Stability Conditions Research Articles

Design of hybrid controller for broadband vibration isolation with active negative stiffness and ground-hook

This paper presents a novel hybrid control strategy that integrates active negative stiffness (ANS) with the ground-hook principle, aiming to enhance the vibration isolation system’s performance across both low and high-frequency ranges. Firstly, to improve vibration isolation performance, this study analyzes the existing ANS model. It identifies key factors affecting ANS stability and proposes a control parameter adjustment scheme based on stability conditions. This approach effectively refines ANS control theory and provides theoretical support for the application of ANS by ensuring stability. Secondly, addressing the limitations of ANS in high-frequency vibration isolation, this study proposes targeted solutions based on the ground-hook principle. While ANS excels in low-frequency isolation, this work tackles its shortcomings to enhance high-frequency vibration isolation. These solutions include the implementation of relative velocity feedback (RVFB) control and absolute velocity feedforward (AVFF) control to enhance high-frequency vibration isolation performance, and AVFF exhibits superior advantages over RVFB. Furthermore, the stability of different control strategies is analyzed. The findings reveal that sky-hook significantly enhances the control stability margin of the ANS loop, while RVFB decreases it, with AVFF having a minimal impact. Finally, comprehensive experiments validate a significant enhancement in both low and high-frequency vibration isolation performance, providing robust evidence for the practical engineering application of the vibration isolation system.

New global exponential stability conditions for nonlinear delayed differential systems with three kinds of time-varying delays

For a class of nonlinear differential systems with heterogeneous time-varying delays, including distributed, leakage and transmission time-varying delays, a novel global exponential stability (GES) analysis method was developed. Based on the GES definition, some sufficient conditions and rigorous convergence analysis of nonlinear delayed differential systems are presented directly, which ensure all states to be globally exponentially convergent. The proposed analysis method not only avoids the construction of the Lyapunov–Krasovskii functional, but also uses some simple integral reduction techniques to determine the global exponential convergence rate. Furthermore, the main advantages and low calculation complexity are demonstrated through a theoretical comparison. Finally, three numerical examples are provided to verify the effectiveness of the theoretical results.

Pre-eruptive magmatic processes at Taranaki volcano from an amphibole perspective

Amphibole phenocrysts in post-1 ka lava domes deposits of Taranaki volcano, an andesite arc volcano in New Zealand, provide an opportunity to explore late-stage changes in melt composition and volatiles in the run up to eruption. Amphibole is a subordinate phase (0–7% of modal phenocrysts) and the phenocrysts display three types of growth history. Type 1 are large compositionally and texturally uniform phenocrysts that have low MgO (<13 wt%) and high K2O (∼1–1.4 wt%) contents. In contrast, Type 2 have similar cores but have been partially resorbed and overgrown by a mafic rim distinguished by high MgO (up to 15 wt%) and low K2O (<1.0 wt%) contents. Type 3 are the least common, and have either normal zoned or concentrically zoned interiors with respect to MgO and FeO. Overall, elemental substitutions and zonation patterns are related to periods of resorption and regrowth that are best explained by changes in melt composition. Based on calculated equilibrium melt compositions, the amphibole crystallisation is consistent with an incrementally grown andesitic to dacitic (SiO2 58–67 wt%) crystal mush that was periodically recharged with more mafic magma (SiO2 ∼ 55 wt%). The melts span a compositional gap (SiO2 ∼ 60–65 wt%) that is not represented in eruption products from the last 8 ka. Such melts were likely brief stages during ongoing fractional crystallisation and magma mixing. Each recharge event disrupted an evolving system and mixed crystals from different parts of it. This concept supports triggering of eruptions by recharge of mafic melts, as also inferred from plagioclase zonation for some eruptions from Taranaki. The outermost rims (0–5 μm) of many amphibole phenocrysts are enriched in fluorine (up to 1.9 wt%) and surrounded by a thick opacitic decomposition growths. We interpret this as the result of slow magmatic ascent and extensive crystallisation that produced a late-stage halogen-rich interstitial melt. This likely extended the conditions for amphibole stability to lower pressure. If F enrichment was accompanied by comparable enrichments in other halogens that preferentially partition into an aqueous phase, then extensive degassing would have occurred during the dome extrusions.

