Perturbation Parameter Research Articles

Intelligent stability monitoring and improvement of grid‐connected converter under weighted average control

AbstractThis article presents an intelligent stability monitoring and improvement method for the grid‐connected converter system. The model of grid‐connected converter, based on the weighted average current feedback (WACF) and weighted average voltage feedforward (WAVF) control, is first established. Then, the time‐varying grid impedance and parameter perturbation of LCL‐filter are precisely identified by artificial neural network (ANN) module in real time. Furthermore, the control parameters are adaptively tuned by certain rules based on the predicted parameters to increase the high‐frequency stability margin of converter system. Simulation and experimental results are given to validate the proposed identification and parameter tuning method. The proposed method is able to monitor the real‐time operation state of the grid‐connected converter and improve the self‐adaptivity of the grid‐connected converter system against parameter perturbation.

Mathieu–Hill Equation Stability Analysis for Trapped Ions: Anharmonic Corrections for Nonlinear Electrodynamic Traps

The stability properties of the Hill equation are discussed, especially those of the Mathieu equation that characterize ion motion in electrodynamic traps. The solutions of the Mathieu-Hill equation for a trapped ion are characterized by employing the Floquet theory and Hill’s method solution, which yields an infinite system of linear and homogeneous equations whose coefficients are recursively determined. Stability is discussed for parameters a and q that are real. Characteristic curves are introduced naturally by the Sturm–Liouville problem for the well-known even and odd Mathieu equations cem(z,q) and sem(z,q). In the case of a Paul trap, the stable solution corresponds to a superposition of harmonic motions. The maximum amplitude of stable oscillations for ideal conditions (taken into consideration) is derived. We illustrate the stability diagram for a combined (Paul and Penning) trap and represent the frontiers of the stability domains for both axial and radial motion, where the former is described by the canonical Mathieu equation. Anharmonic corrections for nonlinear Paul traps are discussed within the frame of perturbation theory, while the frontiers of the modified stability domains are determined as a function of the chosen perturbation parameter and we demonstrate they are shifted towards negative values of the a parameter. The applications of the results include but are not restricted to 2D and 3D ion traps used for different applications such as mass spectrometry (including nanoparticles), high resolution atomic spectroscopy and quantum engineering applications, among which we mention optical atomic clocks and quantum frequency metrology.

Quantum gravity effects on the tachyon inflation from thermodynamic perspective

By considering the Friedmann equations emerging from the entropy-area law of black hole thermodynamics in the context of the generalized uncertainty principle, we study tachyon inflation in the early universe. The presence of a minimal length modifies the Friedmann equations and hence the slow-roll and perturbation parameters in the tachyon model. These modifications, though small, affect the viability of the tachyon inflation in confrontation with observational data. We compare the numerical results of the model with Planck2018 TT, TE, EE +lowE+lensing+BAO+BK14(18) data and Planck2018 TT, TE,EE +lowE+lensing+BK14(18) +BAO+LIGO & Virgo2016 data at 68% and 95% CL. We show that while the tachyon inflation with power-law, inverse power-law and inverse exponential potentials is not observationally viable in comparison with the 1σ and 2σ confidence levels of the new joint data, in the presence of the minimal length the model becomes observationally viable.

A fitted parameter convergent finite difference scheme for two-parameter singularly perturbed parabolic differential equation

The objective of this paper is to develop a numerical scheme that is uniform in its parameters for a specific type of time-dependent parabolic problem with two perturbation parameters. The existence of these two parameters in the terms with the highest-order derivatives results in the formation of boundary layer(s) in the solution of such problems. Solving these model problems using classical methods does not yield satisfactory results due to the layer behavior. Therefore, nonstandard finite difference schemes have been developed as a means to obtain numerical solutions for these problems. To develop the scheme, we employ the Crank-Nicolsondiscretization on a uniform time mesh and apply a fitted operator method with a uniform spatial mesh. We have established the stability and convergence of the proposed scheme. The proposed scheme exhibits uniform convergence of second order in the temporal direction and first order in the spatial direction. However, temporal mesh refinements is employed to enhance the order to two in both directions. Model examples are provided to validate the practicality of the proposed numerical scheme.

