Realization Of Transfer Function Research Articles

New explicit two-dimensional higher order filters

In the present work, a new class of explicit two-dimensional filter is proposed that is significantly different from the conventional one-dimensional Padè type filters. Comparison of performance between one- and two-dimensional filters are made in studying propagation problems and actual viscous flow problems. In this preliminary work, the focus is kept solely on developing central filters with its real transfer function. Many applications related to Navier–Stokes equation have been shown to demonstrate that these two-dimensional filters help in numerical stabilization; control aliasing and control over spurious upstream propagating disturbances. Furthermore, its potential for large eddy simulation (LES) is suggested by band-limiting the solution via filters in post-processing mode.

Robust and Retunable State Realizations of Transfer Functions with known Poles and Zeros

The standard controllable and observable canonical realizations have A-matrices whose eigenvalue locations are highly sensitive to small perturbations to the nonzero entries of the A-matrix that correspond to the coefficients of the characteristic polynomial. On the other hand, the eigenvalue locations of tridiagonal A-matrices are relatively insensitive to similar perturbations. Given a set of known poles and zeros from which the transfer function of a SISO is computed, this paper details an approach to state space realizations with tridiagonal A-matrices using a genetic algorithm and the equivalence of the realization with the controllable canonical form. In addition to the insensitivity of the tridiagonal realization to perturbations, an additional genetic algorithm is used to reconfigure input and output matrices when nonzero gains in the B- and C-matrices are perturbed to zero, i.e., disconnections (shorts/opens) which account for over 70% of field failures. The reconfigured matrices achieve an equivalent realization, thereby maintaining the same input–output behavior. Reconfigurable systems are critical to maintaining exact input–output behavior (automatically) without being able to repair the disconnection.

Interconnection of [formula omitted]-lossless behaviours

In this paper, motivated by the phenomenon of the interconnection of lossless electrical networks, a class of behaviours known as J -lossless behaviours is introduced, where J is a symmetric two-variable polynomial matrix. It is shown that for certain values of J , interconnection of J -lossless behaviours leads to an oscillatory behaviour. Physically this translates to the fact that interconnection of two multi-port lossless electrical networks results in an autonomous lossless electrical network. Finally, the problem of decomposition of an oscillatory behaviour with a given characteristic polynomial as an interconnection of two single-input–single-output behaviours, such that one has a lossless positive real transfer function and the other has a lossless negative real transfer function is also considered. This problem can be viewed as an inverse problem to the one of interconnection of J -lossless behaviours.

The Minimal State Space Realization for a Class of Fractional Order Transfer Functions

In this paper, the minimal state space realization of a fractional order transfer function is investigated in the sense of inner dimension both for commensurate and incommensurate cases. It is shown that while the traditional tools are applicable to check the minimality of a commensurate realization, there is no specific procedure to be certain about the minimality of incommensurate realizations. In this regard, the necessary and sufficient conditions are obtained for a specific class of fractional order transfer functions by which one can verify the existence of minimal realizations with inner dimension 2. Furthermore, a transformation is introduced through which all these realizations can be transformed to each other.

Compact Ridge Waveguide Filters With Arbitrarily Placed Transmission Zeros Using Nonresonating Nodes

Compact size ridge waveguide filters based on the nonresonating node concept are introduced to realize transfer functions with arbitrarily placed attenuation poles. Coupling mechanisms, suitable for the new realization are introduced in diverse E -plane and H -plane configurations and with different input-output interfaces. These coupling structures are studied and characterized in detail in order to simplify the design of the proposed filters. Rigorous mode-matching method is used to accelerate the full-wave design of the filter configurations, whose response is also verified using other numerical techniques and experimental data. To validate the proposed novel designs, a prototype has been built and tested. Measurement results agree well with the predicted theoretical simulations.

Quadratic Stability and Singular SISO Switching Systems

In this note, we consider the problem of determining necessary and sufficient conditions for the existence of a common quadratic Lyapunov function for a pair of stable linear time-invariant systems whose system matrices are of the form <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A</i> , <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A</i> - <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ghT</i> , and where one of the matrices is singular. A necessary and sufficient condition for the existence of such a function is given in terms of the spectrum of the product <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A</i> ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A</i> - <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ghT</i> ) . The technical note also contains a spectral characterization of strictly positive real transfer functions which are strictly proper. Examples are presented to illustrate our results.

Low-voltage log-domain differentiators

A new family of low-voltage log-domain differentiator topologies is introduced in this manuscript. Their attractive characteristic, in comparison to the already published structures, is that the minimum supply voltage requirement is equal to a base-emitter voltage plus twice the saturation voltage of MOS transistors operated in strong inversion, giving potential for employment in modern low-voltage environments. The realization of the corresponding transfer function is achieved by introducing a set of complementary operators which allow the realization of low-voltage active building blocks in the log-domain. Both linear and non-linear performances of the introduced configurations have been studied through simulation results.