Finite-Time Disturbance Observer-Based Adaptive Course Control for Surface Ships

In this paper, a finite-time disturbance observer-based adaptive control strategy is proposed for the ship course control system subject to input saturation and external disturbances. Based on the Gaussian error function, a smooth saturation model is designed to avoid the input saturation of the system and reduce steering engine vibrations, and an auxiliary dynamic system is introduced to compensate for the effect of the rudder angle input inconsistency on the system. By constructing an auxiliary dynamic, a finite-time disturbance observer is designed to approximate the external disturbance of the system; an adaptive updating law is also constructed to estimate the upper bound of the derivative of the external disturbance. Combining the finite-time disturbance observer with the auxiliary dynamic system, a novel adaptive ship course control law is proposed by using the hyperbolic tangent function. Moreover, according to LaSalle’s Invariance Principle, a system stability analysis method with loose stability conditions and easy realizations is designed, while the stability of the closed-loop system and the ultimately uniformly boundedness of all its signals are proven. Finally, the course control simulation analysis of a surface ship is carried out. The results show that the proposed control law has a strong resistance to external disturbances and a strong non-fragility to system parameter perturbations, which ensure that the course control system has great control performance.

Design and fabrication of a large-aperture electrowetting liquid zoom system

In this paper, a continuous zoom system based on large-aperture electrowetting liquid lenses is designed and fabricated. The inner diameter of the electrowetting lens is up to 20 mm, which can tune stably from a focal length of −328.49mm to −∞ with applied voltages of 0 to 115 V. The zoom system mainly consists of two large-aperture electrowetting liquid lenses and a glass lens, getting continuous zoom images by adjusting the voltages applied to the two liquid lenses without any mechanical movement, ensuring a more compact structure than conventional zoom systems. The theoretical formulas of the zoom ratio and image plane stability condition for this optical system are systematically derived based on the matrix optics, laying the foundation for guiding system regulation and finding methods to improve zoom ratio, and corresponding influence factors on the zoom ratio are verified by experiments. The system zoom ratio can reach 1.52 at a fixed working distance, close to the theoretical derivation result. The system is expected to be used for imaging in a variety of scenarios, such as special photography, dynamic measurement, etc.

Harnessing membership function dynamics for stability analysis of T-S fuzzy systems

The main goal of this paper is to develop a new less conservative linear matrix inequality (LMI) condition for the asymptotic stability of continuous-time Takagi-Sugeno fuzzy systems. A key advantage of this new condition is its independence from the bounds on the time-derivatives of the membership functions (MFs), a requirement that presents in the existing approaches. This is achieved by introducing a novel fuzzy Lyapunov function that incorporates an augmented state vector. Notably, this augmented state vector includes MFs and allows their dynamics to be integrated into the proposed LMI condition. This inclusion of additional information about MFs reduces the conservativeness of the suggested stability condition. Finally, examples are given to demonstrate the effectiveness of the proposed method.

Extending gravitational potentials from the surface boundaries of compact objects

The solutions of the Einstein field equations of general relativity (GR) are prone to rendering systems which are physically non-viable as shown by Delgaty and Lake (1998). This does not detract from the success of general relativity but rather suggests the possibility for implementing new solution methods while being cautious that the resulting systems are indeed physically viable. This emphasizes the importance of applying appropriate criteria in closing the system of non-linear, coupled differential equations of GR. In the case of static systems describing massive compact bodies, an intrinsic property is the vanishing of the radial pressure at the surface boundary of the object which is embedded in an empty Schwarzschild exterior spacetime. In attempting to complete the gravitational description, we first assume a standard, physically plausible metric potential such as that of Finch and Skea. We then attempt to solve for the other metric component by imposing an ansatz which assists in extrapolating from the vanishing pressure boundary condition. Our model is guided by the physicality of the sound speed profiles and associated stability conditions.

