Stability Problem Research Articles

Control strategies for mitigating torsional and axial vibrations in rotary oilwell drilling systems

Abstract This paper examines a nonlinear dynamics model to explore the significant factors influencing the coupled torsional-axial vibrations of a drill string. The primary focus lies in effectively modeling, analyzing, and controlling both torsional and axial vibrations occurring in a rotary oil well drilling system. The model employed incorporates a wave equation with a damping term (PDE) connected to an ordinary differential equation (ODE) through a nonlinear function representing the interaction between the drill bit and the rock. We proceed to establish the well-posedness of the coupled PDE-ODE in an appropriate functional space. As a PDE-ODE coupled system, we specifically investigate the stability problem concerning the velocity at the bottom extremity, considering both the presence and absence of the damping term in the wave PDE. To address this, we propose a systematic method based on a Lyapunov approach for designing feedback controllers. These controllers ensure system stability and effectively suppress harmful vibrations.

Finite-time output feedback control for a class of stochastic low-order nonlinear systems with output function

This paper studies the problem of finite-time output feedback stabilisation for a class of stochastic low-order nonlinear systems with output function. Under the assumption that output function is continuous, by generalising the adding a power integrator technique, constructing a new implementable reduced-order observer and using the stochastic finite-time stability criterion, the maximal open sector Ω of output function is given. As long as output function belongs to any closed sector included in Ω, an output feedback controller can be developed to guarantee finite-time stability in probability of the closed-loop system. A simulation example is provided to verify the effectiveness of the proposed design method.

The Problem of Power Variations in Wind Turbines Operating under Variable Wind Speeds over Time and the Need for Wind Energy Storage Systems

One of the most important and efficient sources of green electricity is catching air currents through wind turbine technology. Wind power plants are located in areas where the energy potential of the wind is high but it varies. The time variation of the wind generates fluctuations in the power produced by the wind farms that is injected into the grid. This elevates, depending on the intensity, problems of network stability and the need for balancing energy, thus raising both technical and cost issues. The present paper analyzes the behavior of a wind turbine (WT) over time in varying wind speed conditions, highlighting that without automation algorithms, a WT is far from the operation at the maximum power point (MPP). However, even when it is brought to operate at MPP, there are still significant variations in the power injected into the network. These power variations can be compensated if the wind system has energy storage facilities for the captured wind. All of these assumptions are analyzed using improved mathematical models and processed in simulations, with experimental data used as input from a wind turbine with an installed power of 2.5 [MW] in operation on the Romanian Black Sea coastal area. Consequently, the paper demonstrates that during an operation in the optimal area, from an energy perspective, the wind turbine’s maximum power point requires a storage system for the captured wind energy.

Adaptive anti-unwinding attitude stabilisation with predefined time for rigid spacecraft

In this paper, the problem of attitude stabilisation without unwinding is investigated for rigid spacecraft. To guarantee predefined-time convergence and unwinding-free performance of the closed-loop system, a predefined-time sliding mode function with adjustable parameters is proposed. This sliding mode function contains two equilibrium points. When the states of the closed-loop system are on the sliding mode surface, they converge to the equilibrium point near the initial states. Based on this sliding mode function, an adaptive attitude stabilising control law with tuning parameters is designed to compensate the external disturbances and inertia uncertainty. The presented control law guarantees that the settling time of the closed-loop system and the bounds of the system states can be explicitly determined in advance by adjusting parameters of the sliding mode function and the control law. Finally, numerical simulations are carried out to demonstrate the effectiveness of the presented control law. The simulation results illustrate that the predefined-time convergence and unwinding-free property of the closed-loop system are guaranteed by adopting the presented control law.

