Stability Criterion Research Articles

Motion planning in underactuated systems with impulsive phenomenon via dynamic shaping of virtual holonomic constraints

Rhythmic motions are traditionally achieved by developing predetermined paths for the states of the space system to follow. Since these paths are obtained offline, the dynamic behavior fails to adapt to changes in environmental conditions or user command desires. The solution we propose is a new strategy called dynamic shaping, in which the paths are formed online to allow the system to create an orbit with the characteristics we need. Hereupon, this paper focuses on applying this strategy to Dynamics with One Degree of Under-actuation and Impulsive Phenomenon (DSODUIP) to adapt the characteristics of outcomes to be in line with the demands.This research was conducted by leveraging the advantages of virtual holonomic constraints (VHCs) to establish these paths. Therefore, a novel two-level hierarchical control method is designed considering a stability criterion to avoid divergence. At the Low-Level, the controllers stabilize the output of system to follow the VHCs on the system. At the High-Level, the VHCs are modified to shape an orbit with our desired characteristic in the motion. As an illustrative example, the algorithm is implemented to adjust the average angular velocity of a devil stick and the hip velocity of a Three-Link biped robot. Their results vividly demonstrate smooth adjustments and efficient performance in achieving our desired outcomes.

Low‐frequency oscillations in MMC‐MVDC systems with high PV penetration: Modelling, mechanism, and assessment

AbstractThis study investigates the low‐frequency oscillations (LFOs) in MMC‐MVDC systems with high photovoltaic (PV) penetration, considering the whole operating conditions of the grid‐connected MMC, including both the inverter and rectifier modes. First, the multi‐port impedance models of converters and networks are developed, upon which a stability criterion is defined. The mechanism of LFOs is then identified using bus participation analysis and parameter sensitivity analysis. In addition, the stable zones of the dominant parameters are identified, taking into account the whole operating conditions of the grid‐connected MMC. Interestingly, a phase‐locked loop may induce LFOs in two low‐frequency ranges. Finally, the experimental results confirm the correctness of the theoretical analysis.

Adiabatic Mass Loss in Binary Stars. IV. Low- and Intermediate-mass Helium Binary Stars

The unstable mass transfer situation in binary systems will asymptotically cause the adiabatic expansion of the donor star and finally lead to the common envelope phase. This process could happen in helium binary systems once the helium donor star fills its Roche-lobe. We have calculated the adiabatic mass-loss model of naked helium stars with a mass range of 0.35 M ⊙–10 M ⊙, and every mass sequence evolved from the helium-zero-age main sequence to the cooling track of white dwarf or carbon ignition. In consideration of the influence of stellar wind, massive helium stars are not considered in this paper. Comparing the stellar radius with the evolution of the Roche-lobe under the assumption of conservative mass transfer, we give the critical mass ratio q crit = M He/M accretor as the binary stability criteria of low- and intermediate-mass helium binary stars. On the helium main sequence, the result shows 1.0 < q crit < 2.6, which is more unstable than the classical result of polytropic model q crit = 3. After the early helium Hertzsprung Gap, the q crit quickly increases even larger than 10 (more stable compared with the widely used result of q crit = 4), which is dominated by the expansion of the radiative envelope. Our result could be useful for these quick mass transfer binary systems such as AM CVns, ultra-compact X-ray binaries, and helium novae, and it could guide the binary population synthesis for the formation of special objects such as type Ia supernova and gravitational wave sources.

Sampled-Data Control for T-S Fuzzy Systems Using Refined Looped Lyapunov Functional Approach

This paper studies the sampled-data control problem for Takagi-Sugeno (T-S) fuzzy systems with variable sampling. To lessen the conservatism of stability criteria, we introduce a refined looped Lyapunov functional (LLF). These functionals incorporate additional information on split sampling intervals and delayed states. Moreover, sampling-dependent matrix functions are presented to relax the conservativeness of the developed LLFs. By resorting to the refined LLFs, new stability and stabilization criteria for T-S fuzzy systems incorporating an H∞ performance are established. To validate the established conditions, a nonlinear permanent magnet synchronous motor and the Lorenz system are used to demonstrate the reduced conservatism and the merits of the presented methods.