Manufacturing enterprises digital collaboration empowered by Industrial Internet Platform: A multi-agent stochastic evolutionary game

Digital transformation is a critical way to improve the resilience of the manufacturing industry chain. However, the current digitalization of manufacturing enterprises lacks upstream and downstream linkage. If the level of digitization of upstream and downstream enterprises differs significantly, it will increase transaction costs. Digital transformation with the help of industrial Internet platform has become a trend. For this reason, this study deeply explores the influence mechanism of digitalization collaboration of manufacturing enterprises under the empowerment of industrial Internet platform. This paper constructs a stochastic evolutionary game model with core manufacturing enterprise, supplier and local government as the main players. Consider stochastic differential equations to analyze the stability conditions of game subjects, and explore different incentive mechanisms on enterprise strategy. The results show that the data security of the platform and the network effect coefficients significantly affect the strategy selection results of the players. Additionally, the change of environmental noise affects the strategy evolution process of the subject, and the supplier strategy is more affected by environmental noise compared to the core manufacturing enterprises. Furthermore, the dynamic incentive effect of the government is better than the static incentive, which can better promote the digital collaboration of manufacturing enterprises. Dynamic penalties are less effective than static penalties. The study’s conclusions can provide a reference for the government to implement the gradient digitalization incentive policy and provide a theoretical basis for promoting digital collaboration in manufacturing enterprises.

Evaluation of underground hard rock mine pillar stability using gene expression programming and decision tree‐support vector machine models

AbstractAssessing the stability of pillars in underground mines (especially in deep underground mines) is a critical concern during both the design and the operational phases of a project. This study mainly focuses on developing two practical models to predict pillar stability status. For this purpose, two robust models were developed using a database including 236 case histories from seven underground hard rock mines, based on gene expression programming (GEP) and decision tree‐support vector machine (DT‐SVM) hybrid algorithms. The performance of the developed models was evaluated based on four common statistical criteria (sensitivity, specificity, Matthews correlation coefficient, and accuracy), receiver operating characteristic (ROC) curve, and testing data sets. The results showed that the GEP and DT‐SVM models performed exceptionally well in assessing pillar stability, showing a high level of accuracy. The DT‐SVM model, in particular, outperformed the GEP model (accuracy of 0.914, sensitivity of 0.842, specificity of 0.929, Matthews correlation coefficient of 0.767, and area under the ROC of 0.897 for the test data set). Furthermore, upon comparing the developed models with the previous ones, it was revealed that both models can effectively determine the condition of pillar stability with low uncertainty and acceptable accuracy. This suggests that these models could serve as dependable tools for project managers, aiding in the evaluation of pillar stability during the design and operational phases of mining projects, despite the inherent challenges in this domain.

Khartoum War's echoes in oil and energy sectors: Economic and environmental implications for Sudan and South Sudan

The energy sector is a main driver of African growth, particularly in regions with geopolitical conflicts like Sudan and South Sudan. The oil and gas industry notably influences these regions' economy, politics, humanitarian situation, and social stability. This study seeks to investigate how the Khartoum War affected the energy sector of both Sudan and South Sudan, particularly looking at the disruptions caused by recent conflicts and their impact on oil production, economic stability, and environmental conditions. The study employs a multi-disciplinary approach, utilising different sources such as regional legal agreements, government reports, academic articles, and press releases from international organisations. The key methodology includes qualitative analysis of several documents and quantitative assessment of production data and economic reports. The study's key findings show a significant decline in oil production and transportation due to the shutdown of key oilfields and pipelines, intensifying economic and humanitarian crises. Additionally, the damage to oil infrastructure has presented serious environmental risks, highlighting the delicate balance between resource management and regional stability. In conclusion, the study's findings underscore the intense impact of the Khartoum War on the energy sector of Sudan and South Sudan, and the urgent need for policy recommendations to mitigate these effects and foster sustainable development.