A computational approach for 2D elliptic singularly perturbed weakly coupled systems of convection–diffusion type with multiple scales and parameters in the diffusion and the convection terms

In this work, we consider the efficient resolution of a 2D elliptic singularly perturbed weakly coupled system of convection–diffusion type, which has small parameters at both the diffusion and the convection terms. We assume that the diffusion parameters can be distinct at each equation of the system, and also, they can have different orders of magnitude, but the convection parameter is the same at both equations of the system. Then, in general, overlapping regular or parabolic boundary layers can appear in the exact solution. The continuous problem is approximated by using the standard upwind finite difference scheme, which is constructed on a special piecewise uniform Shishkin mesh. Then, the numerical scheme is an almost first‐order uniformly convergent method with respect to all the perturbation parameters. Some numerical results, obtained with the numerical algorithm for one test problem, are presented, which show the good performance of the proposed numerical method and also corroborate in practice the theoretical results.

Bayesian linearized amplitude variation with offset and azimuth inversion and uncertainty analysis in horizontal transversely isotropic media

AbstractThe stratum can be modelled as a horizontal transversely isotropic medium when a single set of vertically parallel fractures embedded in an isotropic background medium, which facilitates efficient study for fractured reservoirs. Elastic parameters and fracture weaknesses are important parameters to describe the characteristics of fractured reservoirs, and seismic inversion plays a significant role in parameters estimation. The commonly used deterministic inversion methods do not fully utilize the prior information and fails to present the uncertainty analysis of inversion results. To address these shortcomings, we propose a Bayesian linearized amplitude variation with offset and azimuth inversion method tailored for horizontal transversely isotropic media, enabling a more robust analysis of uncertainty. Within the framework of Bayesian inversion, the proposed method successfully derives analytical expressions for the posterior mean and covariance of both elastic parameters and fracture weaknesses. The response characteristics of the anisotropic reflection coefficient are analysed, and it is found that the perturbations of elastic parameters have a greater effect on reflection coefficient compared to fracture weaknesses. Synthetic data examples confirm that the accuracy of estimated P‐ and S‐wave velocities and density surpasses that of fracture weaknesses, and the proposed method still performs well for the case of moderate noise. A field data example demonstrates that the inverted profiles agree well with the logging curve, and the estimated fracture weaknesses display significantly high values in the reservoir area. The estimated reservoir parameters not only contribute to a more accurate representation of the fractured gas‐bearing reservoir but also provide insights into the target gas reservoir through its posterior distribution. Both synthetic and field data examples demonstrate the stability and reliability of the proposed method in characterizing fractured reservoirs. We determine that the proposed method provides an available tool for nuanced evaluation of uncertainty for the inversion results, and it is helpful for the fine description of fractured hydrocarbon‐bearing reservoirs.

Under-Actuated Motion Control of Haidou-1 ARV Using Data-Driven, Model-Free Adaptive Sliding Mode Control Method.

We propose a data-driven, model-free adaptive sliding mode control (MFASMC) approach to address the Haidou-1 ARV under-actuated motion control problem with uncertainties, including external disturbances and parameter perturbations. Firstly, we analyzed the two main difficulties in the motion control of Haidou-1 ARV. Secondly, in order to address these problems, a MFASMC control method was introduced. It is combined by a model-free adaptive control (MFAC) method and a sliding mode control (SMC) method. The main advantage of the MFAC method is that it relies only on the real-time measurement data of an ARV instead of any mathematical modeling information, and the SMC method guarantees the MFAC method's fast convergence and low overshooting. The proposed MFASMC control method can maneuver Haidou-1 ARV cruising at the desired forward speed, heading, and depth, even when the dynamic parameters of the ARV vary widely and external disturbances exist. It also addresses the problem of under-actuated motion control for the Haidou-1 ARV. Finally, the simulation results, including comparisons with a PID method and the MFAC method, demonstrate the effectiveness of our proposed method.

Perturbation theoretical approach to determine optomechanical entanglement in mirror-field systems

An analytical method is developed that can be applied to a large variety of optomechanical systems to study entanglement between two subsystems of interest. The method is based on a system parameter that can be considered as perturbation parameter. It is shown that the method allows researchers to draw both qualitative and quantitative conclusions about the perturbation parameter at hand. First, the conclusion can be drawn whether or not the parameter when scaled up slightly induces entanglement between the subsystems. Second, physical insights into the role of model parameters for the emergence of entanglement can be obtained based on the perturbation theoretical analytical expressions. Third, quantitative predictions of numerical simulations that so far dominate the literature in the field of optomechanical entanglement can be validated at least in the limit of the vanishing perturbation parameter.

Assessing the role of the graphene family nanomaterials (GFNs: Graphene, GO, rGO) in modifying the toxicity potential and environmental risk of flame retardant, tetrabromobisphenol-A (TBBPA) in the marine microalgae Chlorella sp.

