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The present manuscript relates to the movement of three immersed viscous magnetic liquids in porous media that are positioned between three concentric cylindrical interfaces. Every cylindrical layer has an axial extension that extends in both vertical directions to infinity. Moreover, the pressure gradients are the driving force behind the uniform motion of all fluids in a similar upward motion at varying velocities. Permanent magnetic fields are tangentially oriented exert stress on the system. The computations are rendered simpler by applying the viscous potential theory. The Maxwell equations are utilized for the magnetic field, while the Brinkman-Darcy equations define the fluid mobility. Moreover, the rise of the disturbance and the subsequent extraction of fuel from the tiny cracks of the reservoir stone can be managed through the implementation of engineering techniques such as electromagnetic field impacts and oil extraction engineering. Typically, the nonlinear strategy involves incorporating the applicable nonlinear boundary conditions and analyzing the linearized equations of motion. This research offers a framework for verifying theoretical models and simulations based on experimental observations. The inclusion of a homogeneous magnetic field introduces complexity to the system, rendering it a suitable candidate for validating and improving models in the field Magneto hydrodynamics. The originality of the problem lies in the dual nonlinear stability of cylindrical interfaces when subjected to uniform magnetic field. Accordingly, two nonlinear characteristic differential equations controlling the surface displacements are produced. The nonlinear stability prerequisite is met by applying the matrix concept and the multiple scale technique in conjunction with a theoretical analysis of stability. Additionally, the Routh-Hrutwitz criterion is encompassed to judge the stability cofiguration. A detailed examination of the associated nonlinear stability requirements is showed. Meanwhile, the estimated limited solutions of perturbed surfaces are achieved. For the cylindrical middle layer, it is found that the outer cylindrical interface has a more stabilizing effect than the inner one. The approximate solutions for displacements at the interface are calculated. The influence of Weber numeral of the problem on the stability profile is investigated.

The nonlinear instability of a planar interface between two overlapping Rivlin-Ericksen viscoelastic liquids, in the occurrence of fine dust and vertical electric fields throughout permeable media, and the influence of surface tension is studied. The prototype structure is assumed to be a two-dimensional groundwork for the sake of simplicity. The growing approval of several disciplines of practical physics and technology serves as motivation for analyzing this problem. Using viscous potential theory, the mathematical procedure is condensed. To properly control electro convection in liquid crystals, which is widely used in various displays technologies, it was crucial to have a thorough comprehension of stability. Gaining understanding of the behavior of viscoelastic fluids at interfaces was crucial in polymer manufacturing industries. Employing the linear equations of movement with the suitable nonlinear bounder circumstances forms the basis of the considered nonlinear technique. A nonlinear partial differential equation that evaluates the interface movement is the objective of the process. Since linear stability has frequently been investigated, the present situation will be constructed only in the nonlinear sense, where a number of dimensionless physical numerals are achieved. The non-perturbative methodology is used to accomplish the nonlinear standards. The main idea behind the novel performance is to convert an ordinary nonlinear ordinary differential equation into a linear one. The new technique differs from the conventional perturbation methods in that it may be used to exactly and correctly analyze the behavior of the strong nonlinear aspects of the interface displacement. This innovative method is established by using He's frequency formula. Using the nonlinear distinguishing equation, the special situation of the real and the complex coefficients is accomplished. It was observed that the instability zone expands as the electric field, porosity of porous medium, and density ratio of two fluids rise. The stability configuration is enhanced by the viscoelasticity parameter, Bond number, and ratio of kinematic viscoelasticity.

In this paper, the linear and nonlinear instability of magnetoconvection in a Darcy-Benard setup saturated by a Maxwell fluid with chemical reactions is studied. The governing non-dimension equations are solved using the normal modes, and we obtain the expressions for steady and oscillatory thermal Rayleigh numbers. The effects of different physical parameters such as the Damkohler number ( 0 < D a < 20 ), Hartmann number ( 0 < H a < 1 ), Solute Rayleigh number ( 0 < R S < 1000 ), relaxation parameter ( 0 < λ < 1 ), Magnetic Prandtl number ( 0 < P r < 10 ), Lewis number ( 0 < L e < 100 ) on stationary and oscillatory critical thermal Rayleigh numbers are presented and described. Enhancing the values of the Solute Rayleigh number and Lewis number makes the system unstable. Also, the Hartmann number and Damkohler number have a contrasting effect on stationary and oscillatory convection. Enhancing the value of the relaxation parameter makes the system more stable. In order to study heat transport by convection, the well-known equation, the Landau-Ginzburg equation, is derived. [ABSTRACT FROM AUTHOR]

