Pole Module Research Articles

Globally optimal shape and spin pole determination with light-curve inversion

ABSTRACT Light-curve inversion is an established technique in determining the shape and spin states of an asteroid. However, the front part of the processing pipeline, which recovers the spin pole and area of each facet, is a non-convex optimization problem. Hence, any local iterative optimization scheme can only promise a locally optimal solution. Apart from the obvious downsides of getting a non-optimal solution and the need for an initialization scheme, another major implication is that it creates an ambiguous scenario – which is to be blamed for the remaining residual? The inaccuracy of the modelling, the integrity of the data, or the non-global algorithm? We address the last uncertainty in this paper by embedding the spin pole and area vector determination module in a deterministic global optimization framework. To the best of our knowledge, this is the first attempt to solve these parameters globally. Specifically, given calibrated light-curve data, a scattering model for the object, and spin period, our method outputs the globally optimal spin pole and area vector solutions. One theoretical contribution of this paper is the introduction of a lower bound error function that is derived based on (1) the geometric relationship between the incident and scattered light on a surface and (2) the uncertainty of the gap between the observed and estimated brightness at a particular epoch in a light curve. We validated our method’s ability in achieving global minimum with both simulated and real light-curve data. We also tested our method on the real light curves of four asteroids.

A linear synchronous generator with a power of 30 kW for wave-power engineering

A floating buoy absorber that allows direct conversion of wave energy into electricity using a linear generator is a simple, but promising, device for conversion of wave energy. Results of studies of direct conversion of wave energy using a moored floating point absorber and linear synchronous generator are considered in this paper. The average power and performance of a linear synchronous generator have been determined for a significant wave. An algorithm for calculations of equivalent frequencies and emf amplitudes has been suggested for a modular design of the linear synchronous generator. The analytical expressions and dependences to determine the number of pole pairs and modules, as well as the main dimensions of the machine, have been obtained. It has been concluded that it is necessary to increase the number of poles of a linear generator to obtain an efficient design with reduced weight and overall dimensions. Application of the concentrated winding and permanent magnets with a tangential position has been justified. The parameters of electromagnetic fields and the synchronous generator for different operational conditions have been determined by the finite-element method. The design data and parameters of the six-module, 16-pole SLGPM-30-16 permanent magnet linear generator with a rating power of 30 kW are considered. The design has been optimized by calculations of the electromagnetic field; as a result, a weight of the generator has been reduced and much higher specific ratings than those in similar developments and in other devices for converting ocean-wave energy have been obtained.

A study on the required performance of a 2G HTS wire for HTS wind power generators

YBCO or REBCO coated conductor (2G) materials are developed for their superior performance at high magnetic field and temperature. Power system applications based on high temperature superconducting (HTS) 2G wire technology are attracting attention, including large-scale wind power generators. In particular, to solve problems associated with the foundations and mechanical structure of offshore wind turbines, due to the large diameter and heavy weight of the generator, an HTS generator is suggested as one of the key technologies. Many researchers have tried to develop feasible large-scale HTS wind power generator technologies. In this paper, a study on the required performance of a 2G HTS wire for large-scale wind power generators is discussed. A 12 MW class large-scale wind turbine and an HTS generator are designed using 2G HTS wire. The total length of the 2G HTS wire for the 12 MW HTS generator is estimated, and the essential prerequisites of the 2G HTS wire based generator are described. The magnetic field distributions of a pole module are illustrated, and the mechanical stress and strain of the pole module are analysed. Finally, a reasonable price for 2G HTS wire for commercialization of the HTS generator is suggested, reflecting the results of electromagnetic and mechanical analyses of the generator.

