
Libor PekařTomas Bata University in Zlín · Faculty of Applied Informatics
Libor Pekař
Assoc. Prof. Ph.D.
Time-delay systems, relay-based identification, heating-cooling systems.
Joined the Frost Lab of BIT, China.
About
154
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Introduction
Libor Pekař currently works at the Faculty of Applied Informatics, Tomas Bata University in Zlín. Libor does research in Control Systems Engineering, Engineering Education and Computer Engineering. His research interest constitute all analytics and control tasks related to delayed systems.
He also works as a part-time Assoc. Prof. at the Department of Technical Studies of College of Polytechnics Jihlava.
Additional affiliations
October 2020 - December 2024
September 2024 - August 2029
October 2006 - present
Education
September 2005 - March 2013
September 2002 - June 2005
September 1999 - June 2002
Publications
Publications (154)
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 cons...
In this paper, a direct computational method for the searching and determination of stability switching delays is introduced. The primary procedure is applicable to retarded linear time-invariant time-delay systems and it is based on the iterative (successive) estimation of the dominant pole of the infinite system spectrum by means of the Taylor’s...
The aim of this paper is to utilize an unordinary anisochronic modelling principle on a circuit thermal laboratory plant. The class of anisochronic models is characterized by the existence of state (internal) delays, both distributed or lumped ones. The modelled laboratory appliance was designed at Tomas Bata University in Zlín, Czech Republic, as...
The aim of this contribution is to revise and extend results about stability and stabilization of a retarded quasipolynomial and systems obtained using the Mikhaylov criterion in our papers earlier. Not only retarded linear time-invariant time-delay systems (LTI-TDS) are considered in this paper; neutral as well as distributed-delay systems are the...
A straightforward way of solving global optimization problems is to find all local optima of the objective function. Therefore, the ability of detecting multiple local optima is a key feature of a practically usable global optimization method. One of such methods is a multi-population evolutionary strategy called the Hierarchic Memetic Strategy (HM...
To reduce the negative impact of frost formation on cold surfaces in low-temperature environments, metal wire mesh can be set in the air flow direction from the cold surface to reduce air humidity. To quantitatively determine the effectiveness of dehumidification after passing through a metal wire, the frosting process needs to be studied. To analy...
Icing is a phenomenon that exists widely in daily life and industry, and always brings some disadvantages. The dissolved air tends to become micro bubbles and trapped in ice, which have an effect on the physical properties of the ice. To explore the distribution and growth characteristics of trapped air bubbles in ice, experiments are carried out i...
This paper proposes an innovative framework of a parameter estimation procedure based on the well-established relay-feedback experiment paradigm. The novelty consists in consideration of asymmetric dynamics and non-equal static gains of the identified system. A different system behavior after changing the input variable polarity near the operating...
This example-oriented article addresses the computation of regions of all robustly relatively stabilizing Proportional-Integral (PI) controllers under various robust stability margins α for Linear Time-Invariant (LTI) plants with unstructured multiplicative uncertainty, where the plant model with multiplicative uncertainty is built on the basis of...
The present paper deals with the stabilization, optimization, and control of second-order systems using a PI delayed controller. This study analyzes the control of linear-time invariant (LTI) systems with time delay in the integral and proportional parts of the PI delayed controller and obtains the region of global stability in the two-dimensional...
The aim of this research is to revise and substantially extend experimental modelling and control of a looped heating-cooling laboratory process with long input-output and internal delays under uncertainties. This research follows and extends the authors' recent results. As several significant improvements regarding robust modelling and control hav...
This study aims at an extension and substantial improvement of the recently published relay-feedback parameter identification of an infinite-dimensional system thermal process model. The original procedure has applied the standard on/off relay to get a simplified model. Then, the dominant pole assignment has given rise to the process model characte...
The present paper describes the stabilization and control of second-order systems using a proportional plus integral delayed controller (P/I-delayed controller). The stabilization of closed-loop control systems using a controller comprehends several techniques to increase the control circuit’s stability. Even in some simple second-order plants, the...
In control theory, optimization is a process that makes some system behavior as likelihood, functional, or practical as possible (depending on the design requirements). From a mathematical point of view, optimization is a way to find the minimum or maximum of the mathematical function by which the system is described. Moreover, if there is a time d...
