Pole Trajectories Research Articles

A generalized method of controlled voltage source-fed induction motor vector control using the observer theory

Vector control of induction motors is widely used for industrial applications. On-line parameter identification and speed sensorless control are being studied actively. A representative method for these problems is the application of an adaptive full-order observer. The rotor flux for vector control is estimated by a full-order observer and machine parameters, or the rotor speed is determined by an adaptive algorithm. In this paper, a new vector control scheme with parameter identification is proposed. This method is based on the adaptive full-order observer. However, the observed currents which are usually estimated in the voltage model are considered as command currents and the voltage model is used for the current controller. As a result, the proposed system is simpler than the conventional adaptive full-order observer system. Since the proposed system is composed of an induction motor model in a synchronously rotating reference frame, the well-known slip frequency control block is contained. The arrangement of the poles which are related to the torque transfer function is discussed. A linear model is derived taking into account the effects of the change of the stator and rotor resistances. The trajectories of poles and zeros of the torque transfer function are computed and discussed for various system parameters. Identification of stator and rotor resistances is confirmed by simulation using a nonlinear system model. The proposed idea is applied to a speed sensorless system; this system has a similar configuration to those of existing systems under some assumptions. © 1997 Scripta Technica, Inc. Electr Eng Jpn, 119(4): 66–76, 1997

Magnetoresonances on a lasso graph

We consider a charged spinless quantum particle confined to a graph consisting of a loop to which a halfline lead is attached; this system is placed into a homogeneous magnetic field perpendicular to the loop plane. We derive the reflection amplitude and show that there is an infinite ladder of resonances; analyzing the resonance pole trajectories we show that half of them turn into true embedded eigenvalues provided the flux through the loop is an integer or halfinteger multiple of the flux unit $hc/e$. We also describe a general method to solve the scattering problem on graphs of which the present model is a simple particular case. Finally, we discuss ways in which a state localized initially at the loop decays.

Analysis, synthesis, and perception of Japanese voiceless stop consonants based on a pole-zero model.

The production process of voiceless stop consonants was represented by a non-stationary autoregressive moving-average (ARMA) process, and the trajectories of poles and zeros from the noise burst to the following vowel were extracted from Japanese utterances of CV syllables containing voiceless stop consonants /p/, /t/, and /k/, using the SEARMA method. In order to clarify the relationship between the extracted parameters and the cues for perception of voiceless stop consonants, perceptual tests were conducted using synthetic CV syllables generated under various control conditions for these parameters. The relationship between the perceptual cues of voiceless stops and the acoustical parameters (i.e., the spectra and the duration of the consonantal noise, the orders of the model, the vocalic transition) were revealed.

A Generalized Method of Controlled Voltage Source-Fed Induction Motor Vector Control Using the Observer Theory.

A Vector control of an induction motor is widely used for industrial applications. An on-line parameter identification and the speed sensor-less control are studied actively. The representative method for these problems is an application of the adaptive full order observer. The rotor flux for the vector control is estimated by a full order observer and machine parameters or the rotor speed are determined by an adaptive algorithm. In this paper, a new vector control scheme with parameter identifications is proposed. This method is based on the adaptive full order observer. However, the observed currents which are estimated usually in the voltage model are considered as the commanded currents and the voltage model is used for the current controller instead of the conventional one. As the result, the proposed system is simplified than the conventional adaptive full order observer system. As the proposed system is composed of the induction motor model in a synchronously rotating reference frame, well-known slip frequency control block is contained. An arrangement of the poles which are obtained from the torque transfer function is discussed. A linear model is derived taking into account the effects of the change of the stator and rotor resistances. The trajectories of poles and zeros of the torque transfer function are computed and discussed for various system parameters. An identification of stator and rotor resistances is confirmed by the simulation using a nonlinear system model. The proposed idea is applied to the speed sensor-less system and this system has a similar configuration to the conventional systems under some assumptions.

