Popov's Method Research Articles

Source Voltage Sensor-less Digital Control Using Observer for PWM Converter.

For promotion of low-priced and reliable PWM converters, it is important to decrease the number of parts which comprise a PWM converter. The proposed control method realizes an integrated control circuit using inexpensive DSP (Digital Signal Processor) to offer unity input power factor without a source voltage sensor. In the method, an observer estimates voltage instead of sensing it. Then, the phase-angle error between the estimated voltage wave and a sine wave generating input current command is made zero by a phase controller based on the Fourier series. The stability of the system is shown by the Popov's method. Experiments demonstrate the system achieves sinusoidal input current and unity power factor.

Control of tubular adiabatic homogeneous reactor with recycle for global stabilization of locally stable and unstable steady states

The present study concerns the global stabilization of locally stable and unstable steady states for an adiabatic tubular homogeneous reactor with recycle. The automatic regulation is employed consisting in a continuous correction of the flow rate of the recycle stream. The correction is carried out according to the transfer function of a regulator based on the observation of a state variable (concentration or temperature) at the reactor outlet. The stability is studied by analysing the bifurcation diagram or, alternatively, using Popov's method.

THE FADDEEV–POPOV METHOD FOR THE RELATIVISTIC LANDAU PROBLEM

We use the Faddeev–Popov method to calculate explicitly the path integral propagator for a relativistic spinless charged particle in the presence of a constant magnetic field. We obtain the conservation laws in the path integral approach. We also establish the equivalence between the Faddeev–Popov method and the Fock–Schwinger proper time approach. Finally, after proposing a suitable regularization prescription for the non-relativistic problem, we obtain the Landau levels directly from the path integral result.

Stability analysis of steady-state solutions for porous catalytic pellets

Stability analysis of steady-state solutions has been performed for a model which describes transport phenomena and chemical reaction in a porous catalyst pellet. The model equations have been derived based on the assumption that the resistance to heat transfer is concentrated in a boundary layer around the pellet, while the resistance to mass transfer occurs only inside the pellet. The model, employed in previous publications by the authors, revealed some very interesting new features of the structure of steady-state solutions. In the present work only the stability of stationary solutions with respect to static bifurcation is analysed. Applying Liapunov's indirect method, a local stability condition has been derived in which the kinetics of chemical reaction is represented by the function defining the effectiveness factor of a catalyst pellet. In order to determine the size of the neighbourhood in which a given stationary point remains asymptotically stable, a global stability analysis has been performed based on Popov's frequency method. An analytical condition for the global stability has been derived. The analysis of the stochastic model of the process led to the condition for the asymptotic stochastic stability, which determines the region of asymptotic stability with probability one. This region is smaller than that found for the deterministic model.

Construction of improved Lyapunov functions and extension of transient stability regions for power systems

In this paper different second-order power system models taking into account the effects of damping and transient saliency have been considered, and Lyapunov functions containing higher-order terms of the state variables have been constructed via the operational transform technique (OTT). Transient stability regions computed for different system damping conditions using Lyapunov functions generated by OTT, the trial and error method, the generalized Zubov method, Szego's procedure, the Popov method and the Lagrange-Charpit method are presented for comparison. The stability regions determined by OTT are better than those of the other methods.

The geometrical interpretation of the Faddeev–Popov determinant in Polyakov’s theory of random surfaces

In the context of Polyakov’s theory the geometrical approach, in which the functional measure is defined as a formal volume ∞-form, is developed. The special version of the Fubini theorem on manifolds is derived, which provides the geometrical interpretation of the Faddeev–Popov method. The conformal gauge is studied within this framework. As a result, the explicit form of functional measure in effective Liouville quantum field theory is obtained.

On symmetric and unity interconnections between three nonlinear subsystems

A specific type of interconnection is examined with regard to three nonlinear subsystems in this communique. Further, the two possibilities of this specific linear interconnection are investigated in detail. For each kind of interconnection, conditions for the global stability of the overall system are derived, via the Popov method, which are simple and easy to apply. The conditions are rather conservative in nature, though a certain amount of flexibility does exist in the choice of the various parameters in the event of constraints other than stability are to be satisfied. An example is included to illustrate the utility of the conditions.

Absolute Stability of Pulse-Width Modulated Feedback Systems Containing an Integrator

A frequency domain inequality is developed for the absolute stability of a pulse-width modulated feedback system containing an integrating element by using the second method of Lyapunov. This criterion is found to be identical with Jury and Lee's criterion obtained by Popov's method of stability analysis. A link between the Lyapunov method and the Popov method of analysis of pulse-width modulated feedback systems is thus established.

Signal Stabilization Analysis by DF Method and Popov Method Compared

The minimum amplitude of the dither or the extra high frequency signal at the input to the nonlinear element, to quench the limit cycles present in the system, can be determined by the use of the DF theory. It can also be determined by the application of Popov's criterion, after replacing the original nonlinear element and dither by the altered nonlinearity. The results as obtained by the above two methods for several nonlinearities, are compared and analysed.

