Uncertainty evaluation for estimates from recursive projection algorithms

In this paper we consider parameter estimation of linear systems described by y_i = a θ + e_i, where the ith measurement y_i is linearly dependent on the parameter vector θ ε ?^?p through the regressor vector a ε ?^?p and the measurement error e_i is unknown but bounded. Some properties of previously presented algorithms for recursive parameter identification in the unknown but bounded error (UBBE) context are discussed. In particular it is analysed how different levels of information on the error structure can influence the choice of the identification algorithms and the possibility of evaluating the reliability of the estimates. Attention is also focused on the influence that forgetting schemes have on the estimates and on their confidence evaluation.     

Universal iterative learning control using adaptive high-gain feedback

Convergence theorems for adaptive (universal) iterative learning control systems provide a well-defined convergence criterion parametrized by a single adaptive gain parameter. The convergence is in the weak topology of L(0,T) with T finite and applies to both finite-dimensional systems and a class of infinite-dimensional systems.     

Ultra‐low‐noise large‐bandwidth transimpedance amplifier

Equivalent input current noise and bandwidth are the most relevant parameters qualifying a low‐noise transimpedance amplifier. In the conventional topology consisting of an operational amplifier in a shunt‐shunt configuration, the equivalent input noise decreases as the feedback resistor (R_F), which also sets the gain, increases. Unfortunately, as R_F increases above a few MΩ, as it is required for obtaining high sensitivity, the bandwidth of the system is set by the parasitic capacitance of R_F and reduces as R_F increases. In this paper, we propose a new topology that allows overcoming this limitation by employing a large‐bandwidth voltage amplifier together with a proper modified feedback network for compensating the effect of the parasitic capacitance of the feedback resistance. We experimentally demonstrate, on a prototype circuit, that the proposed approach allows to obtain a bandwidth in excess of 100 kHz and an equivalent input noise of about 4 fA/ , corresponding to the current noise of the 1 GΩ resistor that is part of the feedback network. The new approach allows obtaining larger bandwidth with respect to those obtained in previously proposed configurations with comparable background noise. Copyright © 2014 John Wiley & Sons, Ltd.     

Frequency-dependent OP-AMP gain influence on parameters of the single amplifier biquad filters

The influence of the finite gain and gain-bandwidth product of the operational amplifier on the parameters of the active RC filter has been investigated in the present paper. Single amplifier biquad filters were analysed for the case when the central frequency in the pole pair does not depend on the amplifier gain, i.e. when S = 0. The general results were obtained for such filters, describing well the filter behaviour at low as well as at high frequencies. On the basis of the results obtained, the deviation of the realized parameters from the desired values can be determined, and thereby the necessary correction of the filter calculation can be made. The experimental results agree well with the theoretical ones.     

On the performance characteristics of a synchronous motor fed from a voltage source inverter

Contents Using two axis model the steady state characteristics of a voltage controlled synchronous motor drive are investigated for different modes of operation based on signal flow graph technique. The input voltages are assumed to be quasi square wave. The analysis shows that depending upon the mode employed the machine can be made to possess shunt, series or mixed characteristic. The torque developed is of pulsating nature. All the modes of operation have sixth harmonic pulsations which are roughly 20 percent of the mean value. A voltage fed motor is found to have reduced torque pulsations when compared to a current fed one with the same flux levels.

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Über das Betriebsverhalten eines Synchronmotors mit Spannungszwischenkreisumrichter

Übersicht Aufgrund des Signalfußdiagramms wird das stationäre Verhalten des Spannungsgespeisten Synchronmotorantriebs bei rechteckförmiger Spannung für verschiedene Betricbsarten der Maschine untersucht. Dafür werden die Gleichungen der Maschine auf der Basis des Zweiachsenmodells aufgestellt. Die Untersuchungen zeigen, daß das Drehmoment Schwankungen hat, deren Amplitude um etwa 20 Prozent des Mittelwerts liegen. Weiter wird gezeigt, daß diese Schwankungen kleiner als die des stromgespeisten Synchronmotors sind. Je nach der Betriebsart besitzt die Maschine eine Drehmoment-Drehzahl Kennlinie, die der des Nebenschluß- oder Reihenschlußmotors ähnlich ist.