The stability of solutions to the Cahn–Hilliard equation with concentration dependent mobility with respect to perturbations is studied by means of relative energy estimates. As a by-product of this analysis, a weak-strong uniqueness principle is derived on the continuous level under realistic regularity assumptions on strong solutions. The stability estimates are further inherited almost verbatim by appropriate Galerkin approximations in space and time. This allows to derive sharp bounds for the discretization error in terms of certain projection errors and to establish order-optimal a priori error estimates for semi- and fully discrete approximation schemes. Numerical tests are presented for illustration of the theoretical results. [ABSTRACT FROM AUTHOR]

The stability of a stationary fully developed vertical flow across a porous pipe is investigated. The heating due to viscous dissipation is assumed to be non–negligible and also to be the only effect triggering the onset of thermal convection. An innovative scaling is employed to study the case of small Gebhart number. The viscous heating term present inside the energy balance equation yields a basic stationary flow characterised by dual branches of solutions: for a given vertical pressure gradient, two possible velocity profiles are obtained. The linear and nonlinear stability of the stationary dual solutions is performed. The linear stability is investigated in a usual fashion by employing the normal modes method and then solving the eigenvalue problem obtained by using the shooting method. The nonlinear stability is investigated by simulating numerically the evolution in time of the perturbed system. The linear stability analysis allows one to conclude that the critical wavenumber for the onset of instability is zero and the critical dimensionless velocity at the pipe axis is equal to 3.43631. The results of the nonlinear analysis display subcritical instabilities. Indeed, the onset of instability is obtained for values of the governing parameters which are lower than the critical values obtained by the linear analysis. This feature occurs when the amplitude of the initial disturbance applied to the nonlinear problem is sufficiently high, namely when the dimensionless amplitude is larger than 10 − 2. [ABSTRACT FROM AUTHOR]

Due to the low inertia of the DC microgrid, the DC bus voltage is prone to drop or oscillate under disturbance. It is also challenging to supervise the stability of a DC microgrid since it is a highly nonlinear dynamic system with high dimensionality and randomness. To tackle this problem, this paper proposes a new method using ANN-aided nonlinear dynamic stability analysis for monitoring the DC bus voltage, which is combined with two steps. The first step is to establish six corresponding nonlinear accurate discrete iterative models of six switching modes of the PV-battery-load-based DC microgrid system, based on the Poincaré map theory, in order to judge the stability quantitatively with a promoted stability margin index. The second step is to use artificial neural networks (ANNs) to forecast the operating mode of the system when random changes occur in environmental circumstances and load power; this will aid the first step in being efficient and adaptable while determining stability cases. And the employed ANNs are trained with the datasets, including the circuit data, ambient temperature, irradiance, and load power, which are generated by MATLAB/Simulink simulation. Theoretical and simulation analyses are carried out under different operating conditions to validate the proposed method’s efficacy in judging the DC microgrid’s destabilizing oscillation and stable running.

Purpose: In this study, the nonlinear stability analysis of the porous functionally graded pipes conveying fluid with clamped–clamped, clamped–hinged and hinged–hinged boundary conditions have been investigated based on the Timoshenko beam theory. The functionally graded pipe conveying fluid is assumed to carry both even and uneven porosity distributions. It is considered that the material properties of the pipe are continuously varied through the radial direction. Methods: By applying Von-Karman nonlinear strain and Hamilton's principle, the nonlinear governing equations of motion are derived. Results: The importance of considering rotary inertia and shear deformation and the effects of various parameters such as, porosity volume fraction, porosity distribution, initial tension, power-law index and radius-length ratio of the pipe, on the bifurcation diagrams, critical fluid velocity and buckling configuration of the pipes have been numerically studied and discussed in detail. Conclusions: This work fills the gap of study in the field of the stability of the fluid-conveying pipes by presenting exact analytical solutions for the buckling configuration and critical fluid velocity of the porous functionally graded pipes conveying fluid which have not been studied in former investigations by considering porosity and different boundary conditions. [ABSTRACT FROM AUTHOR]

The problem of input-to-state stability (ISS) and its integral version (iISS) are considered for switched nonlinear systems with inputs, resets and possibly unstable subsystems. For the dissipation inequalities associated with the Lyapunov function of each subsystem, it is assumed that the supply functions, which characterize the decay rate and ISS/iISS gains of the subsystems, are nonlinear. The change in the value of Lyapunov functions at switching instants is described by a sum of growth and gain functions, which are also nonlinear. Using the notion of average dwell-time (ADT) to limit the number of switching instants on an interval, and the notion of average activation time (AAT) to limit the activation time for unstable systems, a formula relating ADT and AAT is derived to guarantee ISS/iISS of the switched system. Case studies of switched systems with saturating dynamics and switched bilinear systems are included for illustration of the results. [ABSTRACT FROM AUTHOR]