In recent years, a growing concern has emerged regarding the environmental implications of flame retardants (FRs) like tetrabromobisphenol-A (TBBPA) and graphene family nanomaterials (GFNs), such as graphene, graphene oxide (GO), and reduced graphene oxide (rGO), on marine biota. Despite these substances' well-established individual toxicity profiles, there is a notable gap in understanding the physicochemical interactions within the binary mixtures and consequent changes in the toxicity potential. Therefore, our research focuses on elucidating the individual and combined toxicological impacts of TBBPA and GFNs on the marine alga Chlorella sp. Employing a suite of experimental methodologies, including Raman spectroscopy, contact angle measurements, electron microscopy, and chromatography, we examined the physicochemical interplay between the GFNs and TBBPA. The toxicity potentials of individual constituents and their binary combinations were assessed through growth inhibition assays, quantifying reactive oxygen species (ROS) generation and malondialdehyde (MDA) production, photosynthetic activity analyses, and various biochemical assays. The toxicity of TBBPA and graphene-based nanomaterials (GFNs) was examined individually and in combinations. Both pristine TBBPA and GFNs showed dose-dependent toxicity. While lower TBBPA concentrations exacerbated toxicity in binary mixtures, higher TBBPA levels reduced the toxic effects compared to pristine TBBPA treatments. The principal mechanism underlying toxicity was ROS generation, resulting in membrane damage and perturbation of photosynthetic parameters. Cluster heatmap and Pearson correlation were employed to assess correlations between the biological parameters. Finally, ecological risk assessment was undertaken to evaluate environmental impacts of the individual components and the mixture in the algae.

Trajectory Tracking Control of Unmanned Underwater Vehicle Based on Projected Perpendicular Guidance Method with Disturbance Observer

Unmanned underwater vehicles (UUVs) possess impressive maneuverability and versatility, but controlling them during trajectory tracking can be challenging due to their susceptibility to external disturbances and perturbations in their model parameters. Additionally, the UUV has four degrees of freedom underwater, but only three control inputs, making it a typical underactuated system. To address these issues, this paper introduces a novel optimize sliding mode control (OPSMC) algorithm grounded in projected perpendicular guidance (PPG). The PPG algorithm transforms the three-degree-of-freedom path trajectory control into two-degree-of-freedom heading tracking control and surge velocity tracking control by designing virtual posture angles. Optimized sliding mode control, based on sliding mode control, improves control precision and reduces control input chattering by constructing optimization functions for control inputs. During trajectory tracking, UUVs are susceptible to external environmental disturbances and perturbations in system model parameters. Disturbance observers are employed to estimate these disturbances and perturbations. Finally, MATLAB/Simulink is used for numerical simulation experiments. The simulation results demonstrate that the PPG algorithm effectively enables underactuated UUVs to achieve trajectory tracking control. The designed optimized sliding mode controller and disturbance observer enhance the control precision and robustness of the system.

Theoretical study on multi-physics coupling problems of functionally-graded lead-free piezoelectric rectangular thin plates

This paper carried out a theoretical research on multi-physics coupling problems of functionally-graded lead-free piezoelectric rectangular thin plates. Firstly, the perturbation theory was used to study the bending problem of functionally-graded lead-free piezoelectric rectangular thin plates, and the nonlinear governing equations for this bending problem were established. Then, the three piezoelectric coefficients reflecting the piezoelectric property were taken as the perturbation parameters, and the nonlinear governing equations were transformed into multiple sets of linear equations by the multi-parameter perturbation method. Finally, the solutions of these linear equations were solved by the semi-inverse solving method. Based on the finite element simulations, the effectiveness of the perturbation solutions obtained here was verified. The research results showed that it was reasonable to choose three piezoelectric coefficients as perturbation parameters, which was accord with the basic idea of perturbation theory. The analysis results indicated that there was a cross transfer relationship between external loads and perturbation solutions of every order, which could be used to simplify the perturbation expansion. Moreover, the deformation of the functionally-graded lead-free piezoelectric thin plate was less than that of the functionally-graded thin plate, that is, piezoelectric properties in lead-free piezoelectric materials had a piezoelectric enhancement effect.

Dynamic analysis and optimal control of stochastic information cross-dissemination and variation model with random parametric perturbations.