Design of tunable biquadratic filters employing CCCIIs: state variable block diagram approach

A state variable block diagram method is given for the realization of universal biquadratic transfer functions employing second-generation current-controlled conveyors (CCCIIs). Using minimum number of passive components and properly adjusting the bias currents of CCCIIs, the proposed circuits can realize all the tunable frequency standard filter functions: high-pass, band-pass, low-pass, notch-pass, and all-pass by choosing appropriate input branches without changing the passive elements. These presented circuits are in current-mode and voltage-mode separately. The non-ideality analyses of these configurations are given. Additionally, a high-order low-pass filter derived from the proposed voltage-mode biquadratic filter is introduced. PSPICE simulation results are included to verify the theory.

Exact Realization of Optical Transfer Functions With Symmetric Transmission Zeros Using the Double-Microring Ladder Architecture

Arrays of parallel-cascaded microring doublets with inter-stage differential phase shifts are proposed for realizing general optical filter transfer functions whose zeros are located on or symmetrically distributed about the imaginary jomega-axis. Compared to previously proposed microring filters capable of realizing transmission zeros, the double-microring ladder architecture has the advantages in that it is compact and requires only synchronously tuned microring resonators with nonnegative coupling coefficients. Furthermore, the building blocks of the filter are simple symmetric microring doublets, which can be separately optimized to achieve good fabrication tolerance and repeatability. A procedure for exactly synthesizing the device given a prescribed transfer function is developed in both the s- and z-domains. Examples of an optical elliptic filter and a linear-phase filter with flat-top spectral responses in both the amplitude and group delay are presented to illustrate the applications of the proposed ladder filter architecture. Sensitivity analysis also shows that the device is robust with respect to microring loss as well as variations in the coupling parameters and phase shift factors.

A Note on Canonic Lattice Realization of Arbitrary FIR Transfer Functions

This note presents some simple alternative solutions to the cases requiring modification of the procedure given in [1] for canonic lattice realization of arbitrary transfer functions.

A New Feedback Configuration for Canonical Realization of IIR Filters and its Application to Lattice Realizations

A feedback configuration is presented for canonical realization of an arbitrary IIR transfer function H(z) = P(z) / Q(z) with M = P(z)0 < N = Q(z)0, which does not appear to have been discussed in the literature. It consists of an IIR transfer function F(z) of degree R in the forward path, where M ≤ R < N, and an FIR transfer function G(z) of degree N – M, In which the first R − M + 1 terms are absent in the feedback path. F(z) and G(z) can be realized by any structure including lattice, if applicable. Application of this method is shown to solve the problem of canonical lattice realization of any IIR transfer function H(z) = P(z) / Q(z) in which M < N and the constant term in P(z) is absent.

An efficient algorithm for positive realizations

We observe that successive applications of known results from the theory of positive systems lead to an efficient general algorithm for positive realizations of transfer functions. We give two examples to illustrate the algorithm, one of which complements an earlier result of [L. Benvenuti, L. Farina, An example of how positivity may force realizations of ‘large’ dimensions, Systems Control Lett. 36 (1999) 261–266]. Finally, we improve a lower-bound of [B. Nagy, M. Matolcsi, A lower-bound on the dimension of positive realizations, IEEE Trans. Circuits Syst. I 50 (2003) 782–784] to indicate that the algorithm is indeed efficient in general.

Optimal Approximation, Simulation and Analog Realization of the Fundamental Fractional Order Transfer Function

Optimal Approximation, Simulation and Analog Realization of the Fundamental Fractional Order Transfer FunctionThis paper provides an optimal approximation of the fundamental linear fractional order transfer function using a distribution of the relaxation time function. Simple methods, useful in systems and control theories, which can be used to approximate the irrational transfer function of a class of fractional systems for a given frequency band by a rational function are presented. The optimal parameters of the approximated model are obtained by minimizing simultaneously the gain and the phase error between the irrational transfer function and its rational approximation. A simple analog circuit which can serve as a fundamental analog fractional system is obtained. Illustrative examples are presented to show the quality and usefulness of the approximation method.

Schur-class multipliers on the Arveson space: De Branges–Rovnyak reproducing kernel spaces and commutative transfer-function realizations

An interesting and recently much studied generalization of the classical Schur class is the class of contractive operator-valued multipliers S ( λ ) for the reproducing kernel Hilbert space H ( k d ) on the unit ball B d ⊂ C d , where k d is the positive kernel k d ( λ , ζ ) = 1 / ( 1 − 〈 λ , ζ 〉 ) on B d . The reproducing kernel space H ( K S ) associated with the positive kernel K S ( λ , ζ ) = ( I − S ( λ ) S ( ζ ) ∗ ) ⋅ k d ( λ , ζ ) is a natural multivariable generalization of the classical de Branges–Rovnyak canonical model space. A special feature appearing in the multivariable case is that the space H ( K S ) in general may not be invariant under the adjoints M λ j ∗ of the multiplication operators M λ j : f ( λ ) ↦ λ j f ( λ ) on H ( k d ) . We show that invariance of H ( K S ) under M λ j ∗ for each j = 1 , … , d is equivalent to the existence of a realization for S ( λ ) of the form S ( λ ) = D + C ( I − λ 1 A 1 − ⋯ − λ d A d ) −1 ( λ 1 B 1 + ⋯ + λ d B d ) such that connecting operator U = [ A 1 B 1 ⋮ ⋮ A d B d C D ] has adjoint U ∗ which is isometric on a certain natural subspace ( U is “weakly coisometric”) and has the additional property that the state operators A 1 , … , A d pairwise commute; in this case one can take the state space to be the functional-model space H ( K S ) and the state operators A 1 , … , A d to be given by A j = M λ j ∗ | H ( K S ) (a de Branges–Rovnyak functional-model realization). We show that this special situation always occurs for the case of inner functions S (where the associated multiplication operator M S is a partial isometry), and that inner multipliers are characterized by the existence of such a realization such that the state operators A 1 , … , A d satisfy an additional stability property.

