Sensitivity of third- and higher-order filters

For any realization of a network function F(s) = N(s)/D(s), the sensitivities that can be most readily calculated are those of the coefficients in N(s) and D(s). A simple relationship is derived that enables one to calculate the root (pole and zero) sensitivities of F(s) in terms of the coefficient sensitivities. The root sensitivities, in turn, enable one to calculate the root pair Q and root frequency sensitivities, which can be used to characterize and compare different realizations of F(s). Application to 3rd- and 4th-order filters reveals formulations that are more elegant than those already known in the literature.     

Schwarz lemma for driving point impedance functions and its circuit applications

In this paper, a boundary version of the Schwarz lemma is investigated for driving point impedance functions and its circuit applications. It is known that driving point impedance function, Z(s) = 1 + c_p(s − 1)^p + c_{p + 1}(s − 1)^{p + 1} + ..., p > 1, is an analytic function defined on the right half of the s-plane. Two theorems are presented using the modulus of the derivative of driving point impedance function, |Z′(0)|, by assuming the Z(s) function is also analytic at the boundary point s = 0 on the imaginary axis with . In the obtained inequalities, the value of the function at s = 1 and the derivatives with different orders have been used. Finally, the sharpness of the inequalities obtained in the presented theorems is proved. Simple LC circuits are obtained using the obtained driving point impedance functions.     

Existence condition of state equations of linear active networks over F(z)

If the physical parameter of each branch of a linear active network is considered to be an independently variable parameter, then it is called a network over the field F(z) of all rational functions in its physical parameters. This paper discusses the existence condition of state equation over F(z) for the active network. The condition depends only on the network structure, and is applied to two examples, which shows that the method is straightforward. Copyright © 2006 John Wiley & Sons, Ltd.     

A new method of inhomogeneous ladder network synthesis

A procedure to synthesize ladder networks in which each series arm impedance is f_iz(s) and each shunt arm admittance is g_iy(s) is presented. Given a specified network function T(s), the function G = z(s)y(s) is first established by a polynomial decomposition. Then the appropriate chain parameters associated with T(s) are constructed as polynomials in G. The constants f_i, g_i are determined from a straightforward continued fraction expansion of a related RL impedance function in G. Necessary and sufficient conditions for the steps in the procedure are established and examples are included.     

Is absolute noninvasive temperature measurement by the Pr[MOE-DO3A] complex feasible

Recently, the feasibility of the praseodymium complex of 10-(2-methoxyethyl)-1,4,7,10-tetraaza-cyclododecane-1,4,7-triacetate (Pr[MOE-DO3A]) for non-invasive temperature measurement via¹H spectroscopy has been demonstrated. Particularly the suitability of the complex for non-invasive temperature measurements including in vivo spectroscopy without spatial resolution as well as first spectroscopic imaging measurements at low temporal resolution (≥4 min) and high temporal resolution (breath hold, ∼20 s) has been shown. As of today, calibration curves according to the particular experimental conditions are necessary. This work aims to clarify whether the Pr[MOE-DO3A] probe in conjunction with¹H-NMR spectroscopy allows non-invasive absolute temperature measurements with high accuracy. The measurement results from two different representative media, distilled water and human plasma, show a slight but significant dependence of the calibration curves on the surrounding medium. Calibration curves in water and plasma were derived for the temperature dependence of the chemical shift difference (F) between Pr[MOE-DO3A]'s OCH₃ and water withF=−(27.53±0.04)+(0.125±0.001)^* T andF=−(27.61±0.02)+(0.129±0.001)^* T. respectivel, withF in ppm andT in °C. However, the differences are minuscule even for the highest spectral resolution of 0.001 ppm/pt, so that they are indistinguishable under practical conditions. The estimated temperature errors are ±0.18°C for water and ±0.14°C for plasma and with that only slightly worse than the measurement accuracy of the fiber-optical temperature probe (±0.1°C). It can be concluded that the results obtained indicate the feasibility of the¹H spectroscopy method in conjunction with the Pr[MOE-DO3A] probe for absolute temperature measurements, with a maximum accuracy of ±0.2°C.     

SSOR preconditioned GPBiCG method for the linear interference cancellation of asynchronous CDMA systems

The decorrelator or the linear minimum mean-squared-error (LMMSE) detector has its computational complexity of O(K ³) where K is the number of users. On the other hand, the computational complexity of iterative detector algorithms such as conjugate gradient (CG) and generalized product bi-conjugate gradient (GPBiCG) methods only require the computational complexity O(K ²) per iteration. In this paper, the symmetric successive overrelaxation (SSOR) preconditioning scheme is applied to the GPBiCG method. The performance of the detectors is investigated and it is found that the SSOR preconditioned GPBiCG method can provide significantly faster convergence.     