On the natural frequencies of an annular ring above a conducting half space

The natural resonant frequencies of an object embedded in a stratified conducting medium are considered. The special case of an annular ring is considered in detail. Extensive numerical results are examined for the case of a ring in free space above a conducting half space. This simple problem provides insight into the behavior of the natural frequencies of airborne radar targets above the earth, ice, or sea surface. Results reveal an intricate pattern of pole trajectories in the complex plane. These trajectories are studied for various combinations of height, ring geometry, constitutive parameters, and modal index.

Light-induced states of H and H-, shadow states, and the dressed potential.

Light-induced bound'' states of atoms originate from the movement of poles of the multichannel scattering matrix on the Riemann energy surface. The appearance of additional bound'' states of the negative hydrogen ion, recently predicted in the high-frequency theory, is related to the motion of resonance poles that correspond to autoionizing states in the absence of the field. Various pole trajectories leading to light-induced states are described for photodetachment from a one-dimensional square potential well. Certain light-induced states in atomic hydrogen are discussed in relation to the spectrum of the dressed Coulomb potential.

Exact Disk Solution of the Einstein Equation

The 4-soliton solution with complex pole trajectories to the vacuum Einstein equation is studied. The solution describes a static and axisymmetric gravitational field with asymptotic flatness, which is produced by a thin disk. We obtain the energy-momentum tensor of the to reveal its properties. The soliton technique 1 ) to solve the gravitational field equation gave us a new viewpoint on the exact solutions of the vacuum Einstein equation. There is an infinite series of solutions which are characterized by the soliton number n. In the stationary case with axial symmetry the series includes the Kerr-NUT solution as a 2-soliton solution and the Tomimatsu-Sato solution as a certain limit of 4-soliton solution. In the static case 2 ),3) there is an infinite series of the Weyl solutions, which is interpreted as a nonlinear superposition of multi-Weyl solutions. Two of the present authors 3 ),4) showed that the soliton technique gives not only these series of solutions but a series of ring-type solutions by adopting complex pole trajectories in the static case. The first non-trivial example of this series is the Weyl solution expressed in the oblate spheroidal coordinates,5) which has a ring-type curvature singularity. In our classification this solution is interpreted as the 2-soliton solution with non-complex-conjugate pole trajectories. The next example is the 4-soliton solution in which there are two types. One is just a nonlinear superposition of the above 2-soliton solutions, which has two ring-type singularities with different radii. The other, which is more important, is the 4-soliton solution constructed from two pairs of complex conjugate pole trajectories. This was referred to as the two­ ring solution, because the curvature invariants have finite limits at two rings although the metric coefficients diverge there. This fact contrasts with the fact that the curvature invariants diverge at the ring in the 2-soliton case. The purpose of this paper is to study the detailed structure of the two-ring solution. It will be shown that the solution should be called a solution rather than a ring solution. The properties of the will be also clarified by calculating the energy-momentum tensor. In the next section we give the solution in an explicit form and investigate its mathematical structure. From this we find that the plane containing the rings is separated into a regular region inside the inner ring and a region with the discontinuity of curvature outside the inner ring. We shall call this outer region a disk because of its non-zero energy density as will be.discussed in § 3. The is further divided into two parts by the outer ring. In § 3 we obtain the

Exact Disk Solution of the Einstein Equation

The 4-soliton solution with complex pole trajectories to the vacuum Einstein equation is studied. The solution describes a static and axisymmetric gravitational field with asymptotic flatness, which is produced by a thin disk. We obtain the energy-momentum tensor of the disk to reveal its properties.

Numerical behaviour of a fixed-point implementation of the aplitted generalized LeRoux-Gueguen algorithm

The splitted generalized LeRoux-Gueguen algorithm performs a least-squares estimate of autoregressive parameters. Due to its lattice structure and finite memory length it seems to be well suited to fixed-point arithmetic implementation. In the present paper the effect of round-off errors caused by such implementation is studied. This is done by computer simulation of the fixed-point implementation with varying wordlengths for characteristic quantities and comparison with a floating-point implementation as a reference. Input signals are determined by pole trajectories of the transfer functions of their autoregressive model filters. Comparison between the two implementations is carried out by a likelihood ratio. The simulation results lead to empirical guidelines for the choice of wordlengths.