Information dissemination has a significant impact on social development. This paper considers that there are many stochastic factors in the social system, which will result in the phenomena of information cross-dissemination and variation. The dual-system stochastic susceptible-infectious-mutant-recovered model of information cross-dissemination and variation is derived from this problem. Afterward, the existence of the global positive solution is demonstrated, sufficient conditions for the disappearance of information and its stationary distribution are calculated, and the optimal control strategy for the stochastic model is proposed. The numerical simulation supports the results of the theoretical analysis and is compared to the parameter variation of the deterministic model. The results demonstrate that cross-dissemination of information can result in information variation and diffusion. Meanwhile, white noise has a positive effect on information dissemination, which can be improved by adjusting the perturbation parameters.

Multiaxial yield behavior of 2D re-entrant auxetic cellular materials

A series of re-entrant honeycombs (RH) with different off-axis angles and perturbation parameters are constructed and utilized to numerically explore the multiaxial yield behavior for 2D auxetic cellular materials. The off-axis angle significantly affects the anisotropic properties and Poisson's ratio of RH. The effects of microstructural irregularity on the multiaxial yield surfaces are also evaluated for all of the topologies. Simulation results under principal stress space, mean stress-effective stress space and normal stress-shear stress space reveal that the unique microstructure of auxetic cellular materials makes its mechanical properties significantly different from conventional cellular materials with positive Poisson's ratio. Furthermore, a pressure-dependent anisotropic phenomenological yield criterion is proposed for 2D auxetic cellular materials, which can effectively capture the multiaxial yield behavior of RH with different topologies in principal stress space. The present conclusions provide fresh insights into the microstructural design of auxetic cellular materials and pave the way for their future engineering applications.

Coordinated discrete-time super-twisting sliding mode controller coupled with time-delay estimator for PWR-based nuclear steam supply system

The coordination control problem for the core thermal power of the nuclear reactor (NR) and the water level of the nuclear steam generator (SG) is a crucial challenge for real-time model-based control of a pressurized-water reactor (PWR)-based nuclear steam supply system (NSSS). In this paper, a new coordinated discrete-time super-twisting sliding mode controller (CDTSTSMC) coupled with time-delay estimators (TDEs) is proposed, tackling the coordination control problem for the core thermal power of the NR and the water level of the nuclear SG in the presence of unknown dynamics, such as unmeasured system states, model uncertainties, parameter perturbations, and disturbances. First of all, the continuous-time dynamical models of both the NR and the SG in the PWR-based NSSS are described with consideration of unknown dynamics and then are transformed into discrete-time forms using the Euler approximation method. Two TDEs capable of estimating the unknown dynamics existing in the NR and the SG, respectively, are developed, which rely merely on the measurements of the PWR-based NSSS without the upper bounds of the uncertain dynamics being known. After that, a CDTSTSMC strategy, based on the discrete-time dynamical models describing both the NR and the SG, is proposed, allowing the core thermal power to be driven to a desired value while at the same time maintaining the desired water level in the SG with the help of TDEs. It is proved from stability analysis using a Lyapunov approach that under the proposed CDTSTSMC strategy coupled with the TDEs, the stability of the controlled PWR-based NSSS can be ensured in a wide range of load, where the control errors of both the NR and the SG are driven to a neighbor of zero. Finally, the proposed CDTSTSMC strategy coupled with the TDEs is compared with the previous discrete-time optimized proportional–integral–derivative controller (DTOPIDC) and fuzzy weighting controller (FWC). The simulation results reveal that the proposed CDTSTSMC strategy coupled with the TDEs outperforms the DTOPIDC and the FWC, particularly in rejecting unknown dynamics while maintaining both the core thermal power in the NR and the water level in the SG in their desired ranges.

Disturbance Rejection Control of Grid-Forming Inverter for Line Impedance Parameter Perturbation in Weak Power Grid

When a grid-forming (GFM) inverter is connected to a low- or medium-voltage weak power grid, the line impedance with resistive and inductive characteristics will cause power coupling. Typical GFM decoupling control strategies are designed under nominal line impedance parameters. However, there are deviations between the nominal line impedance and actual parameters, resulting in poor decoupling effects. Aiming at this problem, this paper proposes a power decoupling strategy based on a reduced-order extended state observer (RESO). Firstly, the power dynamic model of the GFM is established based on the dynamic phasor method. Then, the model deviation and power coupling due to line impedance parameter perturbation are estimated as internal disturbances of the system, and the disturbances are compensated on the basis of typical power control strategy and virtual impedance decoupling. Good decoupling performance is obtained under different impedance parameters, improving the control strategy’s robustness. Finally, the effectiveness of the proposed method is verified by the results of RT Box hardware-in-the-loop experiments.