This paper presents a nonlinear stability analysis of an unbalanced rotor-bearing system using the numerical continuation method and the numerical integration method. In this study, the effect of unbalance on journal motion is highlighted and a relationship is established between the bifurcation diagram of a balanced rotor and that of an unbalanced rotor. The results show that the stable operating speed range, the shaft motion type, the whirl speed and the chaotic motion occurrence depend on the unbalance level, the bearing geometry, the oil viscosity, and the speed range of unstable limit cycles existence.

• Nonlinear stability analysis of fast reactors has been performed by the method of Largest Lyapunov exponents. • Computer programs are developed to calculate largest Lyapunov exponent by Wolf algorithm and for plotting phase-space diagram by bifurcation theory. • Stability boundary with respect to different reactivity coefficients for MOX and metal fuelled fast reactors has been evaluated. • System behavior beyond stability boundary of a MOX fuelled fast reactor has been studied by bifurcation theory. Nuclear reactors are classical examples of nonlinear dynamical systems defined by using many highly interacting state variables. The instabilities in these systems during operation have to be studied in detail for ensuring their safe operation. The method of largest Lyapunov exponents (LLE) is identified to be a useful diagnosis tool for instability in nuclear reactors. In this paper we apply this methodology for the first time to sodium cooled fast neutron reactors by analysing 500 MWe metal and MOX fuelled fast breeder reactor cores (FBRs). The stability margins and boundaries for various components of reactivity feedback are evaluated and compared with the results from transfer function based linear stability analysis. In a MOX fuelled fast reactor, stability of the system with sodium void propagation is studied by bifurcation theory and Lyapunov exponents. [ABSTRACT FROM AUTHOR]

The linear and nonlinear stability analyses of thermosolutal convection in a non-Newtonian Navier-Stokes-Voigt fluid, considering Soret and Ekman damping effects, are conducted analytically. Instability thresholds are determined for thermosolutal convection within a viscoelastic fluid of the Kelvin-Voigt type, wherein a dissolved salt field exists. Two scenarios are examined: one where the fluid layer is heated from the bottom and concurrently salted from the bottom, and the other where the fluid layer is heated from the bottom and concurrently salted from the top. The governing partial differential equations system includes conservation laws of mass, momentum, energy, and salt concentration. Using the energy method, the disturbances to the fluid system are shown to decay exponentially. Analytical expressions are developed for the eigenvalue as a function of Soret, Lewis, Prandtl, Kelvin-Voigt, and Rayleigh friction numbers. The study illustrates the shift from a stationary mode of convection to an oscillatory mode and provides thresholds that indicate these transitions. It is found that the viscoelastic property of the fluid acts as a stabilizing agent for oscillatory mode convection. Rayleigh friction substantially controls the convection threshold. Upon comparing threshold values between linear and nonlinear theories, a subcritical instability region is observed in the heating bottom-salting bottom case (case-1), whereas such a region is absent in the heating bottom-salting top case (case-2). • Influence of Ekman damping on the convection in Kelvin-Voight fluid is highlighted. • Global nonlinear stability analysis of conduction solution has been performed. • Analytical expressions for the eigenvalue are obtained. • Conditions for the onset of convection are provided. • Transition from stationary convection to oscillatory convection is demonstrated. [ABSTRACT FROM AUTHOR]

A numerical model for a supercritical natural circulation loop is developed to examine the flow instabilities by nonlinear stability analysis. The supercritical natural circulation loop is a loop geometry, which is driven by natural circulation with supercritical fluids as a coolant. A mathematical formulation is developed to study the steady-state and transient solution procedure for supercritical natural circulation loop. This mathematical model is then used to perform various parametric studies with different supercritical fluids (water, CO 2 , R134a, ammonia, R22, propane, and isobutane). The behavior of all the fluids is analyzed on identical geometrical and operating conditions. A comprehensive numerical study of the nonlinear stability analysis is presented with particular emphasis on the feasibility of various fluids in a natural circulation loop environment. The 50% increment in loop diameter and height increased the stable operating zones and shifted the marginal stability boundary upward respectively by approximately three times and 25–40% of the previous value. However, further increase in diameter and height reduces the increment of stable operating zones; hence the marginal stability boundary shifts upward marginally than the previous value. Furthermore, the marginal stability boundaries are generated to identify the stable and unstable zones for the available geometrical and operating conditions. [ABSTRACT FROM AUTHOR]

