Conditions For Absolute Stability Research Articles

System with nano piezoengine under randomly influences for biomechanics

The sufficient condition of absolute stability system with nano piezoengine by using the derivative of the hysteretic piezoengine deformation is determined for the randomly influences. The set of equilibrium positions of the piezoengine in the control system is stable relative to mathematical expectations, when the condition of absolute stability with the maximum piezo module is met. The statistical linearization method is using for the determination condition of absolute stability control system with the nano piezoengine.

Controller design and performance study of DC-DC bidirectional converter for speed regulation of permanent magnet direct current machine

This paper presents the design of a controller for a bidirectional DC-DC converter for speed control of a permanent magnet DC machine (PMDC). In recent years, this electric drive system has often been used in electric vehicles or hybrid electric vehicles. In this application, the development of a controller is required to support the various functions of the machine. The design methodology of the controller should provide satisfactory dynamic performance under both motor and generator operation of the PMDC machine. In this regard, the control of the bidirectional DC/DC converter is necessary. From the perspective of speed control, the condition for absolute stability is derived from the small-signal model of the PMDC drive system. Then the Ziegler-Nichols tuning table is used to determine the gain of the proportional-integral (PI) controller in the conventional way. From further investigation, it was found that the transient response and stability margin of the speed control loop in the conventional case are

Absolute Stability and Synchronization in Second-Order Neural Fields with Conduction Delays

We consider a class of neural field models represented by a second-order nonlinear system of integro-differential equations with space-dependent delays. Such a system models interaction of populations of neurons, each with a continuum description. We justify the existence and uniqueness of solution for the system in a suitable function space. Global existence and boundedness of solutions for the system are confirmed. Two methodologies, the comparison argument and sequential contracting, are developed to establish sufficient conditions for absolute stability and synchronization among different populations of the system. Finally, we present some numerical examples to demonstrate the theoretical results.

Two‐phase states of the generalized van der Waals gas: Conditions of absolute and neutral shock wave stability

AbstractIn this work we discuss an approach to the construction of the areas of two‐phase states for real gases, state equations for which are from the article by Fogelson and Likhachev in 2004 and formulate conditions that define absolute and neutral stability of the shock waves.

Vibration isolation performance and optimization design of a tuned inerter negative stiffness damper

A tuned inerter negative stiffness damper (TINSD) is a vibration isolation and energy dissipation device providing a negative stiffness effect, which has the dual damping enhancement effect of negative stiffness and inertance. To date, there have been several studies on TINSDs; however, these studies are incomplete in terms of optimization, isolation system parameter analysis and application in seismic engineering. Therefore, a systematic study of a TINSD in an isolation system is needed. This paper presents a theoretical and numerical study of a SDOF-TINSD system and a realistic structure-TINSD subjected to ground motion. The absolute transmissibility and stability condition of the SDOF-TINSD are derived, and the absolute stiffness value of the negative stiffness element should be less than the primary structural stiffness. The TINSD parameters are optimized based on the H∞ and H2 norms, and analytical solutions for the optimal parameters are obtained. The parameter and sensitivity analyses of the TINSD are carried out. For a known inertance-mass ratio, the vibration isolation performance can be improved by the negative stiffness. The TINSD is very sensitive to deviations of the positive stiffness ratio, and its optimal parameters require special attention. Finally, the vibration control effect of the optimal TINSD is evaluated for harmonic excitation, stationary random excitation and seismic excitation, and an optimization method based on nonstationary random seismic waves (NRSW) for isolators in realistic structures is proposed. The control effect of the TINSD is better than that of the TID and TVMD with the same inertance-mass ratio. Moreover, the TINSD optimized by NRSW has a better seismic response control effect than the H∞ and H2 optimization methods.

Exponential stability analysis for a class of switched nonlinear time-varying functional differential systems

This paper proposes a unified approach for studying global exponential stability of a general class of switched systems described by time-varying nonlinear functional differential equations. Some new delay-independent criteria of global exponential stability are established for this class of systems under arbitrary switching which satisfies some assumptions on the average dwell time. The obtained criteria are shown to cover and improve many previously known results, including, in particular, sufficient conditions for absolute exponential stability of switched time-delay systems with sector nonlinearities. Some simple examples are given to illustrate the proposed method.

