The state-space realization of an n-dimensional transfer function

In this paper the non-minimal real state-space realization for n-dimensional transfer functions with polylinear numerators and denominators is stated and proved. It is also shown that the every existing realization of an n-dimensional transfer function can be achieved from the companion matrix of some (n + 1)-variable polynomial linear with respect to one of its variables.     

On Improved Representation Theorems For Multidimensional Lossless Bounded Matrices

An improved form of representation of multidimensional (k-D) discrete lossless two-ports in a form similar to the well-known Belevitch canonical form of classical one-dimensional network theory is presented. Representations of the transfer function matrix, chain matrix and hybrid matrix associated with discrete lossless multidimensional twoports are derived on the basis of our earlier result. An improved form of representation of multidimensional (k-D) discrete lossless two-ports in a form similar to the well-known Belevitch canonical polynomial associated with the system. This fact is true for both discrete and continuous systems and apparently has remained unnoticed even in ID.     

Realization of a general all‐pole current transfer function by using CBTA

In this article, a general all‐pole current transfer function synthesis procedure using current backward transconductance amplifiers (CBTAs) is proposed. The proposed configuration uses n current backward transconductance amplifiers and n grounded capacitors as the only type of passive elements. The circuit is eligible to realize any all‐pole transfer characteristics with a given strictly Hurwitz (stable) denominator polynomial. Further, it is straightforward to find the values of the passive elements from the coefficients of this polynomial by using the Routh–Hurwitz algorithm as in the realization of a two‐element kind passive network synthesis. In this sense and as far as the author's knowledge, it is the only active structure that can be synthesized like a passive two‐element kind Cauer circuit. The simulations that are performed using PSPICE exhibit satisfactory results coherent with the theory. Copyright © 2011 John Wiley & Sons, Ltd.     

On the design of multiband transmission functions synthesized by one wave digital lattice structure

In this contribution, the design of multiband transmission functions is considered. Independent and arbitrary number of bands can be designed. Moreover, the whole transmission function is synthesized by one wave digital lattice structure. The approximation process starts by extracting the scattering matrix properties of multiband reference lattice structures. Consequently, the approximation problem reduces to generating a polynomial Q of degree n, which is the degree of the filter. The degree n is depending on the number of the designed bands. Hence, if the number of bands is even, n will be odd, and if the number of bands is odd, n will be even. The polynomial Q will approximate the difference phase function of the two branch polynomials. It is composed of two subpolynomials, one of them is Hurwitz and the other is anti‐Hurwitz. The degrees of these subpolynomials differ by odd number if the number of bands is even and differ by even number if the number of bands is odd. Q is generated according to iterative interpolation and using explicit recursive formulas. After obtaining Q, the two subpolynomials are calculated and the two branch all‐pass functions are constructed. Consequently, the filter is synthesized in the digital frequency domain. The method is applied through an illustrative example. Copyright © 2011 John Wiley & Sons, Ltd.     

Synthesis of low-sensitivity orthogonal digital filters

A novel method is proposed for the synthesis of low-sensitivity digital filters meeting any prescribed transfer function. The method is based on extracting an orthogonal matrix from the filter state matrix, resulting in structures that need n Givens rotations and at most n+1 multipliers. Thus the proposed realization is canonic in the sense that it has the same degrees of freedom as the original transfer function. It is also shown that when the filter transfer function is a reciprocal reactant bounded function, it can be decomposed into allpass functions that need only Givens rotations for their realization. As the basic module in the realization is the Givens rotation, the CORDIC computation algorithm can be applied directly. This means considerable savings in computation time and complexity. It also results in structures that are less sensitive to the effects of finite word length. Illustrative examples, including the design and synthesis of linear phase selective filters, are given to show the extremely low sensitivity with respect to finite word length of the resulting realizations when compared with other methods. © 1997 by John Wiley & Sons, Ltd.     