The study examines the stability of parallel airflow within a tall vertical coaxial circular annulus filled with a highly permeable porous medium under stable stratification. The linear stability theory predicts that the least unstable mode can be either axisymmetric or non-axisymmetric, depending on the values of the governing parameters. The curvature parameter, defined as the gap between coaxial circular cylinders, contributes to the stabilization of the flow. Depending on various controlling parameter values, the stably stratified non-isothermal annular parallel flow (SNAPF) can manifest three instability modes: thermal-shear, thermal-buoyant, and mixed or interactive. The instability type can change abruptly with Reynolds number, curvature parameter, and media permeability. A finite-amplitude instability analysis is examined using weakly nonlinear stability theory. The analysis demonstrates both subcritical and supercritical bifurcations near the instability boundary. The range of Reynolds numbers for subcritical bifurcation expands when switching from axisymmetric to non-axisymmetric disturbance. Bifurcation transitions between supercritical and subcritical occur due to changes in the least stable azimuthal mode. The study also investigates the equilibrium/threshold amplitude within the supercritical/subcritical instability regime, and it verifies the existence of subcritical/supercritical bifurcation through nonlinear kinetic energy balance. Furthermore, the finite-amplitude analysis anticipates that the lower critical Rayleigh number increases as the Reynolds number, curvature parameter, or media permeability decreases. An increase in the Reynolds number shifts the point of inflection in the velocity profile toward the inner cylinder, which subsequently leads to a reduction in the size of the core vortex region. In the subcritical instability regime, the radius of the primary vortex cell decreased significantly as the Rayleigh number increased. When the curvature is altered, a structural transition occurs in the isotherms from multicellular to unicellular. • Stability analysis of mixed convection flow through an annular domain filled with a porous medium was studied. • The impact of the curvature parameter, media permeability, and form drag coefficient on the flow instability and bifurcation has been explored. • Instability mechanism was explored with the help of the kinetic energy budget. • Secondary flow pattern, both near and away from the instability boundary, was analyzed by examining vorticity and temperature distribution. • A range of Reynolds numbers and Rayleigh numbers corresponding to a subcritical bifurcation has been reported. [ABSTRACT FROM AUTHOR]

This article develops a comprehensive framework for stability analysis of a broad class of commonly used continuous- and discrete-time filters for stochastic dynamic systems with nonlinear state dynamics and linear measurements under certain strong assumptions. The class of filters encompasses the extended and unscented Kalman filters and most other Gaussian assumed density filters and their numerical integration approximations. The stability results are in the form of time-uniform mean square bounds and exponential concentration inequalities for the filtering error. In contrast to existing results, it is not always necessary for the model to be exponentially stable or fully observed. We review three classes of models that can be rigorously shown to satisfy the stringent assumptions of the stability theorems. Numerical experiments using synthetic data validate the derived error bounds. [ABSTRACT FROM AUTHOR]

The study of pedestrian evacuation in channels with different structures is important among optimizing through efficiency, avoiding accidents and designing passageway. It is of significant reference to set up a specific model on account of the real traffic system and design an appropriate controller to apply on it. This paper establishes a macroscopic model for T-shaped channel with a number of controlled entrances basing on the law of mass conservation. Then, with the method of cascade, a kind of sliding mode controller is designed to achieve the control target of avoiding the blocking and maximizing the pedestrian flow of the whole model, the stability of the system is proved by the Lyapunov stability theory, and the boundary layer method is applied to restrain the chattering of the controller. Finally, simulation results show the efficiency of the sliding mode controller and the improvement brought by the boundary layer method. [ABSTRACT FROM AUTHOR]

This paper investigates the nonlinear behavior associated with pure intrinsic thermoacoustic (ITA) modes. Unstable ITA modes dominate acoustic modes and drive system instability in certain parameter regimes of a combustor. Frequency of these modes are independently supported by flame dynamics and not influenced by combustor acoustic field. A network model is developed to examine the stability and bifurcation characters of ITA mode. The flame response is modelled using a second-order low pass filter coupled with n − τ model and amplitude response, which mimics the characteristic features of lean fully premixed turbulent bluff-body stabilized flames. Neutral curve expression obtained for anechoic boundary conditions points out that the bifurcation character of ITA mode strongly depends on gain amplitude response. A stability criterion is devised, where positive and negative slopes of gain amplitude response at A = 0 lead to subcritical and supercritical Hopf bifurcations respectively. In the case of subcritical Hopf bifurcation, fold point amplitude is found to depend only on flame response. However, this behavior is not observed for open-open boundary conditions. It is shown that including open-open boundary conditions with non-zero nonlinear time delay brings the effect of combustor parameters on stability boundary and bifurcation character of ITA modes. [ABSTRACT FROM AUTHOR]