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Nomenclature i _d ,i _q direct and quadrature axis components of stator current - i _D ,i _Q direct and quadrature axis components of damper currents - l _d ,l _q synchronous inductances of direct and quadrature axes respectively - l _D ,l _Q self inductances of damper windings - l _hD ,l _hQ mutual inductances between stator and damper windings - l _hd mutual inductance between armature and field in the direct axis - L _af mutual inductance between phasea and field winding - p operator - P pairs of poles - r _a armature resistance - r _f field resistance - r _D ,r _Q damper winding resistances in the direct and quadrature axes respectively - s Laplace operator - u _d ,u _q direct and quadrature axis components of stator voltages - _d , _q direct and quadrature axis components of stator flux linkages - _D , _Q damper flux linkages in the direct and quadrature axes - _f field flux linkages - synchronous angular velocity     

Partial Discharge Signal Detection by Piezoelectric Ceramic Sensor and The Signal Processing

Partial discharge (PD) in an insulator or on surface of defective conductor emits acoustic wave transmitting through an air or an insulator. The acoustic wave between 20 kHz and several hundred of kHz can be detected by piezoelectric ceramic sensor that converts the acoustic wave into an electrical signal. Piezoelectric ceramic sensor has either the wide resonant band or the local resonant band depending on the ceramic material or the various combinations of each different component in the manufacturing process. This paper presents the piezoelectric ceramic sensor with 0.95 PZT–0.05 PMNS that yields the piezoelectric properties of high k_p, high Q_m. It has the frequency characteristics of local resonant band, such that it can be applied to PD detection. We have demonstrated the properties of the proposed piezoelectric ceramic sensor by comparing with the conventional electrical PD detector. Quantitative analysis is accomplished by comparing the -q_max from a PD detector and the -v_max from the proposed sensor while -n distributions are the same for both the conventional phase-resolved PD analysis method and the proposed one.     

Tangential nevanlinna-pick interpolation problem for bounded real matrices—A network approach

This paper deals with the so-called tangential Nevanlinna—Pick interpolation problem for bounded real matrices. This problem can be formulated as follows: given a set of n pairs {(p_i, K _i)}, where p_i are distinct complex numbers with Re p_i > 0 and K _i stands for 2m × l_i constant matrices, assuming that for every pair (p_i, K _i) with p_i complex there exists a complex conjugate pair (p _i, K _i) and that for every pair (p_i, K _i) in which p_i is real K _i is also real, find an m × m bounded real matrix S(p) such that [ S (p_i) 1_m] K _i = 0 for i= 1,…,n. The solution of this problem is obtained in an inductive way through the construction at each step of a real lossless multiport section that realizes two complex conjugate pairs or one real pair. After each step the number of pairs (p_i, K _i) is reduced by two (if p_i is complex) or by one (if p_i is real). the procedure is continued until all pairs have been considered. After the last step the final section may be terminated with any bounded real load. the scattering matrix S (p) of the resulting cascade multiport network is bounded real and satisfies the desired interpolation conditions. In this way the tangential interpolation problem is reduced to classical network cascade synthesis by the use of real lossless multiport sections.     