The Lasting Calculation Optimization for Wood Poles in Power Lines Designing

Power lines in company „Latvenergo” are designed by program STAAD-111. Information involved in program contains data about the length of wood poles, wood poles strength rate, space between wood poles, the region of wind where the designed power line is intended to be exploited, the division of wood poles in the investigation stages where the data about strength parametrs are needed, the type of wires, the wood pole density, the wood pole module of flexibility . Following parameters are calculated: the support connection reactions, shear resistance, twist moment, bending tension and combined tension. After the analyses of results the assumptive load is applied on wood poles in three- dimension plane is determined. For power lines design optimization there are offered: ? the calculation data based on experimentally obtained wood strength parametrs; ? the statistical appreciation and strength parameters estimation model which is based on technological process distribution into control points; ? the calculation algorithm for the project programm STAAD-111 based on experimentally obtained wood strength parametrs.

Zero principles for implicit feedback systems

A basic control engineer's adage-the poles of a feedback compensator become zeros of the closed-loop system-admits difficulties of interpretation even in the most simple of cases; that of single-input, single-output. An earlier investigation has provided an analysis of this adage in a module-theoretic context for systems in state space form while avoiding restrictive assumptions on system minimality or squareness. The main result is expressed concisely in terms of an exact sequence of modules which include Ω-zero modules corresponding to the feedback system and the plant. Extended zero modules of Ω-type incorporate both finite invariant zero structure, and generic zero information which occurs when a system fails to be right-invertible. In the case of compensation in the feedback path, this main exact sequence reduces to a mathematically clear expression of the aforementioned adage: the Ω-zero module of the feedback system is precisely the direct sum of the Ω-zero module of the plant and the system pole module of the feedback compensator. This paper extends the previous work in order to avoid assumptions on causality in the plant. Implicit dynamical systems are employed, in lieu of systems in state space form. Once again, it is not assumed that the system is one-to-one or onto; and so the concepts of generic zeros and their modules are brought into the arena of implicit systems. The implicit system itself is assumed in this work to be regular; however, decoupling zeros are permitted. Moreover, input-decoupling zeros and system pole feedback relationships are considered.

Coupling operators, wedderburn-forney spaces, and generalized inverses

The pole-zero structure of a transfer function has been analyzed by two distinct approaches: module-theoretic (coordinate-free) and analytic (basis-dependent). The former (the Wyman-Sain-Conte-Perdon school) emphasizes pole modules, zero modules, exact sequences of maps, and abstract realization theory; applications developed include the model-matching problem, zero structure of one-sided inverses, and connections with geometric systems theory. The latter (the Gohberg school) works with pole chains, zero chains, matrix equations, and concrete factorization theory (minimal, Wiener-Hopf, inner-outer) and interpolation (zero-pole, Lagrange- Sylvester, Nevanlinna-Pick). In this paper we make explicit the connection between the two approaches. In particular, we describe the zero-pole exact sequence of a transfer function without a pole or zero at infinity in the coordinate system provided by a global left null-pole triple. An important tool for us, and an object of interest in its own right, is a generalized inverse G × of a transfer function G. We relate the poles of G × with the zeros of G. We also show that if the pole module of G × is isomorphic to the zero module of G, then left (right) pole pairs of G × are left (right) null pairs of G.

Null-pole subspaces of nonregular rational matrix functions

Given a (not necessarily regular) rational matrix function W and a subset σ of the extended complex plane, we associate with it a free module l σ( W) over the ring of scalar rational functions which are analytic on σ, called the null-pole subspace of W over σ. In the scalar case, the information encoded in this module is equivalent to the knowledge of all the poles and zeros, including their multiplicities, at all points of σ; in the general matrix case, the null-pole subspace encodes the more complicated zero-pole structure of a rational matrix function, which is the key tool for the understanding of many factorization problems. In this paper we show how various other modules which have been introduced in the literature in connection with pole-zero structure (e.g. pole module, zero module) can be read off from the null-pole subspace, and how, conversely, the null-pole subspace can be recovered from its various pieces (pole module, null module, a null-pole coupling operator and left annihilator). We give an analytic, coordinate-dependent description of these modules which has connection with realization theory and which is useful for computations. We also solve the converse problem of finding a rational matrix function which has a given admissible module as its null-pole subspace.