On the analysis of static thermal instabilities occurring in two-phase flow systems

In this study, we investigate a novel type of static thermal instability that occurs in two-phase flow systems. The instability is theoretically and experimentally confirmed to occur for flow boiling micro-channel scenarios and flow condensing scenarios. The theory presented is independent of the evaporator geometry as well as flow boiling/condensing situations. A stability criteria is derived using a Reynolds Transport approach applied to the evaporator of a two-phase pumped loop (TPPL) system. The theory is then validated experimentally using a TPPL containing a parallel micro-channel evaporator. The instability is confirmed with pressure, temperature, and void fraction measurements acquired at the exit of the evaporator. The findings reveal that static thermal instabilities can arise when simultaneous heat addition and reduction in system saturation temperature occurs (or vice versa). The implications of the thermal instability result in dramatic changes in evaporator heat flux, as well as a flow transition from stratified laminar flow to vigorous turbulent flow with high void fractions. By identifying the additional instability mechanisms, this work contributes to enhancing system reliability and predictability of TPPL systems.

Studies on multi-frequency synchronization of two pairs of counter-rotating exciters in a split drive double-body vibrating system

In this article, the multi-frequency synchronization characteristics and stability of a split drive double-body vibrating system with two rigid frames (RFs), driven by two pairs of counter-rotating exciters symmetrically mounted on two different RFs, are investigated in detail by theory, numeric, and simulation. Based on Lagrange’s equations, the differential equations of motion of the system are deduced. The theoretical criteria for implementing foundation frequency, double-frequency, and triple-frequency synchronization of two pairs of exciters are obtained by applying the asymptotic method. The stability criteria of the synchronous states are derived according to the Routh–Hurwitz criterion. Then, the synchronous and stable regions and stability ability coefficients of the system are analyzed qualitatively by numeric. The simulations are conducted to verify the validity of the theoretical methods used and the correctness of corresponding theoretical results. It is shown that, under the precondition of realizing the multi-frequency synchronization, the ideal working point of the system should be set in Region I to obtain the larger and more stable superposition vibration amplitude between two RFs in engineering. The present work can provide theory guidance for designing new types of vibrating equipment with two different driving frequencies.

Event‐triggered tracking control for networked control systems under diversified attacks

AbstractThis paper mainly concerns on the tracking control problem for event‐triggered networked control systems (NCSs) with diversified cyber‐attacks. An event‐triggered mechanism (ETM) is exploited to decrease the amount of redundant transmissions, thus saving communication resources. In addition, a novel tracking error model for NCSs is built with consideration of ETM and diversified cyber‐attacks, which involves deception attacks and Denial‐of‐Service (DoS) attacks. On the basis of Lyapunov stability theory and linear matrix inequalities (LMIs), the stability criterion of the tracking error system is constructed, and the controller is designed to ensure the tracking performance of the system. In the end, simulation examples are provided to testify the validity of the proposed method.

The instability marsh phenomenon and marginal stability boundary distortion of density wave oscillation in parallel channels

Density wave oscillation (DWO) in parallel channels is an important problem that has been widely studied. The marginal stability boundary (MSB) is often found to be “L" shaped on the Npch-Nsub plane, but some very different shapes were also reported. In this paper, the instability marsh region which could occur in the traditional instable region but having both instability and stability sections was presented and discussed, which is found to be an explanation of the distortion of MSB. The analysis of the instability marsh region showed that the evolution of instability marsh should be due to the stability change when operation condition changes, which can be estimated with the analysis of the two-phase and single phase pressure drop variation, as well as Ma's stability criterion for different heat flux profiles. Variation of instability marsh with different heat flux profile, inlet and outlet resistance coefficient, mass flow and pressure were obtained and analyzed, and the effects of these parameters on instability marsh variation were found to be well interpreted with stability change. The calculation and analysis of instability marsh showed a clear evolution figure of the distortion of MSB under different conditions, and related research could be helpful in better understanding the flow instability in parallel channels.

Existence and Stability Criteria for Global Synchrony and for Synchrony in two Alternating Clusters of Pulse-Coupled Oscillators Updated to Include Conduction Delays.

37N25, 39A06, 39A30, 92B25, 92C20.