Microwave Dielectric Properties of Ferroelectric BaTiO3 Thin Film

The dielectric properties of c-axis epitaxial BaTiO₃ thin film on LaAlO₃ are investigated at frequencies of 0.5–30 GHz. For the measurements, interdigital capacitors with the Au/Ti electrode configurations of five fingers pairs that are 15 m wide and spaced 2 m apart are prepared by photolithography and lift-off patterning. Finger length varies from 20 to 80 m. The capacitance of epitaxial BaTiO₃ films exhibited no frequency dependence up to 10 GHz with the exception of slightly upward tendency of capacitance in BaTiO₃ film with a finger length of 80 m due to the self resonant frequency at 20 GHz. The Q-factors of the capacitors, defined as Q = 1/CR, are decreased up to 10 GHz with increased frequency. At 10 GHz, the BaTiO₃ film has a tunability [defined as k(V) = [C(0)–C(V)]C(0)] of 1.5% at 15 V, a loss tangent of 0.2 at room temperature. The small tunability can be interpreted as a result of in-plane compressive stress of BaTiO₃ film exhibiting large dielectric anisotropy. For the improvement of tunability and dielectric loss in the interdigital BaTiO₃ capacitor, the tetragonality (c/a) of epitaxial BaTiO₃ film and design of interdigital capacitor should be modified.     

Calculation method of linear induction motor supplied from symmetrical voltage source

Contents A finite length of the primary part of a linear induction motor (LIM) contributes to nonuniform magnetic field distribution in an airgap. It causes the current asymmetry if the primary winding is supplied from a symmetrical voltage source. This paper presents a calculation method of the LIM performance. The method is based on Fourier series technique and takes into account the current asymmetry caused by the end effects. In order to illustrate an influence of current asymmetry the calculation results of electromechanical characteristics of a flat single-sided LIM are presented.

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Die Berechnungsmethode eines linearen Induktionsmotors (LIM) der aus einer symmetrischen Spannungsquelle gespeist wird

Übersicht Die endliche Länge des Primärsteils eines linearen Induktionsmotors (LIM) ruft die ungleichmäßige Verteilung des magnetischen Feldes im Luftspalt hervor. Es bewirkt die Asymmetrie der Ströme, wenn die Wicklung des Primärsteils aus der symmetrischen Spannungsquelle gespeist wird. Dieser Beitrag stellt die Berechnungsmethode der Leistungen von LIM dar. Diese Methode beruht auf der Berücksichtigt der Asymmetrie der Ströme, die von Rand-effekten bewirkt wird. Die Ergebnisse der Berechnungen der elektromechanischen Charakteristiken des einseitigen flach LIM wurden dargestellt, um den Einfluß der Asymmetrie der Ströme zu illustrieren.

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List of symbols and abbreviations B magnetic flux density - b slot opening - d conducting plate thickness - E electric field intensity - E e.m.f. - F force - |I _r | phase current - J current density - imaginary unit - K _t finite primary width correction factor - K _C Carter's coefficient - k, l, i harmonic and wave number - L primary length - P ₁ input power - P _m mechanical power - q number of slots per pole per phase - s slip - |U _r | phase voltage - v secondary speed relative to primary - W primary width - w _c number of wire per coil - w _s secondary width - X reactance - P power losses - Z impedance - conductivity - modified airgap length - _r actual airgap length - permeability - LIM efficiency - ( _s –L) distance between adjacent primaries - _i tooth pitch - _x pole pitch - Q=Q _m exp (jt) Q _m =|Q _m| exp (j) - Q ^* conjugate value ofQ - r number of phase - angular frequency - f frequency     

Effects of internal postoxidation on the oxygen deficiency and dielectric strength of buried oxide formed by the separation‐by‐implanted‐oxygen (SIMOX) process

Effects of internal postoxidation on buried silicon dioxide have been studied. The dioxide examined was the buried insulator in a silicon‐on‐insulator (SOI) structure fabricated by implantation of oxygen ions into Si, or the SIMOX process. Internal postoxidation is an oxidation process applied to the SOI structure after its fabrication. It was observed that the photoluminescence intensity due to neutral oxygen vacancies (O₃≡Si–Si≡O₃, “≡” denotes three separate bonds to oxygens) increased after the internal oxidation. The oxide thickness and the number of E centers (O₃≡Si·, “·” denotes an unpaired electron) were also found to increase similarly. The measurements repeatedly done by changing the oxide thickness revealed that the increased part of oxide by the internal oxidation contains the vacancies with a similar density to the original part. It is concluded that the internal oxidation scarcely affects the oxygen deficiency of the oxide. It was also observed that the number of breakdowns at low electric fields remarkably decreased after the internal oxidation, indicating that electrically weak spots such as silicon pipes were effectively reduced. © 1999 Scripta Technica, Electr Eng Jpn, 130(1): 15–20, 2000     