Regeneration and Genetic Transformation in Eucalyptus Species, Current Research and Future Perspectives

Eucalyptus is an important plantation tree with a high economic value in China. The tree contributes significantly to China’s timber production. The stable and efficient Eucalyptus regeneration system and genetic transformation system are of great significance for exploring the regulatory function and possible genetic breeding capacity of important genes in the species. However, as a woody plant, Eucalyptus has problems, such as a long generation cycle, strong specificity of the regeneration system, and a low genetic conversion rate, which seriously limit the rapid development of Eucalyptus genetics and breeding programs. The present review summarizes the status of research on Eucalyptus regeneration and genetic transformation, with a focus on the effects of explants, media, plant growth regulators (PGRs), and concentrations in the Eucalyptus regeneration process. In addition, the effects of genotype, Agrobacterium, antibiotics, preculture, and co-culture on the genetic transformation efficiency of Eucalyptus are discussed. Furthermore, the study also summarizes the problems encountered in Eucalyptus regeneration and genetic transformation, with reference to previous studies, and it outlines future developments and prospects. The aim was to provide a reference for solving the problems of genetic instability and the low transformation efficiency of eucalyptus, and to establish an efficient and stable eucalyptus regeneration and transformation system to accelerate the process of its genetic improvement.

Novel lattice Boltzmann method for simulation of strongly shear thinning viscoelastic fluids

AbstractThe simulation of viscoelastic liquids using the Lattice–Boltzmann method (LBM) in full three dimensions remains a formidable numerical challenge. In particular the simulation of strongly shear‐thinning fluids, where the ratio between the high‐shear and low‐shear viscosities is large, is often prevented by stability problems. Here we present a novel approach to overcome this issue. The central idea is to artificially increase the solvent viscosity which allows the method to benefit from the very good stability properties of the LBM. To compensate for this additional viscous stress, the polymer stress is reduced by the same amount. We apply this novel method to simulate two realistic cell carrier fluids, methyl cellulose and alginate solutions, of which the latter exhibits a viscosity ratio exceeding 10,000.

On the stability of electrovacuum space-times in scalar–tensor gravity

We study the behavior of static, spherically symmetric solutions to the field equations of scalar–tensor theories (STT) of gravity belonging to the Bergmann–Wagoner–Nordtvedt class, in the presence of an electric and/or magnetic charge. This class of theories includes the Brans–Dicke, Barker and Schwinger STT as well as nonminimally coupled scalar fields with an arbitrary parameter ξ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\xi $$\\end{document}. The study is restricted to canonical (nonphantom) versions of the theories and scalar fields without a self-interaction potential. Only radial (monopole) perturbations are considered as the most likely ones to cause an instability. The static background solutions contain naked singularities, but we formulate the boundary conditions in such a way that would preserve their meaning if a singularity is smoothed, for example, due to quantum gravity effects. These boundary conditions look more physical than those used by other authors. Since the solutions of all STT under study are related by conformal transformations, the stability problem for all of them reduces to the same wave equation, but the boundary conditions for perturbations (and sometimes the boundaries themselves) are different in different STT, which affects the stability results. The stability or instability conclusions are obtained for different branches of solutions in the theories under consideration and are presented in a table form.

Disturbance observer based adaptive predefined‐time sliding mode control for robot manipulators with uncertainties and disturbances

AbstractThis article develops a predefined‐time sliding mode control approach for systems with external disturbances and uncertainties through a nonlinear disturbance observer (DO). For addressing predefined‐time stabilization problem of robotic manipulator system, a predefined‐time sliding mode surface is proposed, ensuring system states converge to origin within a predefined‐time once sliding mode surface is attained. Compared to conventional fixed‐time and finite‐time control strategies, a distinctive advantage of this scheme is that system settling time can be explicitly chosen in advance and independent of system states. To achieve predefined‐time performance, a disturbance observer is introduced to generate the disturbance estimate, which can be incorporated into controller to counteract disturbance. To address the systems uncertainty, an adaptive law is employed to estimate the unknown upper boundary of system uncertainties. Finally, the effectiveness and performance of the proposed scheme are illustrated by simulation and experiment.