This paper investigates the nonlinear instability of an interface between two magnetic fluids separated by a cylindrical interface in porous media. The system is influenced by a uniform axial magnetic field. The magnetic field intensities allow a presence of surface currents at the interface. The transfer of mass and heat across the interface is considered. The solutions of linearized equations of motion, under the appropriate nonlinear boundary conditions, lead to a nonlinear characteristic equation that is governed the behavior of the interface deflection. Drawing on the linear stability theory, Routh–Hurwitz's criteria are utilized to judge the stability criteria. The coupling of Laplace transforms and Homotopy perturbation techniques are adopted to obtain an approximate analytical solution of the interface profile. The nonlinear stability analysis resulted in two levels of solvability conditions. By means of these conditions, a Ginzburg–Landau equation is conducted. The latter equation represented the nonlinear stability configuration. The magnetic field intensity was plotted versus the wave number of the surface waves. Therefore, the stability picture was divided into stable and as well as unstable regions. Subsequently, the influence of the various physical parameters was addressed. [ABSTRACT FROM AUTHOR]

The semi-analytical solution for nonlinear stability analysis of imperfect doubly-curved laminated composite shallow shells with rotationally-restrained edges and under in-plane loading is presented. The nonlinear governing equations are established using the Galerkin method, and the arc-length and quadratic control method is implemented to capture the snapping phenomenon of the doubly-curved composite shells. The nonlinear load-displacement relationships of four special curvature radii of doubly-curved shell structures are obtained, and they are compared and validated with the numerical finite element solutions. A parametric study is conducted to evaluate the effects of the initial imperfection, edge rotationally-restrained spring stiffness, various load parameters, and curvature radius on the nonlinear stability behavior of doubly-curved shells. Finally, the computational efficiency and capability of the semi-analytical solution are demonstrated in comparison with the finite element analysis. The present semi-analytical solution can be effectively and efficiently used in simplified nonlinear stability analysis of complex doubly-curved composite shallow shells with periodic and restrained boundary conditions. • The semi-analytical solution for nonlinear stability analysis of imperfect doubly-curved shallow shells is presented. • Material anisotropy, geometrical imperfection, combined loading, edge restraint, and curvature radius are considered. • The snapping phenomenon of the doubly-curved shells is captured. • The computational efficiency and capability of the semi-analytical solution over the finite element analysis are discussed. [ABSTRACT FROM AUTHOR]

• Developing a general model to examine the effect of piecewise actuated substrate. • Introducing piezoelectric actuation to improve the controllability and operation range. • Analyzing the nonlinear pull-in instability of piezoelectric micro-wires. • Adjusting the maximum electrode deflection and threshold voltage by tuning the length and position of non-actuated parts. The main objective of this research is to provide a general nonlinear model of adjustable piezoelectric microwires with the ability to tune the stability conditions. In order to increase the controllability and improve system characteristics, only a part of the substrate is electrostatically actuated and the piezoelectric voltage is also applied. The governing equation of equilibrium (EOE) is derived from the principle of minimum total potential energy. The influences of the surface layer, size dependency, piezoelectricity, and dispersion forces are also included simultaneously. To solve the nonlinear differential equation, a numerical method is implemented and the obtained results are validated with available experimental and numerical results. Afterward, a set of parametric studies is carried out to examine the coupled effects of piezo-voltage, length/position of non-actuated pieces, nonlinear curvature, and molecular forces on the microresonators. It is found that the beam deflection and the pull-in voltage have sensitive-dependence on the system behavior. Furthermore, the beam deflection can increase or decrease with consideration of different positions of non-actuated pieces. This research is expected to fill a gap in the state of the art of the piezoelectric microstructures and present relevant results that are instrumental in the investigation of advanced actuated microdevices. Providing a general nonlinear model of piezoelectric microwires with the ability in adjusting stability conditions to improve the system characteristics. It was implemented by applying the piezo-voltage and/or actuating just a piece of the substrate electrostatically. Image, graphical abstract [ABSTRACT FROM AUTHOR]