Versuch einer genaueren Vorausberechnung des zeitlichen Erwärmungsverlaufes elektrischer Maschinen mittels Wärmequellennetzen

Übersicht Auf einer Untersuchung von Meßergebnissen (des Erwärmungsverlaufs) sowie der wichtigsten Berechnungsmethoden der Enderwärmung elektrischer Maschinen aufbauend, wird eine allgemeine angenäherte Lösung des Problems an Hand der Methode der Wärmequellennetze aufgestellt. Es wird gezeigt, wie diese, praktischen Zwecken angemessen und unter einem Mindestmaß an Rechenarbeit ausgewertet werden kann; die Ausführungen werden sowohl durch praktisch erreichte Ergebnisse, als auch durch eine vollkommen durchgeführte Vorausberechnung des Erwärmungsverlaufs einer Maschine mit Meßergebnissen verglichen und einige Anmerkungen über die Anwendung von automatischen Rechengeräten ergänzt.Übersicht der wichtigsten Bezeichnungen t Zeit - T(x), T(x, y, z) Temperatur: in (x) resp. im Punkte (x, y, z) - T(x, t), T(x, y, z; t) desgleichen zur Zeitt - , _v, (t) mittlere Erwärmung: eines Körpers, der Wärmequelle (v) zur Zeitt - einspaltige Matrix der mittleren Erwärmung resp. Erwärmungsverlaufs (eines Systems von Wärmequellen, Gl. (14) - p, Zeitkonstante und Koeffizient der Exponentialreihe Gl. (1) - w,W, W, W* Wärmeentwicklung: spezifische, in einer Wärmequelle, einspaltige Matrix Gl. (15) bzw. (5) - ,H Wärmeleitzahl, Wärmeübergangszahl - Q,q;q _v (t) Intensität eines Kühlluftstromes, eines Wärmestromes; zur Anwärmung nötige Wärmeleistung zur Zeitt - r, r _ü,r _in ,R Wärmewiderstand: allgemein, übergangs-, innerer, gesamt - , ^* Matrix (reziproke Widerstände) Gl. (13) resp. (5) - (m c), (m c) _v , C _Q Wärmekapazität: eines Körpers, der Wärmequelle (v), Matrix Gl. (14) - x, l, U, F, S, V Koordinate, Länge, Umfang, Querschnitt, Oberfläche, Volumen - V _v Volumen der Wärmequelle (v) - Koeffizient der Temperaturabhängigkeit der Wärmeentwicklung - c,n Transformationsmatrix Gl. (10), Normalform von ^* Gl. (16) Mit 9 Textabbildungen     

New results on recursive identification of NARX systems

Recursive identification of nonlinear autoregressive system with exogenous inputs (NARX) y_{k + 1} = f(y_k, ldots, y, u_k, …, u) + ε_{k + 1} is considered in this paper. Continuing a work on the same topic by the authors, the present paper covers a larger class of systems, uses less restrictive conditions, and provides deeper results. To be specific, first, by weakening conditions imposed on f(·) the class of systems has significantly been enlarged, for example, it now covers the Hammerstein system as a special case. Second, a technical condition has been removed that was previously imposed on the function coefficient characterizing the rate of convergence to the invariant measure. Third, not only the strong consistency but also the convergence rate of estimates have been established. The behavior of the estimates is demonstrated by some numerical examples. In particular, when applying to a Hammerstein system, the estimate given in this paper is put in a comparison with the Yule–Walker equation‐based identification algorithms existing in the literature. Copyright © 2011 John Wiley & Sons, Ltd.     