Solving the helmholtz equation using multiply propagated fields

Computer models in electromagnetics are based primarily either on integral or on differential equations. The former arise from source integrals using some appropriate Green's function whereas the latter originate from the Maxwell curl equations. Although requiring volume rather than surface sampling even for spatially homogeneous problems, in contrast to integral-equation (IE) models, differential-equation (DE) models are geneally a better choice for problems involving spatial inhomogeneities. This is because such problems require volumetric sampling using either approach, but the DE model produces a sparse matrix rather than the full matrix of the IE formulation. In this paper we describe a new approach based on using multiply propagated fields for numerically solving the banded matrix that results from discretizing the Helmholtz equation. A computer-time savings of N^1/2 and N^2/3 for two-dimensional (2-D) and three-dimensional (3-D) problems, respectively, is made possible, where N is the total number of field samples or unknowns. For even moderate-size problems where 100 samples per linear dimension are used (N₂ = 10,000 and N₃ = 1,000,000), the time savings can be of the order of 100 and 10,000 respectively. Another advantage of this procedure, which we call Helmholtz equation multiple propagator (HEMP), is that the radiation or closure condition needed to terminate the spatial solution mesh for exterior problems can be enforced rigorously with essentially no additional computational cost. The method is illustrated for a 2-D problem by application to plane-wave scattering from an infinite, metal, circular cylinder. Results are presented for the mode amplitudes of the scattered field, the induced surface current, and the bistatic far field as obtained from HEMP, and shown to be in good agreement with the analytical results. Although limited here to the simplest possible application in order to establish its feasibility, the approach's advantage would be its applicability to 2-D and 3-D problems involving inhomogeneous, penetrable objects.     

Line-to-line Voltage Space Vector Modulation for Neutral-point Clamped Multi-level Converter with DC-link Capacitor Voltage Balancing Using Redundant Vectors

This article presents space vector modulation of line-to-line voltage for the three-phase neutral-point clamped n-level converter with DC-link capacitor voltage balancing using redundant vectors. The developed modulation strategy is based on an equivalent matrix structure of the neutral-point clamped n-level converter. The relation between the 3 × (n – 1) switching functions of the matrix converter and gate signals of transistors of the neutral-point clamped n-level converter is given. A line-to-line space vector modulation strategy for a matrix inverter is used to obtain the switching function. For one switching function, there is more than one combination to produce each output voltage. Thus, redundancies of different switch configurations for generation of intermediate voltages are used to limit the deviation of capacitor voltages. The gate signals of the neutral-point clamped n-level converter can be calculated by inversing the modeling parts. Here, line-to-line voltage space vector modulation for a neutral-point clamped n-level converter is designed without using a Parks transform. Moreover, n × (n – 1) redundant vectors are used for DC bus voltage balancing. To highlight the performances of the developed modulation strategy, simulation results are given for five- and seven-level neutral-point clamped converters. Experimental results are given for a neutral-point clamped three-level converter.     

General interpretation of sensitivity functions

A general interpretation of sensitivity functions of linear networks is given in order to determine any nth order sensitivity function with respect to any parameter. The calculation uses an indirect method: ‘transfer function products’ give the desired sensitivities instead of derivation. The interpretation makes it possible to construct a computer program, too, which needs only one matrix inversion for a complete sensitivity analysis (including first- and higher-order sensitivities). It is shown that the adjoint network approach is superfluous and more complicated than the given method.     

A study of the least mean p‐th adaptive notch filter

In this paper we propose a least mean p‐th adaptive notch filter that has a cost function of E[e^p(n)], where e(n) is the estimation error. The structure of the adaptive filter is a tandem connection of the second‐order adaptive notch filter with an all‐pass filter. In general, the bandwidth of the notch filter should be extremely small from the theoretical and practical viewpoints. However, the convergence speed of the weight becomes slow if the bandwidth is reduced. The transfer function of the notch filter has the following special characteristic, that is, zero in the center frequency and unity in other frequencies. The equivalent broad bandwidth can be obtained when the cost function is chosen as E[e^p(n)]. Higher convergence speed and excellent stationary performance are obtained using the combination of E[e^p(n)]. Finally, the convergence performance of the estimation accuracy is verified by the computer simulation. © 2004 Wiley Periodicals, Inc. Electr Eng Jpn, 150(3): 46–53, 2005; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.20045     