Scattering from a thin spherical shell: Higher-order Lamb waves

The acoustic scattering from thin spherical shells is marked by the existence of the thickness quasiresonance in the high-frequency regime. This quasiresonance is due to the existence of a region of negative group velocity surrounding the first symmetric Lamb wave. This article presents results on the existence of higher-order quasiresonancelike phenomena, and it considers the effects of Poisson’s ratio on the quasiresonance. Pole trajectories in the complex ka plane are exhibited for the first dozen modes on a spherical shell. This analysis reveals the existence of regions of negative group velocity surrounding higher-order Lamb waves. A time domain representation of the contributions of higher-order Lamb waves to the scattered field is presented. This analysis reveals the early time arrival nature of the thickness quasiresonance as reconstructed from the poles in the complex ka plane.

Classification of an infinite series of static solutions to the vacuum Einstein equations

We propose a classification of an infinite series of the static solutions to the vacuum Einstein equation by means of their soliton number and the real and/or complex pole trajectories. We also show that in the 4-soliton solution there appears an intriguing ring solution of which the curvature invariant has a finite limit at the rings.

Generalized Lamb waves near mode thresholds of spherical shells.

Pole trajectories as a function of frequency in the complex angular momentum plane for backscattering from empty spherical shells with and without significant fluid loading are presented. These are correlated with Lamb wave threshold features (that depend on Poisson’s ratio) found on a flat plate in vacuum. [R. D. Mindlin, ‘‘Waves and Vibrations in Isotopic, Elastic Plates,’’ in StructuralMechanics (Pergamon, New York, 1960); A. H. Meitzler, J. Acoust. Soc. Am. 38, 835–842 (1965).] The trajectories for the fluid-loaded case are relevant to the high-frequency enhancements and longitudinal (or thickness) resonance of recent investigations [see, e.g., S. G. Kargl and P. L. Marston, J. Acoust. Soc. Am. 89, 2545–2558 (1991)]. The usual poles lie in the first quadrant of the upper half-plane. Near the longitudinal resonance condition a pole associated with a symmetric wave is present in the second and fourth quadrants and is associated with the high-frequency enhancement. Its pole trajectory indicates that the phase and group velocity are oppositely directed over a small range of ka where the enhancement occurs. [Work supported by ONR.]

The acoustic scattering by a submerged, spherical shell. III: Pole trajectories in the complex-k a plane

Previously, a fundamentally oriented analysis was presented of the complex-ka plane pole structure of the S matrix for a thin spherical shell for 0<ka<100 [Sammelmann et al., J. Acoust. Soc. Am. 85, 114–124 (1989)]. In this analysis, it was concluded that fluid loading the first antisymmetric mode of the shell in vacuum had a rather violent effect; the mode bifurcated into two distinct modes near the coincidence frequency. In this article, the relationship of the poles of the diffractive modes of impenetrable spheres and the eigenfrequencies of the shell in vacuum to the modes of the fluid-loaded shell are precisely established by studying the complex-ka plane trajectories of the S-matrix poles under variations of the material parameters of the shell. The evolution of these modes are also examined as the shell thickness is varied from 2% to 50% of the outer radius of the shell. It is found that the limit of an elastic solid is not approached smoothly and that modal reorganizations similar to the bifurcation phenomenon noted above is a common occurrence. The implications of this behavior are examined for both the complex-ka, real-l and the real-ka, complex-l pictures.

S-matrix pole trajectory of the three-body system

We have studied the behaviour of S-matrix poles near the thresholds for some three-body systems. In Amado's simple model for three bosons with an attractive S-wave two-body interaction and specetor angular momentum l=0, the S-matrix pole behaves as Im E ∞ −(Re E) 2 near the threshold in the fourth quadrant of the unphysical complex E-plane. This behaviour is formally the same as that in the two-body scattering with angular momentum l= 3 2 and a three-body resonance shows up near the threshold. In such a case, the Fredholm determinant of the Faddeev equation at zero energy, D F(0), is close to zero. However, it is shown that the value D F(0) does not definitely tell us whether the system is attractive or repulsive in contrast to the case of a two-body system. As physical applications, we have studied Λnn and Σ −nn systems. The S-matrix poles are found to be far away from the physical real axis and do not give rise to observable effects for the two-body interactions reproducing the low-energy scattering data, although the Λnn system could develop a three-body resonance if the Λn interaction were slightly more attractive.