Analytical formula of induced electric fields in a spherical conductor by an ELF dipole magnetic field source

An analytical formula of induced electric field E in a spherical conductor by an ELF dipole magnetic field source is mathematically derived in vector form based on the equivalent mutlipole moment method with reexpansion technique (RE‐EMMM), where M _‖ and are parallel and perpendicular components of M , respectively. The validity of the formula is confirmed in the following three ways: (i) the derivation of the formula from the Sarvas equation with the reciprocity theorem derived by Eaton; (ii) the convergence of the formula to that of homogeneous magnetic field when M _‖ is located at the infinite distance; (iii) comparison of the analytical solutions with numerical solutions by RE‐EMMM. Furthermore, a formula for the trajectory, which satisfies E = 0 , is derived for the field by M _‖. © 2008 Wiley Periodicals, Inc. Electr Eng Jpn, 166(3): 8– 17, 2009; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.20739     

The variable-speed reluctance machine with cageless barrier rotor

Contents The frequency converter supply of rotating-field machines stimulates an interest in machine variants where induced rotor currents are avoided and only imposed rotor currents are permitted.The cageless reluctance machine with barrier rotor is such a variant and its prospects as a substitute for the converter-supplied cage induction motor are investigated.

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Die Reluktanzmaschine mit käfiglosem segmentiertem Rotor

Übersicht Bei Umrichterspeisung von Drehfeldmaschinen besteht Interesse an solchen Maschinenvarianten, die keine induzierten Rotorströme aufweisen und bei denen nur eingeprägte Rotorströme vorkommen können. Die käfiglose Reluktanzmaschine mit segmentiertem Rotor ist eine solche Variante, deren Aussichten als Ersatz für den Käfigläufer-Induktionsmotor bei Umrichterspeisung untersucht werden.

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List of symbols I _d d-axis current component of reluctance machine - L _q q-axis current component of reluctance machine - I _a active current component - I _r reactive current component - N _p number of pole pairs - R ₁ primary resistance - R _2' secondary resistance (referred to the primary) - U(U') primary voltage (behind primary resistance) - (X _d )X _d (per-unit)d-axis reactance of reluctance machine - (X _q )X _q (per-unit)q-axis reactance of reluctance machine - X _o induction machine reactance at zero slip - X induction machine reactance at infinite slip - X _m /X p.u. magnetizing/leakage reactance of induction machine - Z _d /Z _q d/q-axis impedance - d _r rotor diameter - g airgap length - s slip of induction machine - slip-dependent angle of induction machine - load angle of reluctance machine - _p pole pitch     

Polarization Switching in (100)/(001) Oriented Epitaxial Pb(Zr, Ti)O3 Thin Films

Thin films made of (100)/(001)-oriented Pb(Zr, Ti)O₃ (PZT) were deposited by liquid-delivery metal-organic chemical vapor deposition on Ir/MgAl₂O₄/SiO₂/Si(100) substrates. For comparison, PZT thin films were also deposited on Ir/MgO(100) substrates. The X-ray scan spectra for the (202) reflections revealed that the PZT films have four-fold symmetry. It indicates that the PZT films were epitaxially grown as a cube-on-cube structure on both substrates. The switchable polarization (Q_sw) of the PZT capacitors on the silicon substrate was only 23 C/cm² at 1.8 V; however, Q_sw of PZT capacitors on MgO was 99 C/cm². In the case of PZT films deposited on silicon, the volume fraction of (001)-oriented domains (which contribute to polarization switching) was 15.1% (calculated from an XRD pattern). This result is due to the lower Q_sw of PZT capacitors on silicon. By piezoresponse-force microscopy, switchable and unswitchable domains could be identified by imaging color contrast, namely, (001) and (100) domains, respectively. Consequently, domain distribution of the PZT film on a silicon substrate indicates that the (001) domain exists in the (100) domain matrix.     

