Hurwitz Stability Criterion Research Articles

Model experiments and study on regulating stability of isolated hydropower plants

Hydropower shoulders a large portion of the regulation and balancing duty in many power systems all over the world. The stable regulation of hydropower plants (HPPs) is a conventional and crucial research topic, and many meaningful studies have been carried out by theoretical analysis and numerical simulations; however seldom experimental works on this issue are reported. This paper investigates stability of isolated HPPs based on model experiments on an integral experiment platform for transient processes of pumped storage plants in Wuhan University. Theoretical stability analysis is conducted based on Routh – Hurwitz stability criterion, and the stability region of the model power plant is obtained. The experiment results validate the theoretical analysis on the system stability, and the instability of the hydropower system due to poor settings of speed governor parameters are captured and demonstrated. This work presents initial results of experimental study on oscillation characteristics and regulation performance of HPPs for power system stability.

Eliminating the Fluid‐Induced Vibration and Improving the Stability of the Rotor/Seal System Using the Inerter‐Based Dynamic Vibration Absorber

A theoretical research on eliminating the instability vibration and improving the stability of the rotor/seal system using the inerter‐based dynamic vibration absorber (IDVA) is presented in this paper. The modified Jeffcott rotor and Muszynska nonlinear seal force models are employed. The proposed IDVA is the damping element of the traditional dynamic vibration absorber (DVA) replaced by one of the six configurations of the inerter. The instability threshold speed of the system is obtained by applying the Routh–Hurwitz stability criterion. The quantum particle swarm optimization (QPSO) method is utilized to optimize the parameters of the IDVA. The numerical method is applied to investigate the nonlinear dynamic responses and stability. The results show that the IDVA can effectively improve the stability and reduce the instability vibration of the rotor/seal system. Furthermore, the performance of the IDVA is more effective than that of the traditional DVA.

Nonlinear Torsional Vibration Analysis and Control of Semidirect Electromechanical Coupling Transmission System in Shearer

The nonlinear torsional vibration and instability oscillation caused by nonlinear damping in the shearer electromechanical coupling cutting transmission system in shearer driven by the permanent magnet synchronous motor (PMSM) is investigated in this paper. The electromechanical coupling transmission system in the shearer is equivalent to a concentrated mass model for the purpose of establishing the system dynamic model by the Lagrange–Maxwell equation. Then, the Routh–Hurwitz criterion is used to determine the torsional vibration critical point and stability region for the Hopf bifurcation for the cutting transmission system. According to the Routh–Hurwitz stability criterion, the Hopf bifurcation type and the effect of the supercritical Hopf bifurcation in the torsional vibration of the cutting transmission system are analyzed. Furthermore, based on the washout filter, the Hopf bifurcation controller is designed for suppressing the transmission system’s large vibration amplitude and unstable oscillation. In addition, the influences of the linear gain and nonlinear gain on the bifurcation point and the limit cycle amplitude are discussed. Finally, the numerical simulation results indicate the effectiveness of the designed controller. The research achievements can provide a theoretical basis for design or optimize the cutting transmission system of high‐reliability shearer driven by PMSM.

Control of Memristor-Based Simplest Chaotic Circuit with One-State Controllers

This paper deals with the control of the memristor-based simplest chaotic circuit by means of only one-state controller. Three distinct control techniques, namely linear feedback control, sliding mode control, and nonlinear control, are examined for the control. Routh–Hurwitz stability criteria are used for constructing the linear feedback and sliding mode gains. Lyapunov function is used for ensuring the global asymptotic stability of the system with the nonlinear controller. Numerical simulations are demonstrated not only to validate the theoretical analyses, but also to compare the control results. They have shown that even if one-state controller is used, all the methods are effective for controlling the memristor-based simplest chaotic circuit. However, the control is observed in a better time period with the sliding mode controller.

Charge and Discharge Control Method for Grid-Connected Electric Vehicle

A inverter with LCL filter was adopted as a main interface between electric vehicle and power grid. The mathematical model of the LCL filter was built, and then a charge and discharge control method for grid-connected electric vehicle was proposed. This control method employed an outer grid-side current loop and an inner inverter-side current loop. And this control method can protect power switches effectively, but also ensure the system stability and high in-grid power factor. Based on the Hurwitz stability criterion and Lienard Chipart stability criterion, the design method of controller parameters in inner and outer loops is derived. Simulations and experiments of electric vehicle in grid-connected mode have been conducted. Simulation and experiment results validate the correctness and feasibility of the proposed method.