Switched sampled-data-based membership function-dependent [formula omitted] control for PMSG-based WTS with actuator failures

This paper deals with the problem of sampled-data-based H∞ control design for nonlinear permanent magnet synchronous generator (PMSG)-based wind turbine system (WTS) subject to actuator failures. First, the Takagi–Sugeno (T-S) fuzzy system is employed to handle the nonlinearities of presented model. Next, by employing a Bernoulli stochastic variable, the general scenario of switched coupling memory sampled-data control (CMSDC) is designed which contains the sampled-data control (SDC) and memory SDC scheme as special cases. By combining the membership function-dependent (MFD) asymmetric looped-type Lyapunov-Krasovskii functional (LKF) and employing the available information of membership functions in H∞ performance, the delay-dependent stabilization conditions of considered PMSG-based WTS are derived through the switched CMSDC technique. Meanwhile, the disturbances of considered systems are attenuated by taking the advantage of the newly proposed MFD H∞ performance. Eventually, the simulation results are given to demonstrate the efficacy and applicability of the proposed CMSDC technique.

H∞ stabilization of singular networked cascade control systems subject to periodic DoS attack

In this paper, a [Formula: see text] controller with an event-triggered mechanism is designed for a singular networked cascade control system (SNCCS) under periodic denial-of-service (DoS) attacks. The SNCCS is treated as a system of differential-algebraic equations (DAEs) with an index of two and is modeled as a switched system. The paper first establishes sufficient stability conditions, which are formulated as linear matrix inequalities based on multiple Lyapunov functions. These conditions ensure that the system remains regular, free from impulse modes, and stable. Next, state feedback controllers are designed for both the inner loop and the outer loop. However, the outer loop is subjected to periodic DoS cyber-attacks. Finally, the proposed method’s effectiveness is demonstrated through simulation results on a practical thermal cascade control system.

Steady and transient state behavior of a gasification process under fixed-bed downdraft configuration

Gasification is a thermochemical process that has gained significant interest in the field of biomass energy conversion. Despite the level of technological maturity of the process, the dynamic variation of the process as a result of changes in both the properties of the gasifying agent and biomass has not been analysed in sufficient depth. Therefore, the present study characterizes the process dynamically as a function of step-type changes in rice husk biomass moisture content and gasifying airflow. To identify stability conditions and the range for inducing disturbances, steady-state tests were carried out using a 32-factorial design. The experimental results demonstrate that within the tested range of airflow, the gasification process operates in the oxygen-limited zone. Despite increasing the airflow from 20 to 40 standard liters per minute (SLPM) and driving the reaction towards the combustion zone, the high temperatures achieved resulted in the gas reaching a peak Lower Heating Value (LHV) of 2.6 MJ/Nm3 and a gas power of 2.6 kW, with a Cold Gas Efficiency (CGE) of 62%. In contrast, the effect of biomass moisture content was negligible due to the thermal inertia of the reactor and the natural variation of the process. Dynamic evaluation revealed that the oxidation temperature and gas concentration were the variables that took the longest to return to stability after air disturbances. It took approximately 1200 s for the hydrogen (H2) concentration to stabilize, while the gas power required about 300 s. No clear results were observed regarding the impact of the dynamic disturbance in moisture content, which varied between 12.3% w.t and 21.5% w.t.