A Novel Approach for Power Quality Improvement Using D-STATCOM in Wind Integrated Distribution System

Objectives: The major goal of the proposed article is to enhance the power quality of a wind-integrated radial distribution network utilizing D-STATCOM. It is done by the appropriate allocation of wind turbine-based DGs and D-STATCOM. Methods: The multi-objective optimization problem is implemented using a novel and effective Prairie Dog Optimization (PDO) to attain the best-compromised solutions. This optimization tool is well suited for solving complex, non-linear voltage stability problems. The proposed approach is validated for the modified IEEE-13 bus highly unbalanced system using MATLAB. Findings: The findings indicate enhancements in the voltage profile, system losses, and total harmonic distortion (THD). The THD for the load current is 18%, while the THD for the source current is 2.54% for nonlinear loads using the proposed methodology. The voltage profile of 3.25% is enhanced as compared with the existing method, which is 2.15% better than the other obtainable method. Novelty: Prairie Dog Optimization (PDO) was chosen over traditional algorithms for its nature-inspired approach, simplicity, and efficacy in exploring complicated search fields. Its robust exploration and exploitation skills make it excellent for multi-modal optimization challenges. Keywords: Radial distribution system (RDS), D-STATCOM, Power quality, Prairie Dog Optimization, THD

A Lyapunov Theory-Based SEIG–STATCOM Voltage Regulation Control Strategy

To improve the voltage regulation of asynchronous generators during load switching, a Lyapunov-based control strategy has been proposed to stabilize the generator’s voltage by connecting a static synchronous compensator. By constructing a Lyapunov function from the mathematical model, the error tracking problem is transformed into a global asymptotic stability problem of the Lyapunov function at the equilibrium point. The outer loop linearizes the direct current (DC) voltage control process, while the inner loop replaces integral terms with differential terms. The proposed Lyapunov method achieves linearized voltage control with a quadratic outer loop structure and the inner loop differential structure exhibits a shorter transient process, outperforming traditional methods. Simulation and experimental tests were then used, where the latter was a down-scale laboratory prototype experiment. Compared to traditional (voltage-oriented control) VOC, the outer loop (Lyapunov-function-based control) LBC reduces the DC voltage transient processes by approximately 9.4 milliseconds, while the inner loop LBC reduces both alternating current (AC) and DC voltage transient processes by approximately 2.6 ms and 8.7 ms, respectively.

Determining Groundwater Table in Slopes with Horizontal Drains and Design Framework for Length and Spacing

ABSTRACT Horizontal drains (HDs) are commonly implemented in slope stabilization to reduce the pore water pressure (PWP); however, they also cause complex three-dimensional (3D) variations in the groundwater table (GWT), which require intricate 3D flow models. To address this challenge, we propose a novel semi-empirical method based on a series of numerical simulations validated through numerical and field studies to determine the GWT of a slope with HDs. Subsequently, the proposed method was extended to calculate the average PWP (U) acting on a predefined slip surface via linear integration. The decrease of U (ΔU) resulting from HDs can be used to evaluate the performance of HDs. To create design charts that consider the impact of length and spacing of HDs on ΔU for a specific slope, we developed a Python-based computer program. Two case studies were conducted, which showed that ΔU increases with longer HDs and shorter spacing. The results also indicated that extending the HDs beyond a particular length does not significantly affect ΔU; it is highly sensitive to the spacing in short HDs and not sensitive in long HDs. Furthermore, we found that the total length of HDs required to achieve a target ΔU is less in wide spacings than in short spacings. In conclusion, long HDs with wide spacings are more effective and economical. Owing to the unique nature of each slope stability problem, this study offers a practical tool for analyzing the effectiveness of HDs instead of providing a general guide.

Nonlinear Structures of Dispersive Electrostatic Solitary Waves in a Multi‐Ion Partially Ionized Plasma

ABSTRACTThe nonlinear structure and dynamics of dispersive solitons and breather waves described by Korteweg‐de Vries and nonlinear Schrödinger equations are studied. The theoretical and numerical study of the generalized hydrodynamic equations, accounting for wave dissipation and particle production‐loss mechanism, are considered. The reductive expansion method has been used in the context of the instability problem of multi‐fluid dynamics, applied to the study of electrostatic solitons and ion‐acoustic waves. A nonlocal model of interacting solitary‐breather waves has been presented. Applications of the theory, concerning the ion streaming instability in the framework of plasma physics, are presented.