Numerical method for second order singularly perturbed delay differential equations with fractional order in time via fitted computational method

The numerical solution of time fractional parabolic differential equations with singular perturbations and delay is the subject of this article. An arbitrarily small perturbation parameter ɛ(0<ɛ<<1) is multiplied the highest order derivative term. The problem’s solution shows an exponential boundary layer on the right side of the spatial domain for small values of ɛ. The solution and its derivatives are discussed together with their properties and bounds. The Crank–Nicolson approach for time discretization and the fitted operator non-standard finite difference method for space discretization are used to solve the time fractional singularly perturbed time delay problem under consideration. The comparison principle and solution bound are used to examine and analyze the scheme’s stability. The scheme’s uniform convergence is examined and demonstrated. The proposed scheme has a uniform convergence order of Mx−1+(Δt)2−γ. Two numerical illustrations for various values of ɛ are taken into consideration to validate the theoretical analysis of the scheme. The constructed scheme provides a better order of convergence and more accurate results than methods found in the literature.

Analysis of the Dynamical Properties of Discrete Predator-Prey Systems with Fear Effects and Refuges

This paper examines the dynamic behavior of a particular category of discrete predator-prey system that feature both fear effect and refuge, using both analytical and numerical methods. The critical coefficients and properties of bifurcating periodic solutions for Flip and Hopf bifurcations are computed using the center manifold theorem and bifurcation theory. Additionally, numerical simulations are employed to illustrate the bifurcation phenomenon and chaos characteristics. The results demonstrate that period-doubling and Hopf bifurcations are two typical routes to generate chaos, as evidenced by the calculation of the maximum Lyapunov exponents near the critical bifurcation points. Finally, a feedback control method is suggested, utilizing feedback of system states and perturbation of feedback parameters, to efficiently manage the bifurcations and chaotic attractors of the discrete predator-prey model.

Two-wave interaction solutions of perturbation and CKdVE integrability for (2+1)-D CDGKS equation

By the Hirota bilinear method, some new interaction solutions with the complex perturbation for CDGKS equation are obtained. Meanwhile, with the help of the classical nonlinear KdV equation, many new exact solutions of CDGKS equation are derived through the CKdVE method, since it satisfies the CKdVE solvability. Two typical examples also show the local geometric characteristics of the parameter perturbation of these exact solutions.

On the number of limit cycles in piecewise planar quadratic differential systems

We consider piecewise quadratic perturbations of centers of piecewise quadratic systems in two zones determined by a straight line through the origin. By means of expansions of the displacement map, we are able to find isolated zeros of it, without dealing with the unsurprising difficult integrals inherent in the usual averaging approach. We apply this technique to non-smooth perturbations of the four families of isochronous centers of the Loud family, S1, S2, S3, and S4, as well as to non-smooth perturbations of non-smooth centers given by putting different Si’s in each zone. To show the coverage of our approach, we apply its first order, which is equivalent to averaging theory of the first order, in perturbations of the already mentioned centers considering all the straight lines through the origin. Then we apply the second order of our approach to perturbations of the above centers for a specific oblique straight line. Here in order to argue we introduce certain blow-ups in the perturbative parameters. As a consequence of our study, we obtain examples of piecewise quadratic systems with at least 12 limit cycles. By analyzing two previous works of the literature claiming much more limit cycles we found some mistakes in the calculations. Therefore, the best lower bound for the number of limit cycles of a piecewise quadratic system is up to now the 12 limit cycles found in the present paper.

Joint non-fragile automatic generation control and multi-event driven mechanism co-design for wind integrated power system under denial of services attacks

Denial of services (DoS) attacks exist in wind integrated power system. DoS attacks can cause network-induced delay and packages loss in information transmission. Meanwhile, considering the parameter perturbation of controller and system model uncertainty in wind integrated power system, these may cause the system dynamic performances degradation or even instability. Based on the above considerations, the joint non-fragile automatic generation robust control of wind integrated power system under DoS attacks is studied in this paper. In order to ensure the expected system performance and more effectively utilize the limited network communication resources under DoS attacks, a novel dynamic multi-event driven mechanism based joint non-fragile H∞ automatic generation control method is proposed. By constructing a suitable Lyapunov-Krasovskii functional and utilizing the Shur complement lemma to handle nonlinear matrix inequality, the sufficient conditions are derived to guarantee the asymptotic stability of wind integrated power system under DoS attacks. Furthermore, the performance of the proposed non-fragile regulator is demonstrated through a four-area wind integrated power system to show the feasibility and applicability. The analysis result indicates that the proposed scheme provides stronger robustness, higher wind energy utilization efficiency and more efficient communication mechanism.