Reléový test pro anizochronní modely - řešení v časové oblasti

Anisochronic models are characteristic for containing state delays. These models have some practical and attractive features; e.g. they enable to fit the dynamics of systems with very high order. This contribution utilizes an idea of anisochronic models identification based on limit cycle information obtained from relay feedback test is investigated. Unlike conventional approaches connected with the frequency analysis of a plant transfer function, the proposed alternative methodology is based on computation with functional differential equation only, i.e. in time domain. Plant parameters to be identified are obtained analytically. In addition, parameter estimation is also improved using autotune variable (ATV+) technique which required an additional delay element. An illustrative example where parameters of a tenth order system are approximated by a first order anisochronic model is presented.Anizochronní modely jsou význačné tím, že obsahují zpoždění stavových veličin. Tyto modely mají některé zajímavé vlastnosti – například umožňují vystihnout dynamiku konvenčních soustav vyšších řádů a dále matematické modely mnoha procesů vedou právě na anisochronní modely. V tomto příspěvku je prezentována myšlenka identifikace těchto modelů pomocí reléového experimentu. Narozdíl od tradičního pojetí je zde uveden postup pro odhad parametrů modelu přímo z diferenciální rovnice, tedy v časové oblasti. Reléový test je dále vylepšen pomocí metody ATV+ využívající umělého zpoždění. Ilustrační příklad, kde je systém 10. řádu aproximován anizochronním modelem 1. řádu, demonstruje uvedenou metodiku

Spectrum analysis of LTI continuous-time systems with constant delays: A literature overview of some recent results

In recent decades, increasingly intensive research attention has been given to dynamical systems containing delays and those affected by the after-effect phenomenon. Such research covers a wide range of human activities and the solutions of related engineering problems often require interdisciplinary cooperation. The knowledge of the spectrum of these so-called time-delay systems (TDSs) is very crucial for the analysis of their dynamical properties, especially stability, periodicity, and dumping effect. A great volume of mathematical methods and techniques to analyze the spectrum of the TDSs have been developed and further applied in the most recent times. Although a broad family of nonlinear, stochastic, sampled-data, time-variant or time-varying-delay systems has been considered, the study of the most fundamental continuous linear time-invariant (LTI) TDSs with fixed delays is still the dominant research direction with ever-increasing new results and novel applications. This paper is primarily aimed at a (systematic) literature overview of recent (mostly published between 2013 to 2017) advances regarding the spectrum analysis of the LTI-TDSs. Specifically, a total of 137 collected articles-which are most closely related to the research area-are eventually reviewed. There are two main objectives of this review paper: First, to provide the reader with a detailed literature survey on the selected recent results on the topic and Second, to suggest possible future research directions to be tackled by scientists and engineers in the field. © 2013 IEEE.MSMT-7778/2014, FEDER, European Regional Development Fund; LO1303, FEDER, European Regional Development Fund; CZ.1.05/2.1.00/19.0376, FEDER, European Regional Development FundEuropean Regional Development Fund through the Project CEBIA-Tech Instrumentation [CZ.1.05/2.1.00/19.0376]; National Sustainability Program Project [LO1303 (MSMT-7778/2014)

Algebraic robust control of a closed circuit heating-cooling system with a heat exchanger and internal loop delays

This study demonstrates the use of a simple algebraic controller design for a cooling-heating plant with a through-flow air-water heat exchanger that evinces long internal delays with respect to the robustness to plant model uncertainties and variable ambient temperature conditions during the season. The advantage of the proposed design method consists in that the delays are not approximated but fully considered. Moreover, the reduction of sensitivity to model parameters’ variations yields the better applicability regardless modeling errors or environmental fluctuations. The infinite-dimensional mathematical model of the plant has been obtained by using anisochronic modeling principles. The key tool for the design is the ring special of quasipolynomial meromorphic functions (RQM). The Two-Feedback-Controllers (TFC) rather than the simple negative control feedback loop is utilized, which enables to solve the reference tracking and disturbance rejection independently and more efficiently. The eventual controller is then tuned such that robust stability and robust performance requirements are fulfilled. The tuning procedure is supported by a performance optimization idea. Since the originally obtained controller is of the infinite-dimensional nature, a possible way how to substitute it by a simplified finite-dimensional one is proposed for engineering practice. The functionality of both the controllers is compared and verified by simulations as well as by real measurements which prove a very good performance. © 2016 Elsevier LtdEuropean Regional Development Fund under the project CEBIA-Tech Instrumentation [CZ.1.05/2.1.00/19.0376

PPSA: A tool for suboptimal control of time delay systems: Revision and open tasks

Abstract During the development of algebraic controller design in a special ring for time delay systems (TDSs) a problem of a suitable free controller parameters setting appeared. The first author of this contribution recently suggested a natural idea of placing the dominant characteristic numbers (poles) and zeros of the infinite-dimensional feedback control system on the basis of the desired overshoot for a simple finite-dimensional matching model and shifting of the rest of the spectrum. However, the original procedure called the Pole-Placement Shifting based controller tuning Algorithm (PPSA) was not developed and described entirely well. The aim of this paper is to revise the idea of the PPSA and suggest a possible ways how to improve or extend the algorithm. A concise illustrative example is attached to clarify the procedure for the reader as well