Static and dynamic stabilities of modified gradient elastic Kirchhoff–Love plates

The static and dynamic stabilities of modified gradient elastic Kirchhoff–Love plates (MGEKLPs), which incorporate two length-scale parameters related to strain gradient and rotation gradient effects, are comprehensively analyzed under various load forms and boundary conditions (BCs). The study of static stability employs static balance method and an improved energy method by introducing higher-order deformation gradients and corresponding energy terms. Utilizing the variational method, a sixth-order fundamental buckling differential equation for MGEKLPs under both transverse and in-plane loads is derived, serving as the foundation for the static balance method. The static stability analysis of MGEKLPs examines the combined effects of strain and rotation gradients on size-dependent critical buckling loads. Building on generalized strain energy with higher-order deformation energy, the energy method of classical elastic thin plate model is enhanced and applied to the static stability analysis of MGEKLPs. This approach enables the investigation of static stability without being constrained by the need to solve complex differential equations, making it applicable to various BCs and load scenarios. While static stability provides a description of stable state of an elastic system, dynamic stability offers a more scientific and rigorous analysis. The dynamic stability of simplified gradient elastic Kirchhoff–Love plates (SGEKLPs) with curved edges and different BCs is further investigated by combining the generalized strain energy with Lyapunov’s second stability method, presenting the dynamic stability criterion in the form of norms. A strict description of the dynamic stability of a SGEKLP over the entire time domain is provided for different supporting conditions, including case where all edges are supported and case with free edges. The analysis of size-dependent static and dynamic stabilities offers theoretical guidance for designing elastic thin plates with microstructures.

Lagrange Stability of Competitive Neural Networks with Multiple Time-Varying Delays

In this paper, the Lagrange stability of competitive neural networks (CNNs) with leakage delays and mixed time-varying delays is investigated. By constructing delay-dependent Lyapunov functional, combining inequality analysis technique, the delay-dependent Lagrange stability criterion are obtained in the form of linear matrix inequalities. And the corresponding global exponentially attractive set (GEAS) is obtained. On this basis, by exploring the relationship between the leakage delays and the discrete delay, a better GEAS of the system is obtained from the six different sizes of the two types of delays. Finally, three examples of numerical simulation are given to illustrate the effectiveness of the obtained results.

The Ulam Stability of High-Order Variable-Order φ-Hilfer Fractional Implicit Integro-Differential Equations

This study investigates the initial value problem of high-order variable-order φ-Hilfer fractional implicit integro-differential equations. Due to the lack of the semigroup property in variable-order fractional integrals, solving these equations presents significant challenges. We introduce a novel approach that approximates variable-order fractional derivatives using a piecewise constant approximation method. This method facilitates an equivalent integral representation of the equations and establishes the Ulam stability criterion. In addition, we explore higher-order forms of fractional-order equations, thereby enriching the qualitative and stability results of their solutions.

A composite motion control method for quadruped robots in trot gait

This work aims to address the issues of instability in trot gait walking and poor terrain adaptability in rugged environments under conventional control strategies for quadruped robots by proposing a novel composite control strategy. During the support phase, a separated force-position mixing control method is employed, utilizing gravity-compensated PD (Proportional Derivative) control at the lateral swing and knee joints while employing position control at the hip joint. During the swing phase, VMC (Virtual Model Control) is used to construct three sets of virtual spring-damper components, guiding the foot to move along a predetermined trajectory and converting virtual forces into joint torques for the swinging leg. At the body, IMU (Inertial Measurement Unit) feedback data combined with PI (Proportional Integral) control is used to adjust leg length and maintain the robot’s posture stability. Finally, the proposed separated force-position hybrid control method is theoretically validated using the Lyapunov stability criterion, and simulation tests on flat and rugged terrains under the quadruped robot’s composite control method are conducted using MATLAB/Simulink, comparing it with the VMC and position control methods. The findings indicate that the composite control strategy leads to smaller changes in the attitude angles and reduced impact forces at the feet during the quadruped robot’s walk on flat ground while also demonstrating strong adaptability to rugged terrains.

