Rational Transfer Functions

2004 ◽  
pp. 17-40
Author(s):  
Uwe Mackenroth
Keyword(s):  
Transfer Functions ◽  
Rational Transfer

scholarly journals Design of Cascaded and Shifted Fractional-Order Lead Compensators for Plants with Monotonically Increasing Lags

2020 ◽  
Vol 4 (3) ◽  
pp. 37
Author(s):  
Guido Maione
Keyword(s):  
Fractional Order ◽  
Transfer Functions ◽  
Wide Frequency Range ◽  
Frequency Range ◽  
Robust Controller ◽  
Simulation Experiments ◽  
Rational Transfer ◽  
Serial Connection ◽  
Efficiency Performance ◽  
Two Stages

This paper concerns cascaded, shifted, fractional-order, lead compensators made by the serial connection of two stages introducing their respective phase leads in shifted adjacent frequency ranges. Adding up leads in these intervals gives a flat phase in a wide frequency range. Moreover, the simple elements of the cascade can be easily realized by rational transfer functions. On this basis, a method is proposed in order to design a robust controller for a class of benchmark plants that are difficult to compensate due to monotonically increasing lags. The simulation experiments show the efficiency, performance and robustness of the approach.

scholarly journals SYMMETRIC INTERPOLATORY FRAMELETS AND THEIR ERASURE RECOVERY PROPERTIES

2007 ◽  
Vol 05 (04) ◽  
pp. 541-566 ◽  
Author(s):  
OFER AMRANI ◽  
AMIR AVERBUCH ◽  
TAMIR COHEN ◽  
VALERY A. ZHELUDEV
Keyword(s):  
Transfer Functions ◽  
Error Recovery ◽  
Linear Phase ◽  
Recovery Algorithm ◽  
New Class ◽  
Rational Transfer ◽  
Expansion Coefficients ◽  
Redundant Representation ◽  
Frame Expansions ◽  
Recovery Algorithms

A new class of wavelet-type frames in signal space that uses (anti)symmetric waveforms is presented. The construction employs interpolatory filters with rational transfer functions. These filters have linear phase. They are amenable either to fast cascading or parallel recursive implementation. Robust error recovery algorithms are developed by utilizing the redundancy inherent in frame expansions. Experimental results recover images when (as much as) 60% of the expansion coefficients are either lost or corrupted. The proposed approach inflates the size of the image through framelet expansion and multilevel decomposition thus providing redundant representation of the image. Finally, the frame-based error recovery algorithm is compared with a classical coding approach.

scholarly journals An Approximate Transfer Function Model for a Double-Pipe Counter-Flow Heat Exchanger

Energies ◽  
2021 ◽  
Vol 14 (14) ◽  
pp. 4174
Author(s):  
Krzysztof Bartecki
Keyword(s):  
Heat Exchanger ◽  
Transfer Function ◽  
Differential Equations ◽  
Transfer Functions ◽  
Counter Flow ◽  
Transfer Function Matrix ◽  
Rational Transfer ◽  
Flow Heat ◽  
Double Pipe ◽  
Function Matrix

The transfer functions G(s) for different types of heat exchangers obtained from their partial differential equations usually contain some irrational components which reflect quite well their spatio-temporal dynamic properties. However, such a relatively complex mathematical representation is often not suitable for various practical applications, and some kind of approximation of the original model would be more preferable. In this paper we discuss approximate rational transfer functions G^(s) for a typical thick-walled double-pipe heat exchanger operating in the counter-flow mode. Using the semi-analytical method of lines, we transform the original partial differential equations into a set of ordinary differential equations representing N spatial sections of the exchanger, where each nth section can be described by a simple rational transfer function matrix Gn(s), n=1,2,…,N. Their proper interconnection results in the overall approximation model expressed by a rational transfer function matrix G^(s) of high order. As compared to the previously analyzed approximation model for the double-pipe parallel-flow heat exchanger which took the form of a simple, cascade interconnection of the sections, here we obtain a different connection structure which requires the use of the so-called linear fractional transformation with the Redheffer star product. Based on the resulting rational transfer function matrix G^(s), the frequency and the steady-state responses of the approximate model are compared here with those obtained from the original irrational transfer function model G(s). The presented results show: (a) the advantage of the counter-flow regime over the parallel-flow one; (b) better approximation quality for the transfer function channels with dominating heat conduction effects, as compared to the channels characterized by the transport delay associated with the heat convection.

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