A comparison of possible exponential polynomial approximations to get commensurate delays

The paper is aimed at a comparative simulation study on three prospective ideas how to approximate a general exponential polynomial by another one having all its exponents in the exp-function as integer multiples of some real number. This work is motivated by spectral properties of neutral time-delay systems (NTDS) and the contemporary state of the knowledge about the spectrum of NTDS with commensurate delays which are characterized by the latter family of exponential polynomials. The three ideas are, namely, those: Taylor series expansion, the interpolation in points given by dominant roots estimates and the special extrapolation technique presented by the authors recently. The goal is to match dominant parts of both the spectra as close as possible. However, some properties from the so called strong stability point of view can not be, in principle, preserved. The presented simulation example demonstrates the accuracy and efficiency of all the methods.Ministry of Education, Youth and Sports of the Czech Republic within the National Sustainability Programme [L01303, MSMT-7778/2014]; European Regional Development Fund [CZ.1.05/2.1.00/03.0089

Robust stability of thermal control systems with uncertain parameters: The graphical analysis examples

This paper is intended to present the investigation of robust stability for integer order or fractional order feedback control loops affected by parametric uncertainty and time-delay(s) with special emphasis on the thermal control systems. The applied graphical method is based on the numerical calculations of the value sets and the zero exclusion condition. Three robust stability examples inspired by control of the real-world thermal processes are used for demonstration of the technique applicability. Namely, the work deals with the analysis of a shell-and-tube heat exchanger which was identified as the (integer order) time-delay model with parametric uncertainty, a heat transfer process modeled as the fractional order time-delay plant with parametric uncertainty, and a heating–cooling system with a heat exchanger described by the anisochronic model with internal delays and parametric uncertainty. © 2017 Elsevier LtdEuropean Regional Development Fund under the project CEBIA-Tech Instrumentation [CZ.1.05/2.1.00/19.0376]; Ministry of Education, Youth and Sports of the Czech Republic within the National Sustainability Programme [LO1303 (MSMT-7778/2014)

The revision and extension of the R-MS ring for time delay systems

This paper is aimed at reviewing the ring of retarded quasipolynomial meromorphic functions (R-MS) that was recently introduced as a convenient control design tool for linear, time-invariant time delay systems (TDS). It has been found by the authors that the original definition does not constitute a ring and has some essential deficiencies, and hence it could not be used for an algebraic control design without a thorough reformulation which i.e. extends the usability to neutral TDS and to those with distributed delays. This contribution summarizes the original definition of RMS, simply highlights its deficiencies via examples, and suggests a possible new extended definition. Hence, the new ring of quasipolynomial meromorphic functions (R-QM) is established to avoid confusion. The paper also investigates and introduces selected algebraic properties supported by some illustrative examples and concisely outlines its use in controller design.European Regional Development Fund under the project CEBIA-Tech Instrumentation [CZ.1.05/2.1.00/19

Robust stability of fractional order polynomials with complicated uncertainty structure

The main aim of this article is to present a graphical approach to robust stability analysis for families of fractional order (quasi-)polynomials with complicated uncertainty structure. More specifically, the work emphasizes the multilinear, polynomial and general structures of uncertainty and, moreover, the retarded quasi-polynomials with parametric uncertainty are studied. Since the families with these complex uncertainty structures suffer from the lack of analytical tools, their robust stability is investigated by numerical calculation and depiction of the value sets and subsequent application of the zero exclusion condition. © 2017 Matusu et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.European Regional Development Fund under the project CEBIA-Tech Instrumentation [CZ.1.05/ 2.1.00/19.0376]; Ministry of Education, Youth and Sports of the Czech Republic within the National Sustainability Programme [LO1303, MSMT-7778/2014

Improved and innovated universal DAQ microcontroller unit

This paper is aimed at the description of hardware design, software equipment and the functionality of the second evolution of the intelligent multipurpose input/output microcontroller converter and control unit designed and assembled by the authors. Preceding stages of the unit development are concisely overviewed first, the deficiencies of which give rise to the primary motivation of this contribution. Then separate hardware parts of the novel unit are described in detail including electronic schematic diagrams. The device firmware and software capabilities are introduced as well. The advantages of the unit are highlighted compared to older versions. Its functionality, performance and efficiency are then verified by a laboratory control-related dynamic responses measurement example. In the contrary to previous evolutions, a more compact hardware design, increased A/D and D/A converter resolutions, added USB communication capability, better and more accurate analog circuits with more advanced operation amplifiers, the use of OLED instead of LCD display, the pulse-width modulated signal generated by the microcontroller unit itself can be considered among the most important improvements. Moreover, the direct use of the serial link may reduce noise significantly and makes the device more universal