Superior transient and stability performance of voltage regulation by battery-fed bidirectional converter for supporting various operational modes of PMDC machine

This paper presents a systematic procedure to design a voltage controller for achieving superior dynamic performance of a battery-fed bidirectional converter for supporting both motoring and regenerative operations of a permanent magnet direct current (PMDC) machine. In this respect, derivation of a small signal model of overall system is given. Next, the condition for absolute stability is calculated from the model on the basis of the Routh-Hurwitz criterion. Then, gains of the proportional-integral (PI) controller have been tuned using the Ziegler-Nichols tuning chart as per the conventional approach. But, the calculated gains from Ziegler-Nichols tuning chart do not provide satisfactory dynamic performance and sound stability margin under variable voltage conditions. Thus, performance of voltage regulation is deeply investigated and redesign of the voltage controller is emphasised through further mathematical analysis for achieving both superior dynamic performance and significantly stronger stability margin. Superiority of this proposed approach is verified in MATLAB-SIMULINK software based modelling of the physical system and also, in experimental platform.

Absolute versus stochastic stability of the artificial bee colony in synchronous and sequential modes

The artificial bee colony (ABC) is a population-based optimization algorithm that mimics the foraging behavior of honeybees. Here, we focus on the parameter setting that ensures the ABC algorithm stability. Therefore, this paper introduces a matrix-iterative model, taking into account the coupling within bees. Moreover, the model considered the difference between update modes, i.e., synchronous or sequential. The necessary conditions for absolute stability were derived under the quasi-deterministic assumption. We further investigated the criteria for first and second-order stochastic stability. These criteria report on the ranges for setting the uniform distributions of the ABC algorithm. Finally, some supporting simulations were carried out on CEC 2017 benchmark functions in different search space dimensions (10, 30, and 50) and on twenty real-world problems (CEC 2011). Six considered ABC variants tested the derived and state-of-the-art criteria in different update modes. Moreover, ABC algorithms were compared with some state-of-the-art metaheuristics (Particle Swarm Optimization, Gravitational Search Algorithm, and Grey Wolf Optimizer). The overall results show that stochastic stability proffers ABC competitiveness. The two update modes may alter the ABC performance only slightly or drastically, depending on the problem, with no evidence on the supremacy of one of them.

Tools for assessing the financial stability of the enterprise

This article describes in detail one of the main tools for assessing the financial stability of an enterprise. The study describes a method for analyzing the financial stability of an enterprise based on relative indicators: its own working capital, the aggregate of its own and long-term funds, the total amount of sources for the formation of reserves and costs of an economic entity, and shows practical calculations on the example of an economic entity. The study reveals the essence of the method for determining one of the four types of financial situation: absolute stability, normal stability, unstable and crisis financial condition. The types are characterized based on the values of the threecomponent indicator of financial stability. Based on the results of the analysis of financial stability based on relative indicators, conclusions and proposals are made, with emphasis on the stabilization of the financial situation. The advantages and disadvantages of using the studied tool for assessing the financial stability of the enterprise are also highlighted.

Delay stability of reaction systems

Delay differential equations are used as a model when the effect of past states has to be taken into account. In this work we consider delay models of chemical reaction networks with mass action kinetics. We obtain a sufficient condition for absolute delay stability of equilibrium concentrations, i.e., local asymptotic stability independent of the delay parameters. Several interesting examples on sequestration networks with delays are presented.

Exponential Stabilization of Linear Time-Varying Differential Equations with Uncertain Coefficients by Linear Stationary Feedback

We consider a control system defined by a linear time-varying differential equation of n-th order with uncertain bounded coefficients. The problem of exponential stabilization of the system with an arbitrary given decay rate by linear static state or output feedback with constant gain coefficients is studied. We prove that every system is exponentially stabilizable with any pregiven decay rate by linear time-invariant static state feedback. The proof is based on the Levin’s theorem on sufficient conditions for absolute non-oscillatory stability of solutions to a linear differential equation. We obtain sufficient conditions of exponential stabilization with any pregiven decay rate for a linear differential equation with uncertain bounded coefficients by linear time-invariant static output feedback. Illustrative examples are considered.

