An alternative method for windup prevention

Windup effects can be subdivided into controller windup and plant windup. Controller windup can be prevented by stabilizing the compensator during saturation and plant windup by an additional dynamic element. When using a compensating design, i. e., the zeros and poles of the plant are compensated by the poles and zeros of the controller, plant windup does not occur. The compensating control is parametrized by one parameter allowing nearly arbitrary disturbance attenuation. This type of control is restricted to minimum-phase systems. But it has a number of advantages. It simplifies the SISO and especially the MIMO design of compensators with integral action considerably, it has good robustness properties and it allows a diagonal decoupling of the reference behavior for arbitrary MIMO system. Two examples demonstrate the results achievable.

Distributions of zeros and poles of -point Padé approximants to complex-symmetric functions defined at complex points

UDC 517.5 The knowledge of the location of zeros and poles Padé and -point Padé approximations to a given function provides much valuable information about the function being studied.In general PAs reproduce the exact zeros and poles of considered function, but, unfortunately, some spurious zeros and poles appear randomly.Then, it is clear that the control of the position of poles and zeros becomes essential for applications of Padé approximation method.The numerical examples included in the paper show how necessary for the convergence of PA is the knowledge of the position of their zeros and poles.We relate our research of localization of poles and zeros of PA and NPA in the case of Stieltjes functions because we are interested in the efficiency of numerical application of these approximations. These functions belong to the class of complex-symmetric functions.The PA and NPA to the Stieltjes functions in different regions of the complex plane is also analyzed. It is expected that the appropriate selection of the complex point for the definition of approximant can improve it with respect to the traditional choice of All considered cases are graphically illustrated.Some unique numerical results presented in the paper, which are sufficiently regular should motivate the reader to reflect on them.

Inverse Nonlinear Eigenvalue Problem Framework for the Synthesis of Coupled-Resonator Filters With Non-Resonant Nodes and Arbitrary Frequency-Variant Couplings

A novel, general circuit-level description of coupled-resonator microwave filters is introduced in this paper. Unlike well-established coupling-matrix models based on frequency-invariant couplings or linear frequency-variant couplings (LFVCs), a model with arbitrary frequency-variant coupling (AFVC) coefficients is proposed. The engineered formulation is more general than prior-art ones and can be treated as an extension of previous synthesis models, since constant or linear couplings are special cases of arbitrary frequency dependence. The suggested model is fully general, allows for AFVCs with highly nonlinear (even singular) characteristics, loaded or unloaded non-resonating nodes (NRNs), frequency-dependent source-load coupling, multiple frequency-variant cross-couplings, and{/}or multiple dispersive couplings for connecting the source and load to the filter network. The model is accompanied by a powerful synthesis technique that is based on the zeros and poles of the admittance or scattering parameters and the eigenvalues of properly defined eigenproblems. In the most general case, the zeros and poles of the admittance or scattering parameters are related to solutions of nonlinear eigenvalue problems. The synthesis is defined as an inverse nonlinear eigenvalue problem (INEVP) where the matrix is constructed from three sets of eigenvalues. This is accomplished by optimization using an iterative nonlinear least-squares solver with excellent convergence property. Finally, third- and fifth-order examples of bandpass filter topologies involving AFVCs are shown, and the experimental validation of the proposed theory is presented through the manufacturing and characterization of a microstrip filter prototype with transmission zeros (TZs)

Inverse Nonlinear Eigenvalue Problem Framework for the Synthesis of Coupled-Resonator Filters With Non-Resonant Nodes and Arbitrary Frequency-Variant Couplings

A novel, general circuit-level description of coupled-resonator microwave filters is introduced in this paper. Unlike well-established coupling-matrix models based on frequency-invariant couplings or linear frequency-variant couplings (LFVCs), a model with arbitrary frequency-variant coupling (AFVC) coefficients is proposed. The engineered formulation is more general than prior-art ones and can be treated as an extension of previous synthesis models, since constant or linear couplings are special cases of arbitrary frequency dependence. The suggested model is fully general, allows for AFVCs with highly nonlinear (even singular) characteristics, loaded or unloaded non-resonating nodes (NRNs), frequency-dependent source-load coupling, multiple frequency-variant cross-couplings, and{/}or multiple dispersive couplings for connecting the source and load to the filter network. The model is accompanied by a powerful synthesis technique that is based on the zeros and poles of the admittance or scattering parameters and the eigenvalues of properly defined eigenproblems. In the most general case, the zeros and poles of the admittance or scattering parameters are related to solutions of nonlinear eigenvalue problems. The synthesis is defined as an inverse nonlinear eigenvalue problem (INEVP) where the matrix is constructed from three sets of eigenvalues. This is accomplished by optimization using an iterative nonlinear least-squares solver with excellent convergence property. Finally, third- and fifth-order examples of bandpass filter topologies involving AFVCs are shown, and the experimental validation of the proposed theory is presented through the manufacturing and characterization of a microstrip filter prototype with transmission zeros (TZs)