On the zeros and poles of a transfer function

The poles and zeros of a linear transfer function can be studied by means of the pole module and the transmission zero module. These algebraic constructions yield finite dimensional vector spaces whose dimensions are the number of poles and the number of multivariable zeros of the transfer function. In addition, these spaces carry the structure of a module over a ring of polynomials, which gives them a dynamical or state space structure. The analogous theory at infinity gives finite dimensional spaces which are modules over the valuation ring of proper rational functions. Following ideas of Wedderburn and Forney, we introduce new finite dimensional vector spaces which measure generic zeros which arise when a transfer function fails to be injective or surjective. A new exact sequence relates the global spaces of zeros, the global spaces of poles, and the new generic zero spaces. This sequence gives a structural result which can be summarized as follows: “The number of zeros of any transfer function is equal to the number of poles (when everything is counted appropriately).” The same result unifies and extends a number of results of geometric control theory by relating global poles and zeros of general (possibly improper) transfer functions to controlled invariant and controllability subspaces (including such spaces at infinity).

On the design of pole modules for inverse systems

When a linear dynamical system admits more than one inverse, it is known that the pole module of any inverse must contain, either as a submodule or as a factor module, a module of fixed poles isomorphic to the zero module of the original system. Design of the pole module for such an inverse system is resolved by introducing a variable pole module for the inverse, by determining necessary and sufficient conditions for a desired module to be a variable pole module, and by studying the manner in which the fixed and variable modules assemble into the pole module of the inverse. If the fixed and variable pole spectra are disjoint, the pole module of the inverse system is a direct sum of the fixedand variable-pole modules; if not, procedures for addressing the Jordan structure are presented. Subject only to mild necessary conditions, design of inverse systems with specified characteristic polynomial (and, therefore, specified state-space dimension) is possible even in the latter case. For pedagogical reasons, most of the paper is cast over polynomial rings. However, one section discusses generalizations to a wider class of useful rings. Examples are provided for three types of rings.

On the causal factorization problem

In this note the formalism of the infinite zero module and of the infinite pole module is used to analyze the causal factorization problem. This allows us to express its solutions in terms of zeros and poles at infinity and to have a better understanding of both the problem and the techniques previously proposed by various authors to solve it. Moreover, we obtain a characterization, in terms of the existence of certain causal factorizations, of the transfer functions having no infinite zeros.

A unified pole-zero module for linear transfer functions

A new module-theoretic tool is presented for the study of linear time-invariant input/output maps (‘transfer functions’). For suitable subrings 0 of the field k(s) of rational functions, an O-module called the structure module can be attached to each transfer function. This structure module naturally contains the classical (Kalman) pole module as a submodule which gives the (Wyman-Sain) multivariable zero module as the corresponding factor module. A posteriori the resulting exact sequence splits, and the structure module is isomorphic to the direct sum of the pole module and the zero module. Calculations over local rings echo valuation-theoretic results obtained by Kung and Kailath.

The zero module and essential inverse systems

The theory of inverse dynamical systems has been and is continuing to be a keystone in the development of the theories of multivariable feedback control systems and of coding theory for reliable cornmunication. Advances in understanding of the role of plant inverses In control system design have brought about additional insights, for example, In the general areas of decoupled design and of realistic possibilities for closed-loop dynamical performance. Surprisingly enough, almost all the existing literature on inverse systems is cast in terms of matrices. Though the weD-known module theoretic approach to systems has been in place for a decade or more, this approach has not been fully exploited to bring out the foundations of a theory for inverse systems. This paper begins to lay such a foundation by developing a definition of zero module for a system. When inverse systems exist, their "pole modules" can be shown to contain the zero module in an appropriate algebraic sense. If the containment is tight, these inverses are called essential. Existence of and constructions for essential inverses are provided.