Условие абсолютной устойчивости системы управления электроупругим актюатором для наномехатроники

An electroelastic actuator for nanomechatronics is used in nanotechnology, adaptive optics, microsurgery, microelectronics, and biomedicine to actuate or control mechanisms, systems based on the electroelastic effect, and to convert electrical signals into mechanical displacements and forces. In nanomechatronic systems, a piezoactuator is used in scanning microscopy, laser systems, in astronomy for precision alignment, for compensation of temperature, gravitational deformations and atmospheric turbulence, focusing, and stabilizing the image. In this study, a condition for absolute stability of an electroelastic actuator control system for nanomechatronics under deterministic and random inputs is obtained. A number of equilibrium positions in an electroelastic actuator mechatronic control system are found, the totality of which is represented by a straight line segment. The electroelastic actuator’s deformation control system dead band relative width is determined for the actuator’s symmetric and asymmetric hysteresis characteristics. Under deterministic inputs and with fulfilling the condition for the derivative of the nonlinear hysteresis actuator deformation characteristic, the set of equilibrium positions of the electroelastic actuator control system for nanomechatronics is absolutely stable. Under random inputs, the system absolute stability with respect to the mathematical expectations of the electroelastic actuator mechatronic control system equilibrium positions has been determined subject to fulfilling the condition on the derivative of the actuator hysteresis characteristic.

Linear Matrix Inequalities in Stability Problems: Retrospective and Theoretical Aspects

Some aspects of the development of the theory of linear matrix inequalities are considered. A number of results obtained at the initial stage of the development of this theory, both in the development of numerical methods and in obtaining analytical conditions for their solvability, are highlighted. The main attention is focused on the system of linear matrix inequalities arising in solving the absolute stabi lity problem. E. S. Pyatnitskiy and his followers showed that the solvability of this system is a criterion for the existence of a quadratic Lyapunov function and a sufficient condition for absolute stability. The prerequisites leading to this result are considered here. The use of the considered system of inequalities for studying the stability of hybrid systems described by differential inclusions and switching systems is shown. An analysis is given of citing some works of Pyatnitskiy’s school on the theory of stability and the theory of systems of linear matrix inequalities, from which the relevance of the results of these works at the present time follows.In developing numerical methods, it was first shown in the work of Pyatnitskiy and Skorodinskiy that the solvability problem for a system of linear matrix inequalities reduces to a convex programming problem. An interesting gradient algorithm for finding solutions to such a system is also presented. In analyzing analytical conditions of solvability, an unsolvability criterion for the system of our interest obtained by Kamenetskiy and Pyatnitskiy is noted. In modern terms, this result can be considered as a description of an admissible set in the dual semidefinite programming problem. A similar result is given in the famous book by S. Boyd et al. The paper shows that the result of Boyd et al. is a simple corollary of the unsolvability criterion. Here the unsolvability criterion is generalized and refined.

Experimental Assessment of Absolute Stability in Bilateral Teleoperation.

Absolute stability analysis of bilateral teleoperation systems are typically model-based. Under borderline conditions of absolute stability, depending on the degree of uncertainty in the dynamic model of the teleoperator and existing noise, the system may behave as potentially unstable when the model-based analysis predicts otherwise. In this article, we propose a methodology to experimentally verify the absolute stability of master-slave teleoperation systems. Since absolute stability demands bounds of all possible environments, we achieve this by conducting only three experiments that are often experienced in teleoperation: free slave, mass-carrying slave and locked slave (rigid environment). We will validate and compare our proposed method with the benchmark Llewellyns absolute stability criterion. Furthermore, we will examine the robustness of the proposed method and will provide guidelines for choosing the mass for the mass-carrying load condition.