Controllable region analysis of active front steering and differential braking system stability control characterized by additional yaw moment

Active Front Steering (AFS) and Differential Braking System (DBS) are commonly used execution systems for vehicle anti-rollover or handling stability control. They regulate the vehicle’s yaw moment by adjusting the lateral tire force and longitudinal tire force, respectively. However, these two systems differ in terms of control capabilities and regulatory sensitivities. In emergency conditions, it becomes crucial to allocate and coordinate the tasks for the execution systems according to their yaw moment control capability and adjustment sensitivity. This paper proposes a method for calculating the controllable region represented by the additional yaw moment. This method allows for the computation of the control capability of AFS and DBS based on the current state. Additionally, the influence of different vehicle states on the controllable regions of the two execution systems is analyzed. Building upon this analysis, the yaw moment adjustment sensitivities of AFS and DBS systems under the current state are further investigated. Finally, a task coordinated strategy between AFS and DBS is developed based on the analysis of controllable regions and sensitivities of different execution systems. Simulink simulations are conducted on yaw stability and roll stability conditions to comprehensively analyze the working process of the proposed task coordination strategy.

The influence of prevention and isolation measures to control the infections of the fractional Chickenpox disease model

In this paper, we propose a mathematical model using the Caputo fractional derivative (CFD) and two control signals to study the transmission dynamics and control of Chickenpox (Varicella) outbreak. The model consists of six compartments representing susceptible, vaccinated, exposed, infected with complications, infected without complications, and recovered individuals. We analyze the theoretical properties of the model, including existence, uniqueness, and boundedness of solutions, and calculate the basic reproduction number (R0). We identify equilibrium points and establish conditions for their stability. Sensitivity analysis helps identify the most influential parameters on R0. We formulate a fractional optimal control problem (FOCP) by incorporating time-dependent prevention and isolation measures. The necessary optimality conditions are derived using Pontryagin’s maximum principle. Numerical simulations based on the Adams–Bashforth–Moulton (ABM) method illustrate the impact of control measures and fractional order on disease propagation. The results highlight the effectiveness of optimal controls and fractional order in understanding and managing epidemics, enhancing stability conditions. The study contributes to a better understanding of Chickenpox transmission dynamics and provides insights for disease control and management, aiding decision-makers and governments in taking preventive measures.

2-D acoustic equation prestack reverse-time migration based on optimized combined compact difference scheme

Abstract Reverse-time migration (RTM) is widely regarded as one of the most accurate migration methods available today. A crucial step in RTM involves extending seismic wavefields forward and backward. Compared to the conventional central finite difference (CFD) scheme, the combined compact difference (CCD) scheme offers several advantages, including a shorter difference operator and the suppression of numerical dispersion under coarse grids. These attributes conserve memory and enhance effectiveness while maintaining the same level of differential precision. In this article, we begin with the five-point eighth-order CCD scheme and utilize the least squares method and Lagrange multiplier method to optimize the difference coefficients. This optimization is guided by the concept of dispersion-relation-preserving (DRP). The result is the acquisition of an optimized combined compact difference (OCCD) scheme, further enhancing the ability to suppress numerical dispersion. We thoroughly compare and analyze dispersion relationships and stability conditions. In addition, we examine several crucial steps in the RTM of the second-order acoustic wave equation. These steps include absorption boundary conditions, boundary storage strategy, and Poynting vector imaging conditions. Finally, we apply both the CCD and OCCD schemes in the RTM of the layered model, graben model, and SEG/EAGE salt model. We compare these results with those obtained from CFD's RTM. Numerical findings demonstrate that, in contrast to the CFD scheme, the CCD scheme effectively suppresses numerical dispersion and enhances imaging accuracy. Moreover, the optimized OCCD scheme further improves the ability to suppress numerical dispersion and can obtain better imaging results, which is an effective reverse time migration method suitable for coarse grid conditions.