Aggregation and the economy prototyping of municipality in the conditions of lability and robust changes

Purpose of the study . The purpose of the scientific paper is the formation of a model of managing the economy of municipality through aggregation and prototyping in conditions of lability and robustness of changes. As part of the stated goal, the author is supposed to conduct the economy prototyping of the municipality based on built-in management platforms; to form an adapted risk assessment model in the implementation of smart-project; to propose an aggregated model for assessing the development of the economy. Materials and methods . While writing a scientific article, the methods of situational and simulation modeling, approximation and grouping of specific elements of the structural object, and the process of algorithmization of functional processes are used. Particular emphasis in this paper is made on the methodological apparatus, which allows drawing conclusions based on subjective author’s opinion, to take into account external changes in the system under study. These methodological approaches include entropy of scientific knowledge, aberration, approximation, robustness. Results. Within the framework of the conducted research the following conclusions are formed: the municipal economy is in the process of transformation, it is possible to obtain positive changes with the help of prototyping the model of municipality; smart- projects as the basis of the economy of the municipality are subject to robustness and lability of changes, provoking negative risks; game theory is a rather important tool, used in the context of the definition of the riskiness of the smart-project the aggregated model for assessing the development of the economy of the municipality makes it possible to formulate certain premises of the Smart City concept in municipalities. Conclusion. For the effective development of municipalities, it is necessary to transform the economies towards the formation of municipality based on using prototyping and aggregation tools in conditions of lability and robustness of the changes. Presented in the scientific paper, the aspect of aggregation and prototyping of the economy of the municipal formation is the initial stage in the development of the concept of management of the Smart Economy of the municipal formation. The transformation of municipal economies regulates the need for a new tool for the development of these territories. The author of the scientific article proposes to use the adapted model of risk assessment of Smart-design based on game theory and the aggregated model for assessing the development of the economy of a municipal formation. The adapted model of risk assessment of Smart-design on the ground of the theory of games is based on the use of the Bayes criterion, Wald’s maximin criterion, the Savage decision-making criterion, the Hurwitz stability criterion, the Hodges-Lehmann criterion. The selected criteria contribute to the definition of the least risky Smart- project with the aim of its implementation in the municipal economy. The aggregated model for assessing the economy development of the municipal entity projects the regression parameter data algorithm – Constructive Coste Model (COCOMO) on the basis of which a conclusion is given about the level of the economy development of the municipal formation. In the future, simulation models of economic management can supplement this study in conditions of the prevalence of knowledge and intelligence, as well as methods for assessing the quality of urban technological infrastructure.

The Modeling Dynamics of HIV and CD4 $$^{+}$$ + T-cells During Primary Infection in Fractional Order: Numerical Simulation

This article is devoted to introduce a numerical treatment using Adams–Bashforth–Moulton method of the fractional model of HIV-1 infection of CD4 $$^{+}$$ T-cells. We study the effect of the changing the average number of viral particles N with different sets of initial conditions on the dynamics of the presented model. The fractional derivative is described in Caputo sense. Special attention is given to present the local stability of the proposed model using fractional Routh–Hurwitz stability criterion. Qualitative results show that the model has two equilibria: the disease-free equilibrium and the endemic equilibrium points. We compare our numerical solutions with those numerical solutions using fourth-order Runge–Kutta method (RK4). The obtained numerical results of the proposed model show the simplicity and the efficiency of the proposed method.

Dynamics and nonlinear feedback control for torsional vibration bifurcation in main transmission system of scraper conveyor direct-driven by high-power PMSM