On the design of multi notch filters

A methodology for designing FIR multi notch filters (NFs) derived from second‐order prototype IIR NFs is suggested. Rejection bandwidth for the designed filter can be controlled by suitable choice of ‘r’, the pole radius of the IIR prototype NFs. The suggested multi NF can also be adapted to eliminate second‐, third‐ and fourth‐order harmonics of periodic noise besides the fundamental noise frequency component. A special case when two notch frequencies ω₁ and ω₂ are such that [(cosω₁)(cosω₂) = ? 1/2] has also been discussed. The IIR multi NF design for this special case results in reduction of the number of multipliers without affecting the response of the desired NF. For the aforereferred condition, the required coefficients of impulse response of FIR multi notch filter get reduced to almost half in number resulting in reduced computations. The number of zero coefficients further reduces with increase in ‘r’ value. In addition, the frequency response becomes better, with reduced ripples in the pass bands, when ‘r’ is increased and length ‘L’ of the FIR NF is chosen appropriately. Copyright © 2010 John Wiley & Sons, Ltd.     

Berechnungsgrundlagen für Transversalflußmaschinen

Übersicht Ausgehend von der Transversalfluß-Anordnung des magnetischen Kreises wird für permanentmagneterregte Synchronmaschinen die Berechnungsmethode beschrieben. Hierbei ist vorausgesetzt, daß durch Wechselrichterspeisung die Stromform näherungsweise trapezförmig vorgegeben ist. Für ein- und zweiseitige Statoranordnungen sowie Erregersysteme in Flachmagnet- und Sammlerkonfiguration werden die mathematischen Beziehungen zwischen Feld- und Stromgrößen und den Abmessungsparametern angegeben. Es wird auf verschiedene Verfeinerungsstufen des Berechnungsverfahrens, etwa durch Berücksichtigung von Streuflußkomponenten und Sättigung des Eisenwegs, hingewiesen. Vergleiche mit der dreidimensionalen FE-Methode und mit Messungen an einem Modellmotor beschließen die Arbeit.

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Calculation and design consideration for synchronous machines with transvers flux configuration

Contents For synchronous machines based on permanent magnet excitation and the transvers flux concept an analytical approach for field and force calculations is being described. One of the assumptions is a known trapezoidal wave form of the armature current, maintained by appropriate frequency inverter and terminal voltage. The analysis covers one and two-sided armature configurations as well as different configurations of the excitation (magnet) system of the rotor. Refinements of the analysis can be achieved by taking into account magnetic leakage components and saturation effects. Comparisons with the 3-dimensional FE-computation and with results from measurements are presented.

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Verwendete Symbole A _a Ankerstrombelag - B _a Induktionskomponente des Ankers - B ₀ Leerlaufinduktion im Spalt (Flachmagnet) - B _0d Leerlaufinduktion vond-Magnet - B _0q Leerlaufinduktion vonq-Magnet - B _r Remanenzinduktion - B _rd Remanenzinduktion, vond-Magnet - B _rq Remanenzinduktion, vonq-Magnet - b _M Polabmessung in Umfangsrichtung - F Umfangskraft - F _A(F) Kraftdichte (Flachmagnet) - F _A(S) Kraftdichte (Sammler) - G _am Stromdichte der Ankerwicklung (maximal) - H _c Koerzitiv-Feldstärke - H _cd Koerzitiv-Feldstärke (d-Magnet) - H _cq Koerzitiv-Feldstärke (q-Magnet) - h _d Magnethöhe (d-Magnet) - h _q Magnethöhe (q-Magnet) - h _i Hohlabmessung, axial - h _M Magnethöhe (Flachmagnet) - i _a Ankerstrom - i _am Ankerstrom (maximal) - k Mittelwert-Koeffizient - k _b Mittelwert-Koeffizient für Rechteckstrom - k _F Korrektur-Koeffizient (Ber. v. Streuung u. Sätt.) - k _d Korrektur-Koeffizient beid-Magneterregung - k _q Korrektur-Koeffizient beiq-Magneterregung - L _a Ankerinduktivität - l _M Magnetabmessung, radial - N _p Polzahl - P _mech Mechanische Leistung - R _a Magnetischer Widerstand (M W), Ankerelement - R _dM M W, d-Magnet - R _j M W, Rückschlußjoch - R _M M W, Flachmagnet - R _qM M W, Quermagnet - R M W, Luftspalt - R ₁ M W, Luftspaltanteil - R ₂ M W, Luftspaltanteil - R _N M W, Streuanteil-Nut - R _M M W, Streuanteil-Pollücke - R _d ,R _q M W, Kombinationswert - T Periode der Feld- und Stromschwingung - T ₁ Halbe Kommutierungszeit - T ₂ Halbe Anstiegszeit vonu _i - T _k Kommutierungszeit - T ₀ Kommutierungsabschnitt - T _a Ankerzeitkonstante - U _k1 Kommutierungsspannung - U _i Induzierte Spannung, maximal - u _i Induzierte Spannung - u _i0max Induzierte Spannung, Leerlauf, maximal - u _imi Induzierte Spannung, Mittelwert - v Umfangsgeschwindigkeit - w Windungszahl der Ankerwicklung - W _m Magnetische Energie - _a Ankerdurchflutung - _Md, _Mq Magnetdurchflutung fürd, q-Magnet - _M Magnetdurchflutung (Flachmagnet) - _d Abmessungsquotient,d-Zweig - _q Abmessungsquotient,q-Zweig - _dg Abmessungsquotient - Luftspaltlänge - ^x Modifizierter Luftspalt - ₀ Permeabilität, Luft - _p Relativ Permeabilität, Permanentmagnet - Polteilung - _a Ankernutzfluß - _p Polfluß - _ai Ankerfluß, ideal - Spezifischer Widerstand     