Absolute Stability Condition Derivation for Position Closed-Loop System in Hydraulic Automatic Gauge Control

In the metallurgical industry, hydraulic automatic gauge control (HAGC) is a core mechanism for thickness control of plates used in the rolling process. The stability of the HAGC system’s kernel position closed-loop is key to ensuring a process with high precision, speed and reliability. However, the closed-loop position control system is typically nonlinear, and its stability is affected by several factors, making it difficult to analyze instability in the system. This paper describes in detail the functioning of the position closed-loop system. A mathematical model of each component was established using theoretical analysis. An incremental transfer model of the position closed-loop system was also derived by studying the connections between each component. In addition, based on the derived information transfer relationship, a transfer block diagram of disturbance quantity of the system was established. Furthermore, the Popov frequency criterion method was introduced to ascertain its absolute stability. The results indicate that the absolute stability conditions of the position closed-loop system are derived in two situations: when spool displacement is positive or negative. This study lays a theoretical foundation for research on the instability mechanism of an HAGC system.

Solution Estimates for Semilinear Non-autonomous Evolution Equations with Differentiable Linear Parts

In a Hilbert space we consider the equation $$du(t)/dt=A(t)u(t)+F(t,u(t))$$ , where A(t) is an unbounded operator, having a bounded strong derivative, and F is a continuous mapping. We derive norm estimates for solutions of the considered equation. These estimates give us the $$L^2$$ -stability and absolute stability conditions. To the best of our knowledge an absolute stability test for nonautonomous evolution equations has been obtained for the first time. Our main tool is the norm estimate for the derivative of a solution of the time-dependent Lyapunov equation.

On the melting of interstitial alloys FeH, FeSi and FeC with a body-centred cubic structure under pressure

Taking the model of interstitial alloy AB with a body-centred cubic structure and the condition of absolute stability for the crystalline state, we derive analytic expression for the temperature of the limit of absolute stability for the crystalline state, the melting temperature, and the equation for the melting curve of this alloy using the statistical moment method. The results allow us to determine the melting temperature of alloy AB under pressure as well as at zero pressure. In limit cases, we obtain the melting theory of main metal A with a body-centred cubic structure. The theoretical results are numerically applied for alloys FeH, FeSi and FeC using different potentials.

A Multi-loop Switching Controller for Aircraft Gas Turbine Engine with Stability Proof

In this paper, a Min-Max switching controller containing multiple state feedback regulators and fuel flow rate saturation is designed for a high bypass two-spool turbofan engine. Due to the switching nature of Min-Max algorithm and the presence of saturation function, stability analysis is an important issue in the process of controller design. Therefore, a methodology is presented to analyze the stability of the closed loop system. For this objective, the Min and Max selectors and the saturation block are replaced by their nonlinear equivalents and the structure of the control system is transformed into the canonical configuration of Lure’s system. Then, the condition for absolute stability is extracted using the Multivariable Circle Criterion. An asymptotic stability proof is achieved for the closed loop system and the performance of the designed multiregulator Min-Max controller in tracking a desired fan speed scenario and limit management is compared with the well-known Min-Max/SMC technique.

Study on the melting of interstitial alloys FeH and FeC with BCC structure under pressure

From the model of interstitial alloy AB with BCC structure and the condition of absolute stability for crystalline state we derive analytic expression for the temperature of absolute stability for crystalline state, the melting temperature and the equation of melting curve of this alloy by the way of applying the statistical moment method. The obtained results allow us to determine the melting temperature of alloy AB at zero pressure and under pressure. In limit cases, we obtain the melting theory of A main metal with BCC structure. The theoretical results are numerically applied for alloys FeH and FeC with using different potentials.

Constrained Dendritic Growth and Solute Concentration Effects in Rapidly Solidified Co-Cr Alloys

Growth temperature and dendrite tip radius equations were employed in this work in order to predict the experimental conditions under which a Co-Cr alloy was produced having a single γ-phase microstructure free from interdendritic segregation. The outcome of these predictions indicated that in Co alloys containing 20 to 25 wt pct Cr, single γ-phase dendritic microstructures are achieved independently of the implemented solidification growth velocities. Moreover, these alloys are found to be essentially free from interdendritic segregation. Co alloys containing 30 to 35 wt pct Cr exhibit both the γ-phase and the eutectic constituent when solidification rates (V) are below 0.1 and 0.5 mm/s, respectively. Alternatively, the eutectic constituent is suppressed when the solidification growth velocities exceed these values. In particular, it is found that a single-phase microstructure can be achieved when the solidification growth rates exceed the transition velocity between constitutional supercooling and the absolute stability conditions.