With the increase of vehicles, traffic congestion has become a prominent problem. Environmental pollution, energy waste and even traffic accidents are easily caused by congestion. Nowadays, with the help of V2V and V2I communications, real-time interaction of vehicle information can be achieved. Vehicles can easily get information about other vehicles. In reality, a driver looks at the following car (i.e. upstream traffic condition) as well as the preceding car while driving. However, the effect of upstream condition is rarely analyzed. In the paper, a term describing the upstream traffic condition is added in Nagatani's model. The effect of the upstream traffic condition to linear stability is obtained by applying the perturbation method. Nonlinear stability equations, such as the mKdV equation, are also derived. Theoretical results of linear stability and nonlinear stability are shown intuitively through numerical simulations. It can be found that traffic is more stable when the upstream traffic condition is considered. [ABSTRACT FROM AUTHOR]

A new nonlinear approach on the buckling and postbuckling of functionally graded orthogonal and/or spiral-stiffened circular cylindrical shells subjected to torsional loads is proposed in this paper. The shells skin are stiffened by eccentrically rings, stringers, and/or spiral stiffeners at the surface of shells assuming that the material distribution laws of shell skin and stiffeners are graded by two distribution models. Lekhnitskii's smeared stiffeners technique is improved for spiral stiffeners with effect of thermal terms. This is the significant novelty and scientific contribution of this paper. Theoretical formulations were established by using the Donnell shell theory taking into account the geometrical nonlinearity of von Kármán. The obtained results investigated in numerical forms show effects of volume fraction exponent of shell skin and stiffeners, geometrical parameter and stiffeners on the torsional buckling, and postbuckling behavior of functionally graded cylindrical shells. Especially, very large effects of spiral stiffeners on torsional stability behavior are obtained in comparison with same quantity material of orthogonal stiffeners. [ABSTRACT FROM AUTHOR]

Traffic congestion has attracted considerable attention in modern society. Many researchers have proposed tremendous traffic flow models. These models can be divided into microscopic model, mesoscopic model and macroscopic model. With the progress of technology, it is possible to get the information of the preceding vehicles, i.e. the downstream traffic condition. Drivers can adjust their driving behaviors according to the downstream condition. This mechanism has been considered in microscopic model, and it is found that this mechanism can not only stabilize the traffic, but also bring about some new phenomena, such as synchronized traffic pattern. In the macroscopic model, what will the traffic flow be after considering the mechanism? In this paper, a term describing the downstream traffic condition is added in Nagatani's single-lane lattice model. Through theoretical study and numerical simulation, it can be found that traffic is more stable when the downstream traffic condition is considered. Besides, the modified model can reproduce the soliton wave, kink wave properly. Moreover, the amplitude and frequency of density wave with different influence forms of the front lattices on the current lattice are almost the same as found to reflect the different influence forms do not have significant effect on the stability. [ABSTRACT FROM AUTHOR]

This paper proposes a new nonlinear stability analysis for the acceleration-based robust position control of robot manipulators by using disturbance observer (DOb). It is shown that if the nominal inertia matrix is properly tuned in the design of a DOb, then the position error asymptotically goes to zero in regulation control and is uniformly ultimately bounded in trajectory-tracking control. As the bandwidth of a DOb and the nominal inertia matrix are increased, the bound of error shrinks, i.e., the robust stability and performance of the position control system are improved. However, neither the bandwidth of the DOb nor the nominal inertia matrix can be freely increased due to practical design constraints, e.g., the robust position controller becomes more noise-sensitive when they are increased. The proposed stability analysis provides insights into the dynamic behavior of DOb-based robust motion control systems. It is theoretically and experimentally proved that nondiagonal elements of the nominal inertia matrix are useful in improving the stability and in adjusting the tradeoff between robustness and noise sensitivity. The validity of the proposal is verified by simulation and experimental results. [ABSTRACT FROM AUTHOR]

In this paper, a new lattice two-lane hydrodynamic model is proposed by considering the lane changing and the optimal current change with memory effect. The linear stability condition of the model is obtained through the linear stability analysis, which depends on both the lane-changing rate and the memory step. A modified Korteweg–de Vries (mKdV) equation is derived through nonlinear analysis to describe the propagating behavior of traffic density wave near the critical point. To verify the analytical findings, numerical simulation was carried out, which confirms that the optimal current change with memory of drivers and the memory step contribute to the stabilization of traffic flow, and that traffic congestion can be suppressed efficiently by taking the lane-changing behavior into account in the lattice model. [ABSTRACT FROM AUTHOR]

In this study we will estimate the region of attraction (RoA) of the lateral dynamics of a nonlinear single-track vehicle model. The tyre forces are approximated using rational functions that are shown to capture the nonlinearities of tyre curves significantly better than polynomial functions. An existing sum-of-squares (SOS) programming algorithm for estimating regions of attraction is extended to accommodate the use of rational vector fields. This algorithm is then used to find an estimate of the RoA of the vehicle lateral dynamics. The influence of vehicle parameters and driving conditions on the stability region are studied. It is shown that SOS programming techniques can be used to approximate the stability region without resorting to numerical integration. The RoA estimate from the SOS algorithm is compared to the existing results in the literature. The proposed method is shown to obtain significantly better RoA estimates. [ABSTRACT FROM AUTHOR]