Sensitivity and robust tuning of PID controllers with real differentiation

We analyze the operation of PID controllers both with ideal differentiation and with taking into account a real transfer function used to differentiate deviations of a controlled variable. A comparison is carried out between the sensitivities of automatic control systems equipped with a PID controller tuned to the minimum of the integral criterion for modulus and to the minimum of the linear integral criterion with the same stability margin in terms of the specified frequency indicator of oscillatory behavior. We also consider the possibility of setting a robust trade-off tuning guaranteeing that the specified stability margin will be preserved under the predicted pattern of change in the dynamics of the controlled plant.

A versatile signal flow graph realization of a general current transfer function

A general synthesis procedure is given for a versatile signal flow graph realization of a general current transfer function by using multi-output second generation current controlled current conveyors (MO-CCCIIs). The proposed configuration uses n + 1 multi-output second generation current conveyors (MO-CCIIs), n capacitors and at most 2 ( n + 1 ) resistors. This number of resistors can be reduced to n for special cases. Using MO-CCCIIs instead of MO-CCIIs, the resistors can be removed completely for the nth-order universal structure. The general transfer function having any numerator dynamics can be derived from the universal structure by using a single MO-CCCII and at most n + 1 resistors. It is very easy to find the values of the passive elements from the coefficients of the transfer function to be realized. The validity of the proposed synthesis is verified through PSpice simulations.

A New Canonic Lattice Realization of Arbitrary FIR Transfer Functions

A new lattice structure is presented for realizing a pair of arbitrary FIR transfer functions of the same order, which is canonic in multipliers as well as delays. By a simple modification of the procedure, one can also obtain a canonic realization of a single FIR transfer function. The problem cases have been discussed, along with their solutions, and the limitations of the method have been pointed out. Examples have been worked out to illustrate the theory.

A New Canonic Lattice Realization of Arbitrary IIR Transfer Functions

A new lattice realization is presented for any arbitrary stable IIR transfer function, which is always canonic in multipliers as well as delays, except for two degenerate cases, which require one (or more) additional delay(s), but no additional multipliers. In contrast to the existing lattice realization of such a transfer function, which uses an all-pass lattice combined with a ladder, the new structure is a truly lattice one. Also, for achieving multiplier canonicity in the conventional structure, one has to use special single multiplier lattice sections; in the new structure, canonicity evolves automatically.

LQG Balancing for Continuous-Time Infinite-Dimensional Systems

In this paper we study the existence of linear quadratic Gaussian (LQG)-balanced realizations for continuous-time infinite-dimensional systems. LQG-balanced realizations are those for which the optimal cost operator for the system and its dual system are equal (and diagonal). The class of systems we consider is that of distributional resolvent linear systems which includes well-posed linear systems as a subclass. We prove the existence of LQG-balanced realizations under a finite cost condition for both the system and its dual system. We also show that an LQG-balanced realization of a well-posed transfer function is well-posed. We further show that approximately controllable and observable LQG-balanced realizations are unique up to a unitary state-space transformation. Finally, we show that the spectrum of the product of the optimal cost operator of a system and its dual system is independent of the particular realization. Our method of proof shows the connections with coprime factorizations, Lyapunov-balanced realizations, and discrete-time systems. The main reason for studying LQG-balanced realizations is that truncated LQG-balanced realizations provide a good approximation of the original system. We show that, under certain conditions, this is also true in the infinite-dimensional case by proving an error bound in the gap-metric.

A Self-Adjusting Simple Hyperstable Adaptive Recursive Algorithm

Adaptive infinite impulse response (IIR), or recursive, filters are less attractive mainly because of the stability and the difficulties associated with their adaptive algorithms. Hyperstability theory when simplified and adapted for digital signal processing offers a new class of IIR filters, simple hyperstable adaptive recursive filters (SHARFs), which is directly related to strictly positive real (SPR) transfer functions. One of the most important drawbacks of the SHARF algorithm is the presence of the unknown denominator in the transfer function that must be SPR in order to ensure convergence. In this paper, SHARF is investigated with SPR transfer functions designed without any priori knowledge of the filter parameters by the pole–zero placement on the unit circle method and made self-adjusting. To demonstrate self-adjustment of the algorithm, SHARF algorithm using constraint least-mean square (LMS) method is applied to a pure four-pole autoregressive process.