Robust gain-scheduled control for vibration suppression

Limited control authority is a key issue in the field of structural control and is a major research area since most of the practical control problems are dominated by constraints on the control signal. The paper presents a simple and practical gain-scheduled controller design procedure for active vibration suppression of a three-storey flexible structure. First, system identification experiments are performed and the plants uncertainty is derived. Next, robust controller design with constraint on the control signal is presented. For a better trade-off between control performance and control constraint a gain-scheduling approach is investigated. Stability analysis of the gain-scheduled controller is analysed using a parameter-independent Lyapunov function (quadratic stability) as well as a parameter-dependent Lyapunov function (biquadratic stability). Finally, the gain-scheduled controller is tested experimentally when the flexible structure is excited with a scaled historical earthquake record (1940 El Centro record). Successful experimental results show that the proposed robust gain-scheduled control approach offers good performance in the case of control authority limitation.Nomenclature M mass matrix - C damping matrix - K stiffness matrix - q relative displacement vector to base - m_a active mass - active mass acceleration - ground (base) acceleration - K_gap transfer gain of the displacement sensor - K_acc transfer gain of the acceleration sensor - K_AMD transfer gain of the active mass damper - _id frequency range of system identification experiments - r control reference - u control signal - d external disturbance - y control output - e control error - x state vector - p(t) time-varying parameter - N_p parameter boxs dimension - V(x) Lyapunov function - V(x,p) parameter-dependent Lyapunov function - largest parameter box where quadratic stability holds - S(s),T(s) sensitivity and complementary sensitivity transfer functions - G_n(s),G(s) transfer function of nominal and real plant - K_rate rate feedback gain - P_n(s) transfer function of nominal plant modified by rate feedback - P(s) transfer function of real plant modified by rate feedback - G_red transfer function of the reduced-order plant - _m(s) multiplicative uncertainty - W_S(s),W_T(s) performance and robustness weighting functions - G_c(s) controllers transfer function - G_c1(s),G_c2(s) transfer function of robust controller for vertex 1 and vertex 2 - G_cs(p,s) transfer function of the gain-scheduled controller - u_A amplitude of the control signal - K_min,K_max minimum and maximum controller gain - K(p) scheduled controller gain - J₁,J₂,J₃,J₄,J₅ performance evaluation parameters     

A sufficient condition of controllability of RLCM active networks over F(z)

This paper defines the separability of an RLCM active network and finds a sufficient condition that the active network is controllable and observable over F(z) if its passive network is controllable and observable over F(z). So the controllability (observability) criteria in (Proc. IEEE ISCAS, 2005) can be used to analyse and design active networks. Copyright © 2006 John Wiley & Sons, Ltd.     

Controllability and observability criteria of RLC networks over F(z)

RLC networks are a class of important linear systems. This paper discusses the problem of controllability and observability of RLC networks over the field F(z) of rational functions in independently variable parameters. Copyright © 2001 John Wiley & Sons, Ltd.     

Sliding mode-based minimum variance and generalized minimum variance controls with O( T 2) and O( T 3) accuracy

The paper deals with the discrete-time sliding mode control with O(T ²) and O(T ³) accuracy, based only on input/output measurements. The linear parts of the control algorithms, recognized as the traditional minimum variance and the generalized minimum variance controls, enable the implementation of the sliding mode control on minimum and non-minimum phase plants. The chattering phenomenon is suppressed by filtering the high-frequency control signal of the sliding mode component through the discrete-time integrator.     

Development of a unified library of sodium properties

A new approach for describing the properties of sodium vapor is described. An equation for the state of sodium vapor is obtained as a dependence s(p, h), which can be used for engineering calculations of power installations with a sodium coolant.     

New theorems in the synthesis of passive multiplexers

Coupling networks that divide the frequency spectrum into separate frequency bands and also provide desired filtering are known as multiplexers. In this paper we present four new theorems concerning the synthesis-theoretic structure of lumped passive multiplexers constructed as lossless reciprocal n-ports. In particular we prove in Theorem 1 that any set of n – 1 admissible power gains, complementary or otherwise, can be realized by a series interconnection of n–1 appropriately chosen non-Foster positive-real functions. In Theorems 2–4 we establish various necessary and sufficient conditions for the realization of bounded-real gains s₂₁(p),…, s_n1(p) given both in magnitude and phase. These conditions reveal that the general problem is one of Nevalinna-Pick interpolation. Lastly, five worked examples are used to illustrate all facets of the theory.     