SOME NOTICES ON ZEROS AND POLES OF MEROMORPHIC FUNCTIONS IN A UNIT DISK FROM THE CLASSES DEFINED BY THE ARBITRARY GROWTH MAJORANT

In [4] by the Fourier coefficients method there were obtained some necessary and sufficient conditions for the sequence of zeros $(\lambda_{\nu})$ of holomorphic in the unit disk $\{z:|z|<1\}$ functions $f$ from the class that determined by the majorant $\eta :[0;+\infty)\to [0;+\infty )$ that is an increasing function of arbitrary growth. Using that result in present paper it is proved that if $(\lambda_{\nu})$ is a sequence of zeros and $(\mu_ {j})$ is a sequence of poles of the meromorphic function $f$ in the unit disk, such that for some $A>0, B>0$ and for all $r\in(0;1):\ T(r;f)\leqslant A\eta\left(\frac B{1-|z|}\right)$, where $T(r;f):=m(r;f)+N(r;f);\ m(r;f)=\frac{1}{2\pi }\int\limits_0^{2\pi } \ln ^{+}|f(re^{i\varphi})|d\varphi$, then for some positive constants $A_1, A’_1, B_1, B’_1, A_2, B_2$ and for all $k \in\mathbb{N}$, $r,\ r_1$ from $(0;1)$, $r_2\in(r_1;1)$ and $\sigma\in(1;1/r_2)$ the next conditions hold $N (r,1/f) \leq A_1 \eta\left(\frac{B_1}{1-r}\right)$, $N(r,f)\leq A'_1\eta \left( \frac{B'_1}{1-r}\right) $, $$\frac1{2k}\left|\sum\limits_{r_1 <|\lambda_{\nu}|\leqslant r_{2}} \frac1{\lambda_{\nu}^k} -\sum\limits_{r_1 < |\mu_j|\leqslant r_2} \frac 1{\mu_j^{k}} \right| \leq \frac{A_{2}}{r_{1}^{k}}\eta\left(\frac{B_{2}}{1 -r_1}\right ) +\frac{A_{2}}{r_{2}^{k}}\max\left\{ 1;\frac 1{k\ln \sigma}\right\}\eta\left(\frac{B_{2}}{1 -\sigma r_{2}}\right)$$ It is also shown that if sequence $(\lambda_{\nu})$ satisfies the condition $N (r,1/f) \leq A_1 \eta\left(\frac{B_1}{1-r}\right)$ and $$\frac1{2k}\left|\sum\limits_{r_1 <|\lambda_{\nu}|\leqslant r_{2}} \frac1{\lambda_{\nu}^k} \right| \leq \frac{A_{2}}{r_{1}^{k}}\eta\left(\frac{B_{2}}{1-r_{1}}\right) +\frac{A_{2}}{r_{2}^{k}}\max\left\{ 1;\frac 1{k\ln \sigma}\right\}\eta\left(\frac{B_{2}}{1 -\sigma r_{2}}\right)$$ there is possible to construct a meromorphic function from the class $T(r;f)\leqslant \frac{A}{\sqrt{1-r}}\eta\left(\frac B{1-r}\right)$, for which the given sequence is a sequence of zeros or poles.

Two semigroup rings associated to a finite set of meromorphic functions

We fix z0 ∈ ℂ and a field 𝔽 with ℂ ⊂ 𝔽 ⊂ 𝓜z0 := the field of germs of meromorphic functions at z0. We fix f1, …, fr ∈ 𝓜z0 and we consider the 𝔽-algebras S := 𝔽[f1, …, fr] and $\begin{array}{} \overline S: = \mathbb F[f_1^{\pm 1},\ldots,f_r^{\pm 1}]. \end{array} $ We present the general properties of the semigroup rings$$\begin{array}{} \displaystyle S^{hol}: = \mathbb F[f^{\mathbf a}: = f_1^{a_1}\cdots f_r^{a_r}: (a_1,\ldots,a_r)\in\mathbb N^r \text{ and }f^{\mathbf a}\text{ is holomorphic at }z_0],\\\overline S^{hol}: = \mathbb F[f^{\mathbf a}: = f_1^{a_1}\cdots f_r^{a_r}: (a_1,\ldots,a_r)\in\mathbb Z^r \text{ and }f^{\mathbf a}\text{ is holomorphic at }z_0], \end{array} $$and we tackle in detail the case 𝔽 = 𝓜<1, the field of meromorphic functions of order < 1, and fj’s are meromorphic functions over ℂ of finite order with a finite number of zeros and poles.