Droplet freezing on inclined surfaces exists widely in engineering fields. To accurately predict and control the freezing process of a sessile water droplet on inclined surface, a theoretical model based on the heat-enthalpy method is presented in this study, with two types of dynamic behavior considered, deformation and spreading. After the valida...
Following the introduction of the socio-cognitive caste-based algorithms into the classic evolutionary metaheuris-tics, in this paper we focus on similar task regarding agent-based universal optimization methods. We tackle EMAS and DE algorithms and enrich them also with TOPSIS-inspired mechanism. Besides giving the details of the methods and the b...
Metaheuristics are universal optimization algorithms which should be used for solving difficult problems, unsolvable by classic approaches. In this paper we aim at constructing novel socio-cognitive metaheuristic based on castes, and apply several versions of this algorithm to optimization of time-delay system model. Besides giving the background a...
Metaheuristics are universal optimization algorithms which should be used for solving difficult problems, unsolvable by classic approaches. In this paper we aim at constructing novel socio-cognitive metaheuristic based on castes, and apply several versions of this algorithm to optimization of time-delay system model. Besides giving the background a...
The focus of this contribution is twofold. The first part aims at the rigorous and complete analysis of pole loci of a simple delayed model, the characteristic function of which is represented by a quasi-polynomial with a non-delay and a delay parameter. The derived spectrum constitutes an infinite set, making it a suitable and simple-enough repres...
This article deals with the calculation of all robustly relatively stabilizing (or robustly stabilizing as a special case) Proportional-Integral-Derivative (PID) controllers for Linear Time-Invariant (LTI) systems with unstructured uncertainty. The presented method is based on plotting the envelope that corresponds to the trios of P-I-D parameters...
This article deals with the computation of robustly performing Proportional-Integral (PI) controllers for interval plants, where the performance measures are represented by the worst-case Gain Margin (GM) and Phase Margin (PM) specifications, in the event of multiple Phase Crossover Frequencies (PCFs) and/or Gain Crossover Frequencies (GCFs). The m...
Malware is an unwanted software that performs actions in computers or computer networks, which users might disagree with. One of the worst types of malware is ransomware that affects the victim’s data by modifying, deleting, or blocking the access to them. Frequent malware attacks on organizations led to a change in malware detection from external...
The objective of this contribution is twofold. First, it demonstrates a case study on applying the standard single-run relay-feedback parameter identification test to a representative of infinite-dimensional systems. Namely, a delayed mathematical model of a circuit heating laboratory appliance process is used. Second, an initial estimation of the...
This study provides a recursive parametric identification scheme for a liquid-saturated steam heat exchanger system. The recursive identification scheme uses block-structured Wiener and Hammerstein models as model structure and recursive least squares estimation scheme as the parameter estimation method. The estimated block-oriented model provides...
The focus of this contribution is twofold. The first part aims at the rigorous and complete analysis of pole loci of a simple delayed model, the characteristic function of which is represented by a quasi-polynomial with a non-delay and a delay parameter. The derived spectrum constitutes an infinite set, making it a suitable and simple-enough repres...
The paper is focused on the identification, control design, and experimental verification of a two-input two-output hot-air laboratory apparatus representing a small-scale version of appliances widely used in the industry. A decentralized multivariable controller design is proposed, satisfying control-loop decoupling and measurable disturbance reje...
The aim of this study is to present and summarize our numerical algorithm for the determination of stability charts in the delay space for linear time-invariant time systems with constant delays (TDS), both retarded and neutral ones. The core of algorithm lies in a successive (iterative) approximation of the infinite-dimensional characteristic quas...
To accurately control the frosting process, analyzing the influence of different factors on frosting is meaningful and challengeable, especially in the early frosting stage. According to the sensitivity analysis, the influence of different surface wettability and environmental factors on the growth of frost layer were quantitatively analyzed. Based...
This chapter is an extended overview of the author's ideas and contributions to the spectrum-based tuning of controllers designed for linear time-invariant time-delay systems. Numerous control design methods and techniques yield an infinite-dimensional feedback control system. Then we have to deal with infinitely many feedback system poles. The rig...