Properties of bismuth based Bi2A3 (A = S, Se, Te) chalcogenides for optoelectronic and thermoelectric applications

Structural, electronic, optical, mechanical, thermoelectric and dielectric properties of binary Bi2A3 (A = S, Se, Te) chalcogenide semiconductors are studied by first-principles approach. Bismuth sulfide (Bi2S3) is found to be structurally stable in orthorhombic structure while bismuth selenide (Bi2Se3) and bismuth telluride (Bi2Te3) are stable in trigonal structure. Calculated mechanical properties reveal that all three Bi2A3 (A = S, Se, Te) compounds fulfil the mechanical stability criteria. Band structure calculations reveal that the Bi2S3 exhibits direct optical band gap (Eg = 1. 58 eV) which lies in the near-infrared (NIR) region, while the calculated Eg of Bi2Se3 and Bi2Te3 are found to be 0.53 eV and 0.35 eV, respectively lying in the far-infrared region. For Bi2S3 and Bi2Se3 compounds, the calculated dielectric properties show strong anisotropic behavior, while negligible anisotropic dielectric behavior is observed for Bi2Te3. Calculated optical properties show that all three Bi2A3 compounds possess high absorption coefficient (> 104 cm−1). For all three Bi2A3 (A = S, Se, Te) compounds, the calculated optical conductivity show prominent peak corresponding to the occurrence of optical conduction at energies 3.36 eV, 2.65 eV and 2.02 eV respectively. Calculated optical results support the results deduced from band structures and density of states spectra. Optical properties and dielectric behavior suggest that the Bi2S3 compound has suitable band gap and has potential to use for photovoltaic applications while Bi2A3 (A = Se, Te) compounds could be used in infrared detectors and other optical devices. Calculated thermal properties reveal that the Bi2A3 (A = S, Se, Te) chalcogenides could be potential materials for thermoelectric applications.

Finite time adaptive recoil controller design for deepwater drilling riser systems

In this paper, we propose a finite-time model reference adaptive controller to attenuate the recoil response of deepwater drilling riser systems following an emergency disconnection. Firstly, a coupled model that characterizes the recoil movements of the riser, wave-excited heave motion, and the frictional resistance due to drilling fluid discharge is developed. Secondly, an adaptive control law is presented, with a portion of the adaptive gain determined through linear matrix inequalities. Thirdly, the stability criteria and updating rules that ensure finite settling time for the recoil control system is established. Then, the effectiveness and robustness of the controller against nonlinear systematic perturbations are verified. It is worth pointing out that: (1) The proposed adaptive controller significantly attenuates the recoil responses of the riser in finite time. (2) Compared to other controllers, the finite-time adaptive controller provides faster convergence for both error states and adaptive gains. (3) Perturbation cases involving nonlinear and unmodeled dynamics are examined, demonstrating the controller’s effectiveness and robustness, which ensures the safety of the drilling riser system.

Analyzing MSW Landfill Failures: Stability and Reliability Evaluations from Five International Case Studies

This study investigates five cases of municipal solid waste (MSW) landfill slope failures in the USA, China, Sri Lanka, and Greece, with the aim of assessing the safety margins and reliability of these slopes. The stability and reliability of the landfill slopes were evaluated under both static and seismic loading conditions, using pre-failure geometries and geotechnical data, with analyses conducted in accordance with Eurocode 7, employing all three design approaches. Under static loading, the factors of safety were close to unity, and reliability indexes ranged from 1.0 to 2.8, both falling below the recommended values set by Eurocode. The landfill slopes failed to meet the stability criteria in Design Approaches 2 and 3, while in Design Approach 1, four out of five landfills met the criteria. Under seismic conditions, safety factors and reliability indexes were significantly lower than the prescribed criteria in all analyses. Sensitivity analyses revealed that in two cases, unit weight and friction angle were the dominant parameters, while cohesion was the dominant parameter in one case. The findings of this study underscore the importance of establishing minimum design requirements for MSW landfill slope stability to mitigate potential risks to public health and the environment.

Stabilization for 2-D switched T–S fuzzy systems under the state-dependent switching

This study focuses on the analysis of stability and stabilization for a class of two-dimensional (2-D) discrete-time switched systems. Owing to the inherent uncertainty and nonlinearity in real-world engineering systems, the Takagi–Sugeno (T–S) fuzzy model is employed to describe the dynamics of the 2-D switched system. The discussion encompasses two primary models for the 2-D discrete-time switched T–S fuzzy system (2DSTSFS), specifically the Roesser model and the Fornasini–Marchesini local state-space model. For 2DSTSFSs, this paper delineates sufficient stability criteria that utilize a state-dependent switching signal, facilitated by the application of the Lyapunov–Metzler inequality, ensuring that state trajectories are globally attracted. Furthermore, the paper articulates sufficient conditions for the stabilization of the 2DSTSFS. Additionally, it elucidates the transformation relationship between the two models. To corroborate the theoretical findings, a practical example is employed, demonstrating the applicability of the proposed theorems.

