements. To study the impact of the rainfall pattern on the probability of instability of loess slopes, the intensity-frequency-duration curve and breakdown coefficient methods were introduced to analyse the effects of the rainfall extremum distribution and time scale, and bounded random cascade simulation were used to generate random rainfall patterns (RRPs). The obtained RRPs under several classical rainfall patterns were compared in terms of the safety factor, rainfall threshold (IaS/IaF), and annual failure probability (AFP) of loess slopes. Finally, soil preferential flow and spatial variability combined with the RRPs were introduced to analyse the change in the stability of rainfall-induced loess landslides under different theoretical frameworks. It was revealed that the use of a uniform rainfall pattern produced conservative stability evaluation results. Considering the RRPs, the calculation of IaS/IaF and AFP should include the common characteristics of various rainfall patterns. By comprehensively evaluating slope stability considering soil spatial variability and rainfall pattern variability, this study revealed that neglecting certain factors may result in incorrect slope stability estimates. Incorporating multiple assumptions in failure probability evaluation could provide more comprehensive slope safety assessment.

Dynamic Short Circuit Ratio for Stability Assessment of Grid Connected VSC-HVDC Systems Considering the Impact of Time-Varying Phase Shift

As more renewable resources are integrated into the receiving-end AC grid through VSC-HVDC, the grid connected VSC-HVDC system is facing a critical dynamic stability issue involving multiple-frequency oscillatory behaviors, which mainly stems from the low-system-strength and the time-varying phase shift. This paper proposes a general stability analysis method to measure the dynamic stability of grid connected VSC-HVDC system from the point of view of input to state stability (ISS). A nonlinear time-varying discrete-time state space model (NTDS <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> M) of the grid connected VSC-HVDC system is built considering the impact of the time-varying phase shift. Then, the NTDS <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> M is decomposed into several interconnected subsystems. The general asymptotic gain matrix (GAGM), whose elements are derived from the proposed dissipative-form sum-type inequalities (DSIs), is constructed to quantify the interactions between multiple subsystems. Finally, a general dynamic stability analysis index, called dynamic short circuit ratio (DSCR), is proposed to effectively explain the critical dynamic instability point of the grid connected VSC-HVDC system, based on the spectral radius property of the GAGM. Moreover, the real-time simulations and multiple comparative studies are implemented in this paper to verify the effectiveness of the proposed NTDS <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> M and stability analysis method by using RT-LAB platform.

Multi-Domain-Mapping-Based Impedance Calculation Method for Oscillatory Stability Analysis of VSC-Based Power System

Multi-Domain-Mapping-Based Impedance Calculation Method for Oscillatory Stability Analysis of VSC-Based Power System

On the Numerical Solutions Based On Exponential Finite Difference Method for Kuramoto-Sivashinsky Equation and Numerical Stability Analysis

In this paper, we solve the Kuramoto-Sivashinsky Equation numerically by finite-difference methods, using two different schemes which are the Fully Implicit scheme and Exponential finite difference scheme, because of the existence of the fourth derivative in the equation we suggested a treatment for the numerical solution of the two previous scheme by parting the mesh grid into five regions, the first region represents the first boundary condition, the second at the grid point x1, while the third represents the grid points x2,x3,…xn-2, the fourth represents the grid point xn-1 and the fifth is the second boundary condition. We also, study the numerical stability by Fourier (Von-Neumann) method for the two scheme which used in the solution on all mesh points to ensure the stability of the point which had been treated in the suggested style, we using two interval with two initial condition and the numerical results obtained by using these schemes are compare with Exact Solution of Equation Excellent approximate is found between the Exact Solution and numerical Solutions of these methods.