The Kalah game represents the most popular version of probably the oldest board game ever—the Mancala game. From this viewpoint, the art of playing Kalah can contribute to cultural heritage. This paper primarily focuses on a review of Kalah history and on a survey of research made so far for solving and analyzing the Kalah game (and some other rela...
One of the oldest games worldwide – the Mancala game – is focused on in this preliminary study. Namely, its the most popular version – the Kalah game – is considered. This contribution is aimed at the analysis of Kalah rules first. Further, based on these rules, some novel deterministic and suboptimal strategies are proposed. It is proved that the...
The paper is focused on robust Proportional-Integral (PI) control of interval plants with gain and phase margin specifications and on the application of this approach to a Continuous Stirred Tank Reactor (CSTR). More specifically, the work aims at the determination of PI controller parameter regions, for which not only robust stability but also som...
This paper discusses algebraic approaches of control design for a set of Single Input-Single Output (SISO) delayed systems that are further developed and discussed. The first principle utilises a special ring RQM,-a set of RQ-meromorphic functions. The second one is based on a ring of proper and stable rational functions RPS and can be considered a...
Advanced Analytic Control Techniques for Thermal Systems with Heat Exchangers presents the latest research on sophisticated analytic and control techniques specific for Heat Exchangers (HXs) and heat Exchanger Networks (HXNs), such as Stability Analysis, Efficiency of HXs, Fouling Effect, Delay Phenomenon, Robust Control, Algebraic Control, Geometr...
Reverse cycle defrosting is widely used for air source heat pumps. When a multi-circuit heat exchanger is vertically installed in a heat pump as an outdoor coil, the melted frost could be kept downwards flowing or locally drained during defrosting by using water collecting trays. To analyze the performance differences of melted frost, two defrostin...
This paper presents a novel frequency-domain approach to reveal the exact range of the imaginary spectra and the stability of linear time-invariant systems with two delays. First, an exact relation, i.e., the Rekasius substitution, is used to replace the exponential term caused by the delays in order to transform the transcendental characteristic e...
This paper deals with one of the possible ways to control multivariable (MIMO) control loops. The suggested control design procedure uses the so-called primary controllers, auxiliary controllers, and also correction members. Parameters of the primary controllers are determined for the optimal control pairs using arbitrary single-variable synthesis...
This chapter is aimed at the possible use of well-established and simple algebraic and robust control techniques for a delayed plant with heat exchangers, the modeling and identification of which were presented in Chapter 2. The algebraic part of the controller design is based on a special ring of stable and proper quasipolynomial meromorphic funct...
This concise introductory chapter is aimed at providing an unacquainted reader with very basic essentials about heat exchangers. There are two main parts of this chapter. Namely, the definition of heat exchangers and several possible classifications are given first. Afterward, the reader is acquainted with some basic mathematical laws that model th...
The so-called anisochronic modeling principle followed by the determination of model parameters values for a looped thermal plant with the water-air heat exchanger are given to the reader in this chapter. This modeling framework is characterized by the inclusion of all significant delays in the mathematical model formed by delay-differential equati...
This paper presents the application of a value-set-based graphical approach to robust stability analysis for the ellipsoidal families of fractional-order polynomials with a complex structure of parametric uncertainty. More specifically, the article focuses on the families of fractional-order linear time-invariant polynomials with affine linear, mul...
This preliminary study aims to verify and present a possible utilization of one of modern proportional-integral-derivative (PID) controller tuning approaches – the balanced (equalization) method – applied to a selected class of stable systems with delays. We first use an elegant algebraic compensation method to get the controller structure of an in...
Modelling and identification of delayed LTI TDS
A presentation for students (Erasmus+)
LTI TDS SPECTRUM, ITS ANALYSIS AND SYNTHESIS; STABILITY
A presentation for students within the Erasmus+
Introduction to time-delay systems.
A presentation for students.
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 th...
This paper is aimed at possible controller tuning of infinite-dimensional controllers of a predictor (compensator) type obtained from an algebraic-based controller structure design method for linear systems with delays. The design procedure is simple enough so that it can attract practitioners. The controllers are of a generalized proportional-inte...