A comparative study of multiple amplifier active RC biquadratic sections

Biquadratic sections play an important role in the design of high order active filters. This paper compares a number of popular multiple amplifier active RC biquads on the basis of their sensitivities as well as ω₀ and Q enhancement effects due to finite amplifier gain–bandwidth products (GB). For sensitivity comparison, statistical sensitivity measures, which take into account the tolerances of various passive and active elements, are used. Simple expressions for gain, phase and transfer function sensitivities are derived for the case of uncorrelated element variations. Graphic illustrations of the effects of increasing ω₀ and Q on the sensitivity measures are presented. In addition, root-loci, which show the effects of GB on the network poles are included. To further facilitate the comparison, graphs demonstrating changes in ω₀ and Q due to GB are also presented.     

Calculation of transverse edge effects of linear induction motor using Fourier's series method

Contents A single sided linear induction motor with a finite width of the primary is considered. Calculations of magnetic flux density, currents, forces and power losses have been performed for two layers of a secondary using Fourier's series method. Conducting plate thickness and currents in the secondary back iron have been taken into account in an idealized LIM model. Obtained computational results have been compared with the experimental measurements.

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Berechnung transversaler Randeffekte beim linearen Induktionsmotor nach der Methode harmonischer Fourierreihen

Übersicht Es wird ein einseitiger linearer Induktionsmotor mit endlicher Breite des Strombelags betrachtet. Berechnungen der magnetischen Induktion, Strom- und Kraftdichte sowie der Leistungsverluste für beide Schichten des Sekundärteiles mit Hilfe der Fourierreihenmethode wurden dargestellt. Am Idealmodell des linearen Induktionsmotors wurden die Breite der Konduktanzlage sowie Ströme im Eisen des Sekundärteiles berücksichtigt. Erhaltene Berechnungsergebnisse wurden mit experimentellen Messungen verglichen.

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List of Symbols and Abbreviations a primary width - B magnetic flux density - d conducting plate thickness - E electric field intensity - f force density - J current density - J ^s primary linear current density - k l i harmonic and wave number - L primary length - s slip - v secondary speed relative to primary - v _k speed ofk field harmonic - p _e power loss density - effective air gap - permeability - secondary conductivity - _s -a distance between adjacent primaries of the idealized LIM model - _z pole pitch - Q=Q _m e^jt Q=|Q _m |e^j - Q* conjugate value ofQ