In this paper, an approach for carrying out bifurcation analysis of out of phase xenon oscillations has been demonstrated using a reduced order model. The reduced order model consists of multipoint kinetic equations coupled with xenon and iodine equations along with a lumped power coefficient feedback. A large Pressurised Heavy Water Reactor (PHWR) has been considered. The reactor core is divided into two regions for the analysis to present a “proof of principle” for this approach. However, extension of this approach for multiple regions, for better accuracy, though not trivial is quite straight forward. Bifurcation analysis has been carried out using nonlinear analysis tools like MATCONT and BIFOR considering the operating power level of operation, power coefficient of reactivity and reactor size as bifurcation parameters. The results show the existence of Generalized Hopf (GH) points which divides the parameter space into subcritical and supercritical Hopf bifurcation regions. The identification of subcritical Hopf bifurcation is important as it shows unstable limit cycles in the region identified as stable by linear stability analysis. [ABSTRACT FROM AUTHOR]

An overview is provided of dynamic artificial neural network models (DANNs) for nonlinear dynamical system identification and control problems, and convex stability conditions are proposed that are less conservative than past results. The three most popular classes of dynamic artificial neural network models are described, with their mathematical representations and architectures followed by transformations based on their block diagrams that are convenient for stability and performance analyses. Classes of nonlinear dynamical systems that are universally approximated by such models are characterized, which include rigorous upper bounds on the approximation errors. A unified framework and linear matrix inequality-based stability conditions are described for different classes of dynamic artificial neural network models that take additional information into account such as local slope restrictions and whether the nonlinearities within the DANNs are odd. A theoretical example shows reduced conservatism obtained by the conditions. [ABSTRACT FROM AUTHOR]

• Equivalence of two-phase flow model and Fitzhugh Nagumo (FHN) model established. • Instabilities in two-phase flow studied using the nonlinear analysis of FHN model. • System dynamics with instantaneous and periodic perturbation have been investigated. • Unattainable periodicity and spiked dynamics observed like many FHN applications. Two-phase flow systems are used in many industries for high heat transfer because these systems utilize latent heat of vaporization. However, these systems are susceptible to two-phase flow instabilities, which have been studied for the last several decades, mainly using numerical simulations and, to some extent, nonlinear stability analysis. These instabilities lead to flow excursions or flow oscillations and have recently been related to various nonlinear phenomena obtained by numerical continuation software. Further research of the instabilities shows that such systems' behavior is like the FitzHugh-Nagumo (FHN) model. Therefore, the existing two-phase flow model (with some reasonable approximations) is modified into a form identical to the FHN model. It is demonstrated that the modified model reasonably captures the physical attributes of the existing model. Moreover, it is shown that the phenomena described in the FHN model are the same as predicted by earlier models. Since FHN models and their various attributes are relatively well established, they can control the instabilities or operate the two-phase system at desired conditions. The characteristics of the system dynamics with various types of disturbance (instantaneous and periodic) have been investigated. The system provides an unattainable periodicity for periodic perturbation. In comparison, it responds with a single large amplitude or spike dynamics for instantaneous perturbation. [ABSTRACT FROM AUTHOR]

In this study we propose a simple, yet inherently fault-tolerant and robust controller utilizing a combination of both feedforward and feedback control schemes. Feedback controllers are known to be robust, but feedforward controllers can be reliable in the context of safety as they can be less dependent on measurements. Though, many combined feedforward and feedback controllers have been proposed in the literature, to the best of our knowledge a controller tolerant to the failure of power feedback signal is nowhere demonstrated. In this scheme, major corrections are effected by a model predictive forward control unit, while bounded uncertain part is corrected by a feedback control unit. The feedforward control is implemented using the inverse equations of the nuclear reactor point kinetics model. The bounded error control is effected by a simpler limited Proportional–Integral–Derivative (PID) feedback controller. Stability analysis of the controller is carried out numerically by Lyapunov's direct method with the help of Particle Swarm Optimization (PSO) technique. The proposed controller (referred to as Inverse Dynamics Corrected Control (IDCC)), is studied for reactor power control with model error plus uncertainty and a principal feedback signal failure case (i.e. power sensor failure). It is shown that the IDCC has excellent load tracking performance for a challenging demand profile with model error, in comparison to Sliding Mode Controller (SMC) and a manually tuned PID controller. For the loss of principal feedback signal case, there is a trade off between the tracking performance of IDCC and safety aspects. While both PID and SMC drive the reactor power to unsafe levels, IDCC maintains the reactor power within a safer bound. • A conceptually new controller tolerant to faults in feedback signal has been designed. • The controller's stability is analysed by Lyapunov's method with the particle swarm optimization. • The controller's fault tolerance, robustness and power tracking ability has been demonstrated. • The controller's performance is compared with PID and SMC controllers. [ABSTRACT FROM AUTHOR]