Reassessing Halm's clinical stability criteria in community-acquired pneumonia management.

Halm's clinical stability criteria have long guided antibiotic treatment and hospital discharge decisions for patients hospitalised with community-acquired pneumonia (CAP). Originally introduced in 1998, these criteria were established based on a relatively small and select patient population. Consequently, our study aims to reassess their applicability in management of CAP in a contemporary real-world setting. This cohort study included 2918 immunocompetent patients hospitalised with CAP from three hospitals in Denmark between 2017-2020. The primary outcome was time to achieve clinical stability as defined by Halm's criteria. Additionally, we examined recurrence of clinical instability and severe complications. Cumulative incidence function or Kaplan-Meier survival curves were used to analyse these outcomes, considering competing risks. The study population primarily comprised elderly individuals (median age: 75 years) with significant comorbidities. The median time to clinical stability according to Halm's criteria was 4 days, with one-fifth experiencing recurrence of instability after early clinical response (stability within 3 days). Severe complications within 30 days mainly comprised mortality, with rates of 5.1% (64/1257) overall in those with early clinical response, 1.7% (18/1045) in the subgroup without do-not-resuscitate orders, and 17.3% (276/1595) among the rest. Halm's clinical stability criteria effectively classify CAP patients with different disease courses, yet achieving stability required more time in this aging population with substantial comorbidities and more severe disease. Early clinical response indicates reduced risk of complications, especially in those without do-not-resuscitate orders.

Synchronization and stability of a vibrating system with two rigid frames driven by two groups of coaxial rotating exciters

This article explores the synchronization, stability and motion characteristics of the generalized dynamical model with two rigid frames (RFs) driven by two groups (even number) of coaxial rotating exciters. In light of this system’s generalized coordinates, we use Lagrange’s equations to derive the generalized differential equation of motion. The responses of absolute and relative motion of the generalized system are obtained using the transfer function method. The synchronization and stability criteria of multiple exciters are derived using the average method and Hamilton’s theory, respectively. Taking a dynamical model driven by two pairs of exciters as an example, the localized studies of generalized results are carried out. The stable synchronous solutions for phase differences and excitation frequency, the stability ability coefficient curves and the response curves are graphically presented considering the effect of two crucial dimensionless parameters on the stable synchronous states. The simulation results of the specific system are obtained using the fourth-order Runge-Kutta algorithms and compared with the numerical qualitative analysis results to reveal the high consistency between them and clarify the used methods’ effectiveness. The strength of this work stems from its use in the field of high power and large scale self-synchronization vibrating machines.

Strange star model in higher dimensions (D ≥ 4) with density-dependent B in pseudo-spheroidal geometry

In this paper, we have developed a class of new solutions for relativistic compact stars in higher-dimensional [Formula: see text] space-time assuming pseudo-spheroidal geometry of the [Formula: see text] metric component. To study the physical properties, we consider equation of state of interior strange matter [Formula: see text], as proposed in MIT bag model in the presence of a density-dependent [Formula: see text] parameter. The interior matter of a quark star may consist of three flavor quarks. We observe some interesting results. The parameter [Formula: see text] depends on the anisotropy [Formula: see text] in the interior, and at the stellar surface, [Formula: see text] attains a constant value independent of [Formula: see text]. At the interior, [Formula: see text] increases with the increase of [Formula: see text]. We also note that the value of B approaches a constant value with increasing spheroidal parameter [Formula: see text]. [Formula: see text] also depends on space-time dimensions and it is interesting to note that [Formula: see text] picks up negative values near core region which limits the number of space-time dimensions available for a stellar model. All the stability criterion and energy conditions hold good for a physically realistic stellar configuration. It is observed that strange quark matter may be stable or metastable or unstable depending upon the value of energy per baryon [Formula: see text]. Strange quark matter will be stable if energy per baryon [Formula: see text]. It is noted that the maximum mass obtainable in this model is [Formula: see text] considering stable strange quark matter when dimension [Formula: see text]. In addition, we observe that the dimensions have some effect on the gross properties of strange stars (SS).