Formulae of resistance between two corner nodes on a common edge of the m × n rectangular network

This paper deals with the equivalent resistance for the m × n resistor network in both finite and infinite cases. Firstly, we build a difference equation driven by a tridiagonal matrix to model the network; then by performing the diagonalizing transformation on the driving matrix, and using the auxiliary function tz(x,n), we derive two formulae of the equivalent resistance between two corner nodes on a common edge of the network. By comparing two different formulae, we also obtain a new trigonometric identity here. Our framework can be effectively applied in complex impedance networks. As in applications in the LC network, we find that our formulation leads to the occurrence of resonances at frequencies associated with (n + 1)?_t = kπ. This somewhat curious result suggests the possibility of practical applications of our formulae to resonant circuits. At the end of the paper, two other formulae of an m × n resistor network are proposed. Copyright © 2014 John Wiley & Sons, Ltd.     

Generalized linear phase polynomials—application in filter synthesis

In this paper, we give explicit expressions for the study of attenuation and phase characteristics of generalized linear phase polynomials (i.e. Jacobi and generalized Bessel polynomials for transmission line and lumped filters respectively). We present an exact method to find the digital transfer function which exhibits [n/2] to (n?1) simultaneous conditions on amplitude and delay.     

A chebyshev rational function with low Q-factors

The presented rational function is a modification of a recently published Chebyshev rational function defined by means of some orthogonal polynomials. the necessary conditions providing for the lowest pole Q-factors for a given ripple are found. the function is a ratio of two similar Chebyshev polynomial transfer functions with multiple poles. The selectivity of the function can be increased by using the Chebyshev rational characteristic function instead of the characteristic polynomials. the minimum number of active elements in the cascade connection is obtained with third-order elliptic characteristic functions. The function is compared with the Cauer (elliptic) and MCPER filters. the distinctive features of the presented function are small Q-factors of the poles, almost ideal dynamic range, simple design and poles with the same multiplicity m, where m designates the number of cascaded blocks.     

Single variable expressions for the efficiency of a reciprocal power transfer system

The analytical expressions for the efficiency of a reciprocal power transfer system as a function of multiple parameters, that is, the elements of its impedance matrix, already exist. In this work, closed expressions for this efficiency as a function of a single parameter, that is, the extended kQ factor, are derived. This is done for three representative configurations: (i) maximum efficiency; (ii) maximum power transfer; and (iii) conjugate image set‐up. The derived formulas are useful for the design and optimization of different types of power transfer systems. Copyright © 2016 John Wiley & Sons, Ltd.     

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     

An indirect model reference adaptive controller based on the multirate sampling of the plant output

The use of sampled-data multirate-output controllers for model reference adaptive control of possibly non-stably invertible linear systems with unknown parameters is investigated. Multirate-output controllers contain a multirate sampling mechanism with different sampling period at each system output. Such a control allows us to assign an arbitrary discrete-time transfer function matrix for the sampled closed-loop system and does not make assumptions on the plant other than controllability, observability and the knowledge of two sets of structural indices, namely the controllability and the observability indices. An indirect adaptive control scheme based on these sampled-data controllers is proposed which estimates the unknown plant parameters (and consequently the controller parameters) on-line from sequential data of the inputs and the outputs of the plant, which are recursively updated within the time limit imposed by a fundamental sampling period T₀. Using the proposed adaptive algorithm, the model reference adaptive control problem is reduced to the determination of a fictitious static state feedback controller owing to the merits of multirate-output controllers. Known indirect model reference adaptive control techniques usually resort to the direct computation of dynamic controllers. The controller determination reduces to the simple problem of solving a linear algebraic system of equations, whereas in known indirect model reference adaptive control techniques, matrix polynomial Diophantine equations usually need to be solved. Moreover, persistent excitation of the continuous-time plant is provided without making any special richness assumption on the reference signals.     