Bayesian Ying-Yang system, best harmony learning, and five action circling

Firstly proposed in 1995 and systematically developed in the past decade, Bayesian Ying-Yang learning¹⁾ is a statistical approach for a two pathway featured intelligent system via two complementary Bayesian representations of a joint distribution on the external observation X and its inner representation R, which can be understood from a perspective of the ancient Ying-Yang philosophy. We have q(X,R) = q(X|R)q(R) as Ying that is primary, with its structure designed according to tasks of the system, and p(X,R) = p(R|X)p(X) as Yang that is secondary, with p(X) given by samples of X while the structure of p(R|X) designed from Ying according to a Ying-Yang variety preservation principle, i.e., p(R|X) is designed as a functional with q(X|R), q(R) as its arguments. We call this pair Bayesian Ying-Yang (BYY) system. A Ying-Yang best harmony principle is proposed for learning all the unknowns in the system, in help of an implementation featured by a five action circling under the name of A5 paradigm. Interestingly, it coincides with the famous ancient WuXing theory that provides a general guide to keep the A5 circling well balanced towards a Ying-Yang best harmony. This BYY learning provides not only a general framework that accommodates typical learning approaches from a unified perspective but also a new road that leads to improved model selection criteria, Ying-Yang alternative learning with automatic model selection, as well as coordinated implementation of Ying based model selection and Yang based learning regularization. This paper aims at an introduction of BYY learning in a twofold purpose. On one hand, we introduce fundamentals of BYY learning, including system design principles of least redundancy versus variety preservation, global learning principles of Ying-Yang harmony versus Ying-Yang matching, and local updating mechanisms of rival penalized competitive learning (RPCL) versus maximum a posteriori (MAP) competitive learning, as well as learning regularization by data smoothing and induced bias cancelation (IBC) priori. Also, we introduce basic implementing techniques, including apex approximation, primal gradient flow, Ying-Yang alternation, and Sheng-Ke-Cheng-Hui law. On the other hand, we provide a tutorial on learning algorithms for a number of typical learning tasks, including Gaussian mixture, factor analysis (FA) with independent Gaussian, binary, and non-Gaussian factors, local FA, temporal FA (TFA), hidden Markov model (HMM), hierarchical BYY, three layer networks, mixture of experts, radial basis functions (RBFs), subspace based functions (SBFs). This tutorial aims at introducing BYY learning algorithms in a comparison with typical algorithms, particularly with a benchmark of the expectation maximization (EM) algorithm for the maximum likelihood. These algorithms are summarized in a unified Ying-Yang alternation procedure with major parts in a same expression while differences simply characterized by few options in some subroutines. Additionally, a new insight is provided on the ancient Chinese philosophy of Yin-Yang and WuXing from a perspective of information science and intelligent system.     

Identification of the return difference matrix of a multivariable linear control system,in terms of its inverse closed-loop transfer matrix

The return difference matrix F (s) of a multivariable control system with respect to its gain elements is obtainable directly from the inverse transfer matrix T ^?1(s), which is in turn derived (by elimination of undriven node groups) from the coefficient matrix of the set of independent differential equations describing the system. Thus, no knowledge of the system's topology is required in order to obtain F (s). Furthermore, the inverse of one of the submatrices of T ^?1(s) yields the idealized response, if all gain elements are assumed to exhibit infinite gain.     

Another FIR lattice structure

A new two multiplier FIR lattice structure is derived by using the digital two‐pair concept, which produces two transfer functions H_i(z) and H_i′(z) having the complementary relationship H_i′(z)=z^?iH_i(–z^?1), in contrast to the mirror image relationship, i.e. H_i′(z)=z^?iH_i(z^?1) satisfied in the conventional FIR lattice structure. The new structure should be useful in crossover networks as well as in multirate signal processing. Copyright © 2005 John Wiley & Sons, Ltd.     

A quasi analytical procedure for determining the optimum commutation angles of PWM converters

Contents A method for calculating the optimum commutation times for PWM converters is proposed. The method is mainly analytical and leads to a simple, fast calculation procedure. The time behaviour of any variable, electrical or non electrical, which is considered to be the most characteristic of the behaviour of the system, can be optimized. The validity of the analytical approach is subject to some hypotheses which are often verified in practice. The computation power required by the method is so limited that, in the majority of cases, a minicomputer can be used.

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Quasi analytische Bestimmung der optimalen Steuerwinkel für pulsbreitenmodulierte Frequenzumrichter

Übersicht Man beschreibt ein meist analytisches Verfahren für die Berechnung der optimalen Steuerwinkel für pulsbreiten-modulierte Frequenzumrichter. Durch dieses Verfahren wird es möglich, den Zeitverlauf der bedeutendsten elektrischen und nichtelektrischen Größen des Systems zu optimieren. Das Rechnungsverfahren beruht auf meistens erfüllten Annahmen; auf Grund seiner einfachen und schnellen Durchführung braucht man in den meisten Fällen nur Minicomputer zum Zweck.