Quantitative analysis of construction risks in shallowly buried biased tunnel portal section

To address the prominent problem of collapse instability in shallow buried soft ground tunnels, a non-invasive stochastic finite element method was introduced. Taking Fujian Puyan Wenbishan tunnel as the background project, ABAQUS finite element software was used to analyze the tunnel excavation mechanics and parameter sensitivity. And developed the software interface program based on Python to output explicit limit state equation for the key mechanical indexes of the tunnel, so as to evaluate the tunnel reliability under different excavation methods, quantitatively. Study results show a significant improvement in efficiency and accuracy when calculating the probability of failure in tunnel excavation by the non-invasive stochastic finite element method. The maximum displacement monitoring points for the Wenbishan tunnel portal section were all vault settlement, with displacements of 33.6 mm, 30.2 mm, and 25.3 mm, respectively, using the annular retained core soil method, single sidewall guide pit and double sidewall guide pit method, with probabilities of failure of 36.11%, 28.03%, and 20.02%. It is found that the reliability of the tunnel is mainly determined by the geotechnical weight, elastic modulus and cohesion of the weak sandy soil layer, which can provide ideas for this type of engineering researches.

Robust finite-time output feedback stabilisation for a class of uncertain planar systems with asymmetric output constraints

This paper considers the finite-time output feedback stabilisation (FTOFS) problem for a class of uncertain planar systems with asymmetric output constraints. The presence of unknown control coefficients, unknown measurement sensitivity and asymmetric output constraints makes the system under consideration essentially different from those in the existing related works. By constructing a new barrier Lyapunov function and applying homogeneous system theory, a simple proportional-derivative like finite-time output feedback controller is explicitly constructed, which only utilises the output information. A rigorous proof demonstrates that not only the closed-loop system is finite time stable, but also the requirement of asymmetric output constraint can be achieved. The novelty of the control approach lies in that it is capable to handle the FTOFS problem for uncertain planar systems with or without asymmetric output constraints in a unified manner, without changing the control structure. The efficiency of the proposed theoretical results are confirmed by simulation results.

Влияние демпфирования по Рэлею на устойчивость земляного полотна железной дороги в условиях сейсмического воздействия

Purpose: to consider the problem of railway subgrade stability under seismic conditions. Show the need to increase stability during an earthquake. Determine the possibility of increasing seismic resistance by introducing a damping layer into the structure. Determine the optimal damping parameters, taking into account the rational use of subgrade materials. Methods: calculations of embankment stability are carried out using the method of G. M. Shakhunyants. An earthquake is taken into account through an increase in shear forces acting on the cells of the sliding massif. The maximum accelerations of the compartments are determined based on the results of finite element method dynamic calculation of a stress-strain state of the embankment during an earthquake, which is specified through an accelerogram. Results: the effectiveness of using a damping layer in the embankment structure, introduced to increase seismic resistance, has been shown. The dependence of the stability coefficient of the embankment on the Rayleigh parameters of the material composing the body of the entire embankment has been determined. For the best material parameters, the optimal thickness and position of the damping layer in the structure are determined, at which the stability coefficient takes on a standard value and the volume of the damping layer is minimal. Practical importance: as an alternative to the normative approach, the possibility of increasing the stability of a railway embankment under earthquake conditions by introducing a damping layer into the structure is presented. An algorithm for selecting optimal damping parameters has been determined in order to increase seismic resistance.

Leader-Following Sampled-Data Consensus of Multiagent Systems With Successive Packet Losses and Stochastic Sampling.