Frequency Domain Stability Criterion for a Pulse Width Modulated Feedback System

The absolute stability of a pulse width modulated feedback system is studied using the second method of Lyapunov. The stability criterion is obtained as a frequency domain inequality which is found to be identical with Jury and Lee's criterion obtained by Popov's method of stability analysis. A link between the Lyapunov method and the Popov method of analysis of pulse width modulated systems is thereby established.

Some guidelines for an easier application of Popov's stability test

This paper compares the graphical and root-locus versions of Popov's stability test. The main purpose of the paper is to make possible the application of Popov's Method for a variety of non-linear elements. The various sectors of confinement are analyzed in detail for different non-linearities, and results are summarized in a table. The paper represents by itself a guide, permitting easier practical application of Popov's criterion, under different conditions.

Multi-parameter sensitivity analysis of power-system stability by Popov's method†

Popov's method of frequency-domain stability criteria is used to conduct the multiparameter sensitivity analysis of power system stability. The two-parameter parametric sensitivity mode] of a one-machine infinite-bus system is developed, This model involves stability measure ξ, defined in terms of Lur'o-type Liapunov functions constructed systematically. Based on the application of the model to a specific numerical example, results and conclusions are given. This type of sensitivity analysis is useful for optimum design and operation of the power system. The criterion of optimality is zero sensitivity. In general, this form of analysis is applicable to any dynamic engineering system.

The change of variables method for equations in Banach spaces

AN approximate method for the solution of equations in Banach spaces is developed. The method is applied to an averaging scheme for integral and differential systems. The fundamental method of investigating non-linear oscillations is the method of averaging proposed by Bogolyubov [ 1]. Averaging is connected with an algorithm for changing the variables, developed for some types of systems of first-order differential equations with a small parameter. At the present time the averaging principle has been extended to a wide class of differential, integral and integro-differential systems [2–4], but there are no algorithms for constructing high approximations for many generalizations of the averaging method. The necessity for the development of the algorithmic side of the averaging method was indicated in the conclusion of the monograph [2]. In this paper algorithms for the construction of changes of variables for equations in Banach spaces are presented. These algorithms may be used in various averaging schemes, and not only for averaging. As an example of its use the algorithm for changing the variables is studied in an application to non-linear integral equations. We obtained high approximations of the averaging method for integral equations in the periodic case and high approximations of the harmonic linearization method in E. P. Popov's form [5]. For this, finite estimates of the error of the change are obtained, and Popov's method is rigorously validated. The proposed method is compared with the classical scheme for the construction of changes.

The E. P. Popov method for quasilinear systems having slowly varying parameters

The E. P. Popov method for quasilinear systems having slowly varying parameters

Circle criterion and transient stability of power systems†

An increasing familiarity of power system engineers with frequency domain techniques has motivated the search for stability criteria for power systems that could be applied in the frequency domain. Following the advent of phase plane methods for second -order systems and the second method of Lyapunov, the Popov method gained popularity. This investigation attempts to apply an extension of Popov's method to determine the transient stability of a single machine infinite bus system under a large transient disturbance. Circle criterion provides simple rules for examining both the linear and non-linear portions of the power system in the frequency domain and for arriving at conditions to be imposed on these portions in order to ensure absolute stability. An upper and lower bound is established for the non-linear gain by treating the system's mathematical model as a set of non-linear algebraic equations and limiting values of gains are estimated by solving these equations. A numerical example is solved to illus...

Application of Popov's criterion to signal stabilization in discrete systems

In a previous paper [1], a new method called the dual input discrete describing function (DIDDF) was presented, which enables one to determine the minimum amplitude of sinusoidal dither to be applied, to stabilize a relay type sampled-data control system. In this correspondence Popov's method is used to find the minimum amplitude of the dither to be applied to quench the limit cycles occurring in relay type nonlinear control systems. Furthermore, the dependence of the minimum value of the dither on sampling time is explicitly seen in Popov's method.

CORRECTIONS- Stability Analysis of Adiabatic Packed-Bed Reactors via Popov's Frequency Method

CORRECTIONS- Stability Analysis of Adiabatic Packed-Bed Reactors via Popov's Frequency Method

Stability Analysis of Adiabatic Packed-Bed Reactors via Popov's Frequency Method

Stability Analysis of Adiabatic Packed-Bed Reactors via Popov's Frequency Method

On the application of diakoptics to nonlinear systems

This paper discusses the application of the principle of diakoptics to the analysis and stability study of nonlinear systems. Part I deals with the application to the analysis of nonlinear systems by means of Taylor-Cauchy transforms. Part II deals with the application to the analysis of nonlinear systems by means of Volterra functionals. Part III deals with the application to the stability study of nonlinear control systems by means of Popov's method, which is closely related to Liapunov's direct method. Illustrative examples are given.

A frequency stability criterion for a class of non-linear sample-data systems with pure delay

Popov's frequency method has been extended to non-linear sampled-data systems with a single non-linearity and the stability condition thus derived has been shown to be the necessary and sufficient condition for the existence of a certain type of Lyapunov's function. It has been proved that Popov's frequency stability condition for continuous systems without delay is also applicable to systems with delay. By combining different area inequalities, the present investigation derived via the state space approach, a stability condition for non-linear systems with delay and containing a single non-linearity. The criterion can be reverted to a, form identical to that for systems without delay. It is also shown that the stability criterion derived is also applicable to systems without delay.