An Application of Model Following Servo (MFS) Control to Vector Controlled INduction Motor Drive System

By using the vector control strategy, PWM inverter-fed induction motor drive system is used in various fields. In this case, a conventional PI speed control is widely used as the major feedback loop. In this paper, the application of model following servo (MFS) control to the vector controlled induction motor drive system is studied to achieve superior performance compared with the PI controller.At first, by assuming ideal vector control, a MFS controller is designed to minimize a specified performance index. Secondly, in order to study the influence of machine parameter change, a linear model is derived by using a small displacement theory. Finally, the computed and the experimental results are discussed from the viewpoints of the trajectories of poles and zeros, and the transient responses. As the result of the analysis, the pole of induction motor is close to the zero by choosing the large value of the weighting constant in spite of the change of rotor resistance. And the superiority of the MFS control as compared with the PI control is maintained when the rotor resistance is changed.

An application of model following servo (MFS) control to vector controlled induction motor drive system

By using the vector control strategy, PWM inverter-fed induction motor drive system is used in various fields. In this case, a conventional PI speed control is widely used as the major feedback loop. In this paper, the application of model following servo (MFS) control to the vector controlled induction motor drive system is studied to achieve superior performance compared with the PI controller.At first, by assuming ideal vector control, a MFS controller is designed to minimize a specified performance index. Secondly, in order to study the influence of machine parameter change, a linear model is derived by using a small displacement theory. Finally, the computed and the experimental results are discussed from the viewpoints of the trajectories of poles and zeros, and the transient responses. As the result of the analysis, the pole of induction motor is close to the zero by choosing the large value of the weighting constant in spite of the change of rotor resistance. And the superiority of the MFS control as compared with the PI control is maintained when the rotor resistance is changed.

Bare Reggeons in asymptotic free theories

Conformal symmetry is used to investigate the Regge asymptotics for the six dimensional scalar φ3 model and the QCD vacuum exchange amplitude. Resulting angular momentum cuts change into series of poles by scale breaking due to renormalization. The Regge pole trajectories are calculated for large momentum transfer.

A linear model for current source inverter-fed induction motor under vector control.

The vector control of an induction motor has made an epoch-making progress in the torque control. If the system is ideal, the torque transfer function should be constant under the vector control. Actually, however, the change of rotor resistance, the control capability of stator currents and the sampling of digital controller cause the transient state. In order to study these unfavorable effects, this paper proposes a linear model for the current source inverter-fed induction motor drive system.Firstly, a linear continuous system model is derived by using a small displacement method, and the ideal characteristics of the vector control are theoretically clarified in the proposed analytical model.Secondly, the system in which the vector control is carried out by a microprocessor is analyzed. A linear sampled-data system model is derived considering the effects of the sampling period and the dead time.The last part of this paper discusses the computed results concerning the trajectories of poles and zeros, and the transient responses to the interesting system parameters such as PI current control gain Ki, rotor resistance and sampling period. What is acquired in the analysis gives vital directions for the design of the system, for example, the selection of the gain Ki, should be a large one to stabilize the system, but it should not exceed an upper bound value caused by the sampling.

Plasmon interactions in metallic gratings: ω- and k-minigaps and their connection with poles and zeros

A numerical analysis is presented of two types of minigaps: ω- and k-gap that are formed in the reflectivity dips when two oppositely propagating plasmon surface waves (PSW's) are excited simultaneously. Their connection with complex trajectories of poles and zeros is revealed: an ω-gap is formed when splitting of poles is observed and a k-gap only exists when a splitting of zeros occurs.

S-matrix pole trajectories for separable interactions

By solving the Lippmann–Schwinger equation in momentum space for a set of two-body separable interactions, we study eir S-matrix pole trajectories. The connection of such a study with the three-body bound-state collapse is also discussed.