In practical applications, sampled-data systems are often affected by unforeseen physical constraints that cause the sampling interval to deviate from the expected value and fluctuate according to a certain probability distribution. This probability distribution can be determined in advance through statistical analysis. Taking into account this stochastic sampling interval, this article focuses on addressing the leader-following sampled-data consensus problem for linear multiagent systems (MASs) with successive packet losses. First, the relationship of the equivalent sampling interval between two successive update instants is established, taking into account the double randomness introduced by both SPLs and stochastic sampling. Then, the equivalent discrete-time MAS is obtained, and the overall leader-following consensus problem is formulated as a stochastic stability problem of the equivalent system by incorporating the sampled-data consensus protocol and properties of the Laplacian matrix. Based on the equivalent the discrete-time system, a consensus criterion is derived under a directed graph by using the Lyapunov theory and leveraging a vectorization technique. By the introduction of a matrix reconstruction approach, the mathematical expectation of a product of three matrices, including the system matrix and its transpose, can be determined. Then, the consensus protocol gain is designed. Finally, an example is provided to validate our theoretical results.

Improving extensions for the global uniform asymptotic stability of continuous-time nonlinear systems

This paper considers the classical problems of global asymptotic stability (GAS) of nonlinear autonomous (time-invariant) systems and global uniform asymptotic stability (GUAS) of nonlinear non-autonomous (time-varying) systems. By imposing new conditions on the Lyapunov function and its derivative, the state convergence to the origin from any initial condition with bounded norm in the classical setting is extended to the initial conditions with unbounded norms in the present work. The proposed new notions of stability are called extended global asymptotic stability (EGAS) and extended global uniform asymptotic stability (EGUAS) in this paper. The proposed Lyapunov-based criteria yield the global asymptotic stability of the origin and fixed-time/predefined-time attractiveness of any selected neighbourhood of the origin. The result is that the dynamical behaviour of the state trajectories from the convergence time point of view is improved considerably. The relationship between the smoothness and input-to-state stability (ISS) properties is also studied from a quantitative point of view. Under some new sufficient conditions, it is shown that dynamical systems with smaller Lipschitz constants represent smaller ultimate bounds, and as a result, are more robust. The desirable dynamical behaviour and robustness property of the proposed stability notion makes it comparable with the finite/fixed/predefined/prescribed (exact) stable systems that are naturally non-Lipschitz at the origin. Numerical results illustrate the effectiveness of the proposed theoretical results.

A Uniqueness Theorem for Stability Problems of Functional Equations

In this paper, we present a uniqueness theorem obtained by using direct calculation. This theorem is applicable to stability problems of functional equations whose solutions are monomial or generalized polynomial mappings of degree n. The advantage of this uniqueness theorem is that it simplifies the proof by eliminating the need to repeatedly and cumbersomely prove uniqueness in stability studies.

On stability of iteration processes convergent to stationary points of semigroups of nonlinear operators in metric spaces

Let C be a closed subset of a complete metric space. In this paper we study the stability problem for some iteration processes that approximate stationary points of pointwise Lipschitzian semigroups of nonlinear mappings acting within C. We show that a large class of well-controlled processes is stable under summable errors. These results are then applied to the stability of some known processes including the generalized Krasnosel'skii-Mann and the two-step Ishikawa iteration processes.

Robust H-Infinity Dual Cascade MPC-Based Attitude Control Study of a Quadcopter UAV

Aimed at the stability problem of quadrotor Unmanned Aerial Vehicle (UAV) flight attitudes under random airflow disturbance conditions, a robust H-infinity-based dual cascade Model Predictive Control (MPC) attitude control method is proposed. Model Predictive Control itself has the capability to minimize the deviation between the prediction error and the control target by optimizing the control algorithm. The robust H-infinity controller can maintain stability in the face of system model uncertainty and external disturbances. The controller designed in this paper divides the attitude control loop into the following two parts: the angle loop and the angular velocity loop. The angle loop, serving as the main control loop of the attitude control, employs the robust H-infinity controller to process the angle of the quadrotor UAV and then transmits the processed value to the MPC controller. This approach reduces the computational load of the MPC controller. Simultaneously, by optimizing the algorithm, MPC minimizes the prediction error and the deviation from the control target. Simulation experiments confirm that the proposed algorithm improves the stability of the UAV attitude under random airflow disturbance conditions, while also achieving accurate tracking of the UAV’s position.