Stability and bifurcations in a model of chemostat with two inter‐connected inhibitions and a negative feedback loop

This paper deals with a model of chemostat with two cross‐feeding species and involving two inhibitions. The excess of hydrogen inhibits the growth of acetogenic bacteria which, in turn, inhibit the growth of methanogenic hydrogenotrophic bacteria. The model is described by a system of four ordinary differential equations. We established the conditions of existence and stability of equilibria with respect to the operating parameters which are the dilution rate and the input substrate concentrations of the species of the model, then we illustrate the operating and bifurcation diagrams. This technique makes it easy to interpret different regions of operating diagrams. Inhibitions let some regions of stability rise and others vanish.

Memory‐based event‐triggered control for networked control system under cyber‐attacks

AbstractThis article focuses on the problem of stability for a class of linear networked control systems (NCSs) subjected to network communication delays and random deception attacks. A new memory event‐triggered mechanism (METM) is proposed to reduce the unnecessary transmitted data through the communication channel and then enhance the network resources. In this context, a new memory stochastic state feedback controller is proposed to stabilize the closed‐loop networked control system. A new randomly occurring deception attacks model is employed to deal with the security problem of NCSs. Sufficient stability conditions are derived based on a suitable Lyapunov‐Krasovskii functional (LKF). The designed methodology is proposed in terms of linear matrix inequality to synthesize both event‐triggered parameters and controller gains, and to reduce the conservatism of the system some integral lemma are exploited to bind the time derivative of the LKF. Finally, two numerical examples are presented to illustrate the effectiveness of the proposed method which provides a maximal upper bound value of the network‐induced delay and less transmitted packet regarding the maximal value delay obtained in other works, so less conservatism results are obtained, compared to previous ones in the literature.

Deterministic approach to assess landslide susceptibility and landslide activity in the Central-Western Region of Slovakia

Quantitative assessments in landslide susceptibility evaluation are typically dominated by statistical analyses. However, this paper employs a deterministic approach to construct such maps, specifically focusing on the stability assessment of shallow landslides with slip surfaces generally not exceeding 5 m in depth at a regional scale. The study area chosen for this research is the landslide-prone region between Hlohovec and Sereď towns in the central-western part of Slovakia. Our focus is on the activation of shallow landslides, representing the youngest, third generation of landslide evolution in the area. For the stability assessment, three scenarios were considered using deterministic analysis: a scenario involving dry slopes, a scenario under partially saturated conditions, and a scenario of fully saturated slopes. This approach enables the assessment of stability conditions based on qualitative parameters derived from both field and laboratory research. The results from the deterministic analysis aid in defining different stages of activity within the landslide body. These Landslide susceptibility maps were verified directly in the field, and most landslides reactivated from 2011 to the present fell into the class with the safety factor below 1.0. In comparison with the landslide hazard map created by using bivariate statistical analysis, it was observed that 89.97% of the area is in a very high level of landslide hazard, given a safety factor below 1.0. This highlights the effectiveness of the deterministic approach in capturing the vulnerability of the region to shallow landslides.

MODELING THE EFFECTS OF PESTS AND PESTICIDE ON CROP YIELDS IN A MULTIPLE CROPPING SYSTEM

Pest infestation poses a significant threat to agricultural crop yields, and to control it, farmers spray chemical pesticides. The persistent use of these chemical agents not only leads to pesticide residues within crops but also exerts collateral damage on the beneficial pest population. In this research work, we formulate a nonlinear mathematical model to assess the impacts of pesticide on crop yields within a multiple cropping system. Model analysis illustrates that crop consumption rates destabilize, and the spraying rate of pesticide stabilizes the system. Furthermore, we determine conditions for the global stability of the coexisting equilibrium and conduct a global sensitivity analysis to identify model parameters that significantly influence pest population density. Our findings emphasize that, for effective pest population control and enhanced crop yields, farmers should choose either pesticides with a high pest abatement rate or those with a higher pesticide uptake rate. Considering the spraying rate of pesticide as time-dependent, we also suggest an optimal control strategy to minimize the pest population and associated costs. We provide analytical results backed by numerical simulations implemented through the non-standard finite difference scheme to support our findings.