The main transmission system of a scraper conveyor direct-driven by the high-power permanent magnet synchronous motor (PMSM) is taken as a study object. With the effect of the nonlinear friction torque caused by the nonuniformity of the transported coal quality in the operation process considered, the torsional vibration bifurcation mechanism and the corresponding control measures for the main transmission system of the scraper conveyor are investigated. Firstly, based on the Lagrange–Maxwell principle, the global electromechanical-coupling dynamic models for the main transmission system of the scraper conveyor are constructed. Secondly, by the Routh–Hurwitz stability criterion, the Hopf bifurcation characteristics of the main transmission system are analyzed to reveal the influence of supercritical bifurcation and subcritical bifurcation on the torsional oscillation of the transmission shafting. Thirdly, in order to suppress the system unstable oscillation caused by the Hopf bifurcation, the motor speed is fed back to construct the nonlinear state feedback controller for the quadrature axis current of the PMSM by the $$I_{d}=0$$ vector control strategy. Similarly, on the basis of the Routh–Hurwitz criterion, the influence of the linear feedback coefficient in the nonlinear state feedback controller on the system bifurcation position is discussed. Meanwhile, by the central manifold theory and canonical form theory, the effect of the square and cubic nonlinear feedback coefficients on the Hopf bifurcation type of the torsional vibration and the amplitude of the stable limit cycle are investigated. Finally, the numerical simulation results show the effectiveness of the designed controller.

Performance analysis of single EWMA controller subject to metrology delay under dynamic models

ABSTRACTThis article mainly focuses on analyzing the performance of a closed-loop system where a single exponentially weighted moving average controller (SEWMA) subject to metrology delay is applied to regulate a semiconductor manufacturing process that exhibits input–output dynamics. Based on the Hurwitz stability criterion, the sufficient and necessary conditions for the stability of the closed-loop system are established. Based on these, it is convenient to study the effect of metrology delay on the feasible region of the weighting factor in the SEWMA controller. Later, under the stability condition, the asymptotical properties of the SEWMA controller are discussed and the performance of the closed-loop control system is analyzed in terms of the asymptotical variation and the transient deviation in the presence of several typical types of process stochastic disturbance. Then an optimization model is built to find the appropriate weighting factor to reduce the overall variation of the process output during production. Finally, extensive simulations are carried out to demonstrate the validity of our theoretical analysis in the context of chemical–mechanical planarization process.

Система автоматической регулировки амплитуды колебаний для однокольцевого RC-автогенератора

Harmonic RC oscillators have long been known and are widely used in various fields of radio engineering. They have become widely used in medical equipment, various sensors, measuring equipment, etc. Their main advantages in operating within short to long wave frequency bands are compact dimensions, simplicity and low cost of manufacturing, possibility of widely retuning the frequency, etc. In our previous articles, we examined several versions of such circuits, including single-loop RC oscillators, which are the simplest ones. It was shown that the major disadvantage of such self-oscillators in generating close-to-sinewave signals is the need to operate them with a very small self-excitation margin. An attempt to increase the self-excitation margin inevitably leads to a growth of higher harmonic components, distortion of the output signal, and failure of oscillations. As a result, additional techniques must be used to secure stable steady-state operation. One of such techniques is automatic amplitude control (AAC). With the AAC circuit switched in operation, the generator output signal amplitude is controlled, due to which a larger self-excitation margin is obtained at the initial time instant, and the required amplitude value is maintained during steady-state operation. The article presents a version of such system taking as an example a single-loop self-oscillator with the Wien bridge in the feedback circuit. As is known, the list of important issues to be taken care of in designing AAC systems includes, among other things, an analysis of their stability and the selection of time constants for the system functional units. There are many methods for analyzing the stability of an AAC system, and all of them involve the need to set up differential equations of the system. A version of addressing this objective is presented to produce the system of differential equations describing the operation of a self-oscillator fitted with the AAC system. The obtained system of equations was applied for selecting — using the Routh–Hurwitz stability criterion — the time constant for the low-pass filter (LPF) of the AAC system amplitude detector (AD). It has been shown that the selection of the time constant for the AD LPF is constrained, on the one hand, by the requirements for the amplitude detector operation mode, and on the other hand, by the need to ensure fast response of the AAC system to variations of the generator voltage amplitude. The time histories of the system response to variations of the generator voltage amplitude and the system phase-plane portrait have been obtained.

On the Design of Output Feedback Controllers for LTI Systems Over Fading Channels

This paper considers linear time-invariant control systems over fading channels in both continuous-time and discrete-time cases and addresses the design of output feedback controllers that stabilize the closed-loop system in the mean square sense. It is shown that a sufficient and necessary condition for the existence of such controllers can be obtained by solving a convex optimization problem in the form of a semidefinite program. This condition is obtained by reformulating mean square stability as asymptotical stability of a suitable matrix comprising plant, controller, and channel, and by introducing modified Hurwitz and Schur stability criteria.