High‐performance V/f control of PMSM using state feedback control based on n–t coordinate system

This paper proposes a new V/f control method for permanent magnetic synchronous motors (PMSMs) without a position sensor. The proposed method uses state feedback control based on an n–t coordinate system, and controls rotational speed and the voltage amplitude. The t‐axis is a tangent line of a constant voltage ellipse, and the n‐axis is a normal line of the ellipse. The t‐axis current is utilized to place the poles of the transfer function at the desired position at low‐speed and high‐speed conditions. The effectiveness of the proposed method was verified by simulation and experimental results.     

Synthesis of n‐port resistive networks containing 2n terminals

This paper is concerned with the realizability problem of n‐port resistive networks that contain 2n terminals. A necessary and sufficient condition for any real symmetric matrix to be realizable as the admittance of an n‐port resistive network containing 2n terminals is obtained. This condition is based on the existence of a parameter matrix. Furthermore, the values of the elements are expressed in terms of the entries of the admittance matrix and the parameter matrix. Finally, a numerical example is used to illustrate the results. Copyright © 2013 John Wiley & Sons, Ltd.     

Short-circuit admittance matrix synthesis with rc common-ground networks and a minimum number of grounded finite-gain phase-inverting voltage-controlled voltage sources

A new procedure for the synthesis of active RC networks when grounded finite-gain phase-inverting voltage-controlled voltage sources serve as active elements is developed. It is proved that an arbitrary n × n matrix of real rational functions of the complex frequency variable can be realized as the short-circuit admittance matrix of a grounded transformerless active RC n-port network containing (n+1) grounded finite-gain phase-inverting voltage-controlled voltage sources (VCVSs). In general all the (n+1) grounded VCVSs are necessary. The structure proposed to prove a general theorem is later simplified for the realization of a restricted but important class of real rational matrices to obtain considerable savings in the computation volume and in the number of passive components used for the realization of the network. Examples are given to illustrate presented synthesis procedures.     

A method of design for a class of 2-D filters

This paper discusses a method of designing quadrantally symmetric cascaded two-dimensional (2-D) digital recursive filters by subjecting a one variable approximating function to successive transformations. the needed approximation is done in the one variable domain rather than in the 2-D domain, hence leading to a large reduction of computational labour. Using cepstral techniques each denominator polynomial is spectrally factorized into recursible non-symmetric half plane components. A significant feature of the method is in decoupling the problems of approximation and stability. Consequently spectral factorization needs to be performed only once for each denominator polynomial. Effects of truncation on filter stability are minimized by ensuring rapid convergence of cepstra. the choice of an adequate DFT size in cepstral computations is shown to be an important consideration for many problems associated with spectral decomposition. Attempts are also made to stabilize the unstable transfer function using an existing 2-D discrete Hilbert transform method. Considerable distortion in magnitude characteristics is shown to result on stabilization. Finally the method is illustrated by two examples.     

Analog circuit design by nonconvex polynomial optimization: Two design examples

We present a framework for synthesizing low‐power analog circuits through global optimization over generally nonconvex multivariate polynomial objective function and constraints. Specifically, a nonconvex optimization problem is formed, which is then efficiently solved through convex programming techniques based on linear matrix inequality (LMI) relaxation. The framework allows both polynomial inequality and equality constraints, thereby facilitating more accurate device modelings and parameter tuning. Compared to traditional nonlinear programming (NLP), the proposed methodology exhibits superior computational efficiency, and guarantees convergence to a globally optimal solution. As in other physical design tasks, circuit knowledge and insight are critical for initial problem formulation, while the nonconvex optimization machinery provides a versatile tool and systematic way to locate the optimal parameters meeting design specifications. Two circuit design examples are given, namely, a nested transconductance(G_m)–capacitance compensation (NGCC) amplifier and a delta–sigma (ΔΣ) analog‐to‐digital converter (ADC), both of them being the key components in many electronic systems. Copyright © 2008 John Wiley & Sons, Ltd.