The focus of this contribution is on the use of two controller tuning techniques for delayed controllers designed by an algebraic approach for linear time-invariant time delay systems. The well-known Chien-Hrones-Reswick (CHR) method and the Equalization Method (EM) are used. The tuning procedure is applied to compensation-type controllers that inc...
The main aim of this paper is to present and compare three approaches to uncertainty modeling and robust stability analysis for fractional-order (FO) linear time-invariant (LTI) single-input single-output (SISO) uncertain systems. The investigated objects are described either via FO models with parametric uncertainty, by means of FO unstructured mu...
This editorial to a special issue in Mathematical Problems in Engineering summarizes the review and editing process, and provides the reader with the overview of published papers including the most significant references to literature sources used by the authors.
This contribution focuses an overview of selected results on time-delay systems stability analysis in the delay space, recently published in outstanding high-impacted journals and top conferences and meetings. A numerical gridding algorithm solving this problem designed by the first author is included as well. The theoretical background and a conci...
An appropriate setting of eventual controller parameters for a derived controller structure represents an integral part of many control design approaches for dynamical systems. This contribution is aimed at a practically applicable and uncomplicated controller tuning method for linear time-invariant time delay systems (LTI-TDSs). It is based on pla...
The economic control of the subsystem of heat energy production consists both in economical distribution of load between individual cooperating sources inclusive of economical distribution of load between individual production units inside the sources, for so called operational variant in the source, and further also in determining suitable operati...
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 c...
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 parametr...
Delay represents a significant phenomenon in the dynamics of many human-related systems—including biological ones. It has i.a. a decisive impact on system stability, and the study of this influence is often mathematically demanding. This paper presents a computationally simple numerical gridding algorithm for the determination of stability margin d...
The eventual approximated leading pole loci for Table 1.
Leading pole estimations of the ACP received from steps 6 and 7 of Algorithm 1, which gives rise to errors introduced in Table 1.
(XLSX)
Results of the numerical experiment according to Algorithm 1.
Signs of the rightmost quasipolynomial roots from the QPmR for Fig 3 are given in part A: The data table includes signs of the CQP roots calculated via the QPmR that give rise to the stable and unstable regions in Fig 3. Computed leading roots of the ACP along the stability border line o...
A simulation scheme of the skater stabilization.
This *.mdl file from MATLAB® enables to test the feedback response for various τ1 and τ2 that can be set inside the "Skater model" block.
(MDL)
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...
Time delay systems own infinite spectra which cannot be simply analyzed or controlled. A way how to deal with this task consists of an approximation of the characteristic quasipolynomial by a polynomial that can be further handled via conventional tools. This contribution is aimed at an improved extrapolation method transforming a retarded quasipol...
This paper is aimed at reviewing the ring of retarded quasipolynomial meromorphic functions (RMS) 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 henc...
This contribution is aimed at a possible procedure approximating quasipolynomials by polynomials. Quasipolynomials appear in linear time-delay systems description as a natural consequence of the use of the Laplace transform. Due to their infinite root spectra, control system analysis and synthesis based on such quasipolynomial models are usually ma...
Controller design for a laboratory circuit heating plant with model feedback delays by means of a branched control system in a robust sense is the aim of this contribution. The reader is concisely acquainted with a mathematical model of then plant that includes all significant delays and latencies first; hence, the model is infinite-dimensional. Re...
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...
Concise complete controller design with simulations for a laboratory circuit heating plant with feedback delays is the aim of this contribution. The particular steps of the design include a mathematical modelling summary of then plant, introduction of relevant algebraic tools, robust controller design and tuning, its discretization and rational sim...
This paper is aimed at the presentation and simulation verification of a novel simple and fast delay dependent stability (DDS) testing algorithm for linear time-invariant time delay systems (LTI TDS). The algorithm can be used for systems with multiple delays and/or those with many controller parameters. Value ranges of delays and tunable parameter...
The paper brings a new combination of biased-relay feedback identification and an algebraic control design method for time-delay systems. The estimation of the controlled process is based on asymmetrical limit cycle data. Then a stable second order transfer function with a dead-time term is identified. The controller is computed through solutions o...