Analysis of dynamic characteristics and stability prediction of gas bearings

PurposeThe prediction model to estimate the stability of a rotor-bearing system is established, which can predict the stability of gas bearings by applying Routh–Hurwitz stability criterion. This paper aims to provide the theoretical foundation for controlling actively the bearing running stiffness and damping and stemming the instability of a gas film.Design/methodology/approachThe nonlinear dynamic lubrication analysis mathematical model of spherical hybrid gas bearings is established. Perturbation control equation is derived by the partial derivative method. The finite difference method is used to discrete the perturbation control equation in generalized coordinate system, and the difference expression of perturbation pressure is derived. The relational expression which involves the relationship between the dynamic characteristic coefficients of HSGHGB systems and perturbation pressure is deduced. So, the transient perturbation pressure distribution of a three-dimensional micro gas film, nonlinear gas film force, dynamic stiffness and dynamic damping coefficients of bearings are numerically computed using VC++6.0 programs.FindingsThe results show that the influence of supply pressure, speed and eccentricity on the dynamic characteristics of bearings is significant.Originality/valueThe influence law of supply pressure, speed and eccentricity ratio on the dynamic stiffness and damping coefficients of HSGHGB systems is researched. The prediction model to estimate the stability of rotor-bearing system is established, which can predict the stability of gas bearings by applying the Routh–Hurwitz stability criterion.

Smith predictor based parallel cascade control strategy for unstable and integrating processes with large time delay

This manuscript presents a modified parallel cascade control structure (PCCS) with Smith predictor for open loop unstable and integrating process models with large time delay. The proposed PCCS consists of a secondary disturbance rejection controller, a primary stabilizing controller and a primary setpoint tracking controller. Parameters of the setpoint tracking controller are obtained by equating the first and second derivatives of desired and actual closed-loop transfer functions at s=0 whereas the secondary disturbance rejection controller is designed using internal model control approach. Routh–Hurwitz stability criterion is used to design the stabilizing controller of the primary loop. An analytical expression for computing the primary closed-loop time constant in terms of known plant model parameters is obtained. Moreover, a suitable value is recommended for the secondary closed-loop time constant based on extensive simulation studies. This is an advantage of the present work over the contemporary Smith predictor based parallel cascade control schemes where the authors provide suitable range of values for the closed-loop time constants. Simulation results illustrate that the proposed method yields significant improvement in closed-loop performance compared to the recently reported tuning strategies for nominal and perturbed process models.

Stabilization of a Network of the FitzHugh–Nagumo Oscillators by Means of a Single Capacitor Based RC Filter Feedback Technique

We suggest employing the first-order stable RC filters, based on a single capacitor, for control of unstable fixed points in an array of oscillators. A single capacitor is sufficient to stabilize an entire array, if the oscillators are coupled strongly enough. An array, composed of 24 to 30 mean-field coupled FitzHugh–Nagumo (FHN) type asymmetric oscillators, is considered as a case study. The investigation has been performed using analytical, numerical, and experimental methods. The analytical study is based on the mean-field approach, characteristic equation for finding the eigenvalue spectrum, and the Routh–Hurwitz stability criteria using low-rank Hurwitz matrix to calculate the threshold value of the coupling coefficient. Experiments have been performed with a hardware electronic analog, imitating dynamical behavior of an array of the FHN oscillators.

Research on slow‐scale bifurcation phenomenon of PFC cascade converter

This study reports a new slow-scale bifurcation phenomenon in linear frequency of power factor correction (PFC) cascade converters, which will offer a useful design reference for PFC power application. Compared with the resistive loads analysed before, the stability of PFC cascade converters is studied, which are more complex but practical. This study has introduced the research method that the secondary efficient point-of-load converter can be equivalent to a constant power load. Based on this method, the small-signal model of the whole system is constructed and the characteristic equations are thus derived. Subsequently, the stable boundary is determined when the coefficients of the characteristic equations are positive according to Routh–Hurwitz stability criterion. Furthermore, the time-domain waveforms and phase portraits between the output voltage and the inductor current are given according to numerical simulation and experimental results at different points. Meanwhile, the total harmonic distortion and the fast Fourier transform diagrams are compared to reveal the influence of the bifurcation phenomenon on power quality of the system. The results provide useful information of parameter space for the design and operation of the converter in the desired fundamental stable regime.