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List of symbols fundamental frequency - x(t) modulated wave (input wave) - y(t) variable to be optimized (output wave) - f ^*() transfer function - f ^*() f ^*() amplitude - ^*() f ^*() phase - f(n) f ^*() evaluated only in correspondence with () _f integer multipliers - a _n x(t) Fourier coefficients relative to the terms cos (n _f t) - b _n x(t) Fourier coefficients relative to the terms sin (n _f t) - a _n ,b _n asa _n ,b _n , but relative toy(t) - y _d (t) required output wave-form - a _d (n), b _d (n) y _d (t) Fourier coefficients - y _s (t) deviation function (defined asy(t)–y _d (t)) - a _s (n), b _s (n) y _s (t) Fourier coefficients - ^* rms value ofy _s - as ^* except for some constants - _i commutation angles - m ₁ commutations number in the first half of the period - m number of independent commutations in the period - _ij , _ij x _ij auxiliary variables dependent on the _i - V _k numerical values relative to the links imposed onx(t)'s,y(t)'s harmonics - peak values ofy(t) andx(t) harmonic of ordern - Y _n ,X _n rms values of ordern harmonics ofy(t) andx(t) - _j Lagrange multipliers - z number of constraints relative tox(t)'s harmonics Research supported by Italian Research Council (C.N.R.)     

Considerations on the equivalence between non‐uniform transmission lines

We investigate the relation of equivalence between non‐uniform lossless transmission lines (LC lines or lines, for short) with sectionally smooth distributed parameters (series inductance L(x) and shunt capacitance C(x) per unit length, x being the spatial variable). The equivalence condition is derived by heuristic and well‐grounded inference. The condition provides us with the basis on which we can generate by rote a line equivalent to a fixed original line according to a specified change of spatial variable (elasticity function). The concept of intermediary lines between a pair of equivalent lines is introduced to enhance precise understanding of the condition and the procedure to generate equivalent lines. In addition, fused parameters are defined as a generalization of distributed parameters, in terms of which the argument and formulas are developed in a brief and inclusive manner. It is shown to be possible, on generating equivalent lines, to preassign a fused parameter of the equivalent line or one of the associated intermediary lines instead of specifying the elasticity function. Equivalent lines thus obtained are called conditioned equivalent lines. We discuss how to get conditioned equivalent lines as well as equivalency tests of arbitrarily given pair of LC lines to present some comprehensible and promising methods involving a versatile, graphical technique. We also refer to such interesting topics as a normalization of LC lines, a kind of conservation law of fused parameters between equivalent lines and the scope of realizable characteristics by LC lines conditioned in an arbitrary way. Some formerly known equivalence conditions are located appropriately in the context of our theory. Further, the equivalence condition is shown to be not only sufficient but also necessary for LC lines whose distributed parameters may have a finite number of points of discontinuity by invoking a theorem for an inverse scattering problem. Copyright © 2005 John Wiley & Sons, Ltd.     

A‐map representations and asymptotically almost periodic responses

It was recently shown that for each member G of a large class of causal time‐invariant non‐linear input–output maps, with inputs and outputs defined on the non‐negative integers, there is a functional A on the input set such that (Gs) (k) has the representation A(F_ks) for all k and each input s, in which F_k is a simple linear map that does not depend on G. In this paper, we consider non‐linear maps G that have such ‘A‐map representations’. We observe that these Gs have extensions to a domain of inputs defined on the set of all integers. We show that these extensions possess some interesting properties including a certain important uniqueness property. As an application, we show that under the (very often satisfied) conditions of time invariance, causality, and approximately finite memory, and under typically mild boundedness and continuity conditions, the response of G to a discrete‐time asymptotically almost periodic input is an output that is always an asymptotically almost periodic function, and that the almost periodic part of the output is independent of the transient part of the input. We also give corresponding results for a continuous‐time case. Copyright © 2001 John Wiley & Sons, Ltd.     

An optimal algorithm for rectilinear steiner trees for channels with obstacles

The channel rectilinear Steiner tree problem is to construct an optimal rectilinear Steiner tree interconnecting n terminals on the upper shore and the lower shore of a channel without crossing any obstacles inside the channel. However, intersecting boundaries of obstacles is allowed. We present an algorithm that computes an optimal channel rectilinear Steiner tree in O(F₁(k)n + F₂(k)) time, where k is the number of obstacles inside the channel and F₁ and F₂ are exponential functions of k. For any constant k the proposed algorithm runs in O(n) time.     

Inversion of the nodal admittance matrix by the use of state equations

Previous methods^1–4 for inverting the nodal admittance matrix when the elements are rational functions of the Laplace transform variable s used pivotal techniques. Problems of numerical stability made this type of approach suitable only for quite small circuits. A new method based on diagonalizing the A-matrix of a set of state equations defining the circuit has greatly improved stability. The state equations are derived directly from the nodal equations using a newly developed algorithm. These equations are then used to compute the inverse of the nodal admittance matrix as a matrix of rational functions of s. An example is presented of the application of these methods to a system of 21 degrees of freedom.