To analyse the steady state behaviour and dynamic density wave instabilities (DWIs) of super-critical pressure fluid (SCF) inside a natural circulation loop (NCL) for a heated section with parallel channels, a numerical thermal-hydraulic (TH) model is developed. The capability of the TH model to simulate the above mentioned aspects for a two channel heated section is validated with the existing numerical results and experimental data points. Steady state analysis is performed mainly to find the loop mass flow rate at different operating conditions. It is also aimed to correlate the loop mass flow rate with the driving head, i.e., with the difference in pressure drops due to gravity and friction. Next, the transient model is integrated with that of the steady state to analyse DWI. The model accounts for compressible flow dynamics of SCF and can deal with any number of parallel channels in the heated section while analysing DWIs. With the transient simulations, it is aimed to bifurcate the operating regime into stable and unstable regions, and find the marginal stability boundary (MSB). Extensive simulations are, next, performed to determine the effect of different parameters on the MSB and the findings are reported accordingly. • This work demonstrates the development of TH model for parallel channel NCL. • The model performs the steady–state and dynamic density wave instability analysis. • The TH model accounts for compressible flow dynamics of supercritical pressure fluid. • Simulates any number of parallel channels by treating boundary conditions naturally. • Identifies the core-wide and regional modes of DWOs in parallel channel NCL. [ABSTRACT FROM AUTHOR]

An improved optimal velocity model, which considers the velocity difference of two adjacent lanes, is presented in this paper. Using linear stability theory, the stability criterion of the new model is obtained and the neutral stability curves are plotted. By applying the reductive perturbation method, the nonlinear stability of the proposed model is also investigated and the soliton solution of the modified Korteweg-de Vries equation near the critical point is obtained to characterize the unstable region. All the theoretical analysis and numerical results demonstrate that the proposed model can characterize traffic following behaviors effectively and achieve better stability. [ABSTRACT FROM AUTHOR]

The stability of dc microgrids (MGS) depends on the control strategy adopted for eachmode of operation. In an islanded operation mode, droop control is the basic method for bus voltage stabilization when there is no communication among the sources. In this paper, it is shown the consequences of droop implementation on the voltage stability of dc power systems, whose loads are active and nonlinear, e.g., constant power loads. The set of parallel sources and their corresponding transmission lines aremodeled by an ideal voltage source in series with an equivalent resistance and inductance. This approximate model allows performing a nonlinear stability analysis to predict the system qualitative behavior due to the reduced number of differential equations. Additionally, nonlinear analysis provides analytical stability conditions as a function of the model parameters and it leads to a design guideline to build reliable (MGS) based on safe operating regions. [ABSTRACT FROM AUTHOR]

To increase the thermal resistance of various structural components in high-temperature environments, the present research deals with nonlinear stability analysis of thin annular spherical shells made of functionally graded materials (FGM) on elastic foundations under external pressure and temperature. Material properties are graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of constituents. Classical thin shell theory in terms of the shell deflection and the stress function is used to determine the buckling loads and nonlinear response of the FGM annular spherical shells. Galerkin method is applied to obtain closed – form of load – deflection paths. An analysis is carried out to show the effects of material, geometrical properties, elastic foundations and combination of external pressure and temperature on the nonlinear stability of the annular spherical shells. [ABSTRACT FROM AUTHOR]

This paper addresses the cubic autocatalator kinetics modeling of coupling via diffusion interchange of autocatalyst. By incorporating the effect of two identical cells, each governed by cubic autocatalator kinetics, considering the possibility of the spatiotemporal structures of two dimensional Turing patterns, a new model is proposed. Unlike previous models, the proposed model has two dimensional spatial variation. First, the equations and the local stability are obtained by linearizing about the spatially uniform solutions. It is shown that the necessary condition for the model undergoes bifurcation by using the singular perturbation theory. Next Landau constant and amplitude functions of two dimensional Turing patterns consisting of rhombic arrays of rectangles and hexagonal is obtain by singular perturbations theory. Finally, by the method of computer simulation of the model, we describe two different patterns. [ABSTRACT FROM AUTHOR]