Dynamic Stability Prediction of Spherical Spiral Groove Hybrid Gas Bearings Rotor System

Taking the hemisphere spiral groove hybrid gas bearings (HSGHGB) as the research object, the nonlinear dynamic lubrication analysis mathematical model of spherical hybrid gas bearings is established with the axis instantaneous position and instantaneous displacement speed as the parameters. The perturbation pressure control equation is solved by means of the finite difference method in generalized coordinate system. The calculation program is prepared based on VC++6.0, and the transient perturbation pressure distribution of three-dimensional (3D) gas film, nonlinear gas film force, and dynamic stiffness and damping coefficients are numerically calculated. The influences of different speeds, eccentricity ratios, and gas supply pressures on the dynamic characteristic coefficients of gas film are studied. The results show that the influence of bearing's supply pressure, speed, and eccentricity on the dynamic characteristics of gas film is significant. The dynamic equations of rotor-bearing system containing the gas film dynamic stiffness and the damping coefficients are established, and the stability of the gas film is predicted based on the Routh–Hurwitz stability criterion. The research provides the theoretical foundation for actively controlling the bearing running stiffness and damping and stemming the instability of gas film.

Stability and Scalability of Homogeneous Vehicular Platoon: Study on the Influence of Information Flow Topologies

In addition to decentralized controllers, the information flow among vehicles can significantly affect the dynamics of a platoon. This paper studies the influence of information flow topology on the internal stability and scalability of homogeneous vehicular platoons moving in a rigid formation. A linearized vehicle longitudinal dynamic model is derived using the exact feedback linearization technique, which accommodates the inertial delay of powertrain dynamics. Directed graphs are adopted to describe different types of allowable information flow interconnecting vehicles, including both radar-based sensors and vehicle-to-vehicle (V2V) communications. Under linear feedback controllers, a unified internal stability theorem is proved by using the algebraic graph theory and Routh–Hurwitz stability criterion. The theorem explicitly establishes the stabilizing thresholds of linear controller gains for platoons, under a large class of different information flow topologies. Using matrix eigenvalue analysis, the scalability is investigated for platoons under two typical information flow topologies, i.e., 1) the stability margin of platoon decays to zero as $0(\mbox{1}/N^{2})$ for bidirectional topology; and 2) the stability margin is always bounded and independent of the platoon size for bidirectional-leader topology. Numerical simulations are used to illustrate the results.

Study of Mathematical Modeling on Effect of Swine Flu

This mathematical model used Routh–Hurwitz Stability Criterion to provide the critical evaluation of the epidemics of Swine Flu. We introduce the Jacobian to determine the effect of variations in the potential of the epidemic for their prediction. Stability of infectious diease through this model is depend upon eigen value λi >,=,< 0; i=1,2,3 and found the given system marginally stable.

Stabilisation of matrix polynomials

A state feedback is proposed to analyse the stability of a matrix polynomial in closed loop. First, it is shown that a matrix polynomial is stable if and only if a state space realisation of a ladder form of certain transfer matrix is stable. Following the ideas of the Routh–Hurwitz stability procedure for scalar polynomials, certain continued-fraction expansions of polynomial matrices are carrying out by unimodular matrices to achieve the Euclid’s division algorithm which leads to an extension of the well-known Routh–Hurwitz stability criteria but this time in terms of matrix coefficients. After that, stability of the closed-loop matrix polynomial is guaranteed based on a Corollary of a Lyapunov Theorem. The sufficient stability conditions are: (i) The matrices of one column of the presented array must be symmetric and positive definite and (ii) the matrices of the cascade realisation must satisfy a commutative condition. These stability conditions are also necessary for matrix polynomial of second order. The results are illustrated through examples.

Linear Generalized Synchronization Using Bidirectional Coupling

Abstract We present a bidirectional coupling strategy to establish targeted linear generalized synchronization between two mismatched continuous chaotic dynamical systems. The strategy is based on Routh–Hurwitz stability criterion. Using the proposed coupling scheme we are able to achieve stable linear generalized synchronization between two mismatched chaotic dynamical systems. The coupling strategy is illustrated using the paradigmatic Lorenz, Rössler and Sprott systems.