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Mathematics
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Advances in Study of Time-Delay Systems and Their Applications
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Advances in Study of Time-Delay Systems and Their Applications

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Dynamical Systems".

Deadline for manuscript submissions: closed (31 March 2021) | Viewed by 11415

Special Issue Editors

Dr. Libor Pekař

E-Mail Website
Guest Editor
1. Department of Automation and Control Engineering, Faculty of Applied Informatics, Tomas Bata University in Zlín, 760 01 Zlín, Czech Republic
2. Department of Technical Studies, College of Polytechnics Jihlava, Tolstého 1556, 586 01 Jihlava, Czech Republic
Interests: control system synthesis; PI control; closed loop systems; delays; frequency-domain analysis; linear systems; polynomials; robust control; stability; MIMO systems; active disturbance rejection control; aerospace components; aircraft control; approximation theory; asymptotic stability; chemical reactors; decentralised control; delay systems; discrete time systems; feedback; invariance; multivariable control systems; optimal control; polynomial approximation; three-term control
Special Issues, Collections and Topics in MDPI journals
Dr. Radek Matušů

E-Mail Website
Guest Editor
Faculty of Applied Informatics, Univerzita Tomáse Bati ve Zlině, 760 01 Zlin, Czech Republic
Interests: robust control; fractional-order systems; uncertainty; (FO)PID controllers

Special Issue Information

Dear Colleagues,

In dynamical systems, delay as a generic part of industrial, communication, economical, biological, etc. processes represents a phenomenon that considerably affects their stability and dynamics. It, moreover, unambiguously deteriorates the quality of control performance in feedback loops. The study of the influence of delays on system stability, dynamics, and control performance poses a challenging mathematic exercise. System and control theories have been dealing with this task for almost a century, since the publishing of the famous work by Volterra (1928). Modern theory is confronted with higher and higher requirements for the quality and performance of control systems in the industry as well as in everyday reality, which can hardly be done by conventional methods. More in-depth knowledge of the controlled delayed systems is a necessary prerequisite to meeting these goals.

This Special Issue in Mathematics is focused on recent developments concerning various approaches to time-delay systems analysis and control design. Papers on system stability and dynamics analysis are solicited, including exponential, asymptotic, strong, delay-dependent, delay-independent, BIBO, H2, H∞, and other types of system stability. Hopf, fold, and pitchfork bifurcation; stability switching; and eigenvalue analyses are welcome as well. Special attention will be given to delays of neutral types and systems given by algebraic-differential equations; however, systems with retarded delays are acceptable as well. Modern control methods and their applications also fall within the scope of this Special Issue, including switched systems, event-triggered control, Lyapunov–Razumikhin- and Krasovskii-type approaches, etc.

All submitted papers will be peer-reviewed and selected on the basis of both their quality and relevance to the scope of this Special Issue.

Dr. Libor Pekař
Dr. Radek Matušů
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Time-invariant and time-variant delayed systems
  • Delay-varying models and their stability
  • Linear and nonlinear delayed systems
  • Dynamics and stability of systems with retarded and neutral delays
  • Delayed systems described by algebraic-differential equations
  • Exponential, asymptotic, strong, BIBO, H2, H∞ stability of time-delay systems
  • Hopf, fold, and pitchfork bifurcation, stability switching, and eigenvalue analysis
  • Delay-dependent and delay-independent stability
  • Finite dimension approximations
  • Filtering and estimation of time-delay systems
  • Switched systems with time delay and event-triggered control
  • Krasovskii-type and Lyapunov–Razumikhin-type stability and control approaches
  • New results in controllability and observability of time-delay systems
  • Robust, algebraic, and adaptive control methods and their applications

Published Papers (5 papers)

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Research

23 pages, 1071 KiB  
Article
2DOF IMC and Smith-Predictor-Based Control for Stabilised Unstable First Order Time Delayed Plants
by Mikulas Huba, Pavol Bistak and Damir Vrancic
Mathematics 2021, 9(9), 1064; https://doi.org/10.3390/math9091064 - 10 May 2021
Cited by 7 | Viewed by 2559
Abstract
The article brings a brief revision of the two-degree-of-freedom (2-DoF) internal model control (IMC) and the 2-DoF Smith-Predictor-based (SP) control of unstable systems. It shows that the first important reason for distinguishing between these approaches is the limitations of the control action. However, [...] Read more.
The article brings a brief revision of the two-degree-of-freedom (2-DoF) internal model control (IMC) and the 2-DoF Smith-Predictor-based (SP) control of unstable systems. It shows that the first important reason for distinguishing between these approaches is the limitations of the control action. However, it also reminds that, in addition to the seemingly lucrative dynamics of transients, the proposed approaches can conceal a tricky behavior with a structural instability, which may manifest itself only after a longer period of time. Instead, as one of possible reliable alternatives, two-step IMC and filtered Smith predictor (FSP) design are applied to unstable first-order time-delayed (UFOTD) systems. Firstly, the 2-DoF P controller yielding a double real dominant closed loop pole is applied. Only then the 2-DoF IMC or FSP controllers are designed, providing slightly slower, but more robust transients. These remain stable even in the long run, while also showing increased robustness. Full article
(This article belongs to the Special Issue Advances in Study of Time-Delay Systems and Their Applications)
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14 pages, 2815 KiB  
Article
Delay Equivalences in Tuning PID Control for the Double Integrator Plus Dead-Time
by Mikulas Huba and Damir Vrancic
Mathematics 2021, 9(4), 328; https://doi.org/10.3390/math9040328 - 07 Feb 2021
Cited by 12 | Viewed by 2315
Abstract
The paper investigates and explains a new simple analytical tuning of proportional-integrative-derivative (PID) controllers. In combination with nth order series binomial low-pass filters, they are to be applied to the double-integrator-plus-dead-time (DIPDT) plant models. With respect to the use of derivatives, it [...] Read more.
The paper investigates and explains a new simple analytical tuning of proportional-integrative-derivative (PID) controllers. In combination with nth order series binomial low-pass filters, they are to be applied to the double-integrator-plus-dead-time (DIPDT) plant models. With respect to the use of derivatives, it should be understood that the design of appropriate filters is not only an implementation problem. Rather, it is also critical for the resulting performance, robustness and noise attenuation. To simplify controller commissioning, integrated tuning procedures (ITPs) based on three different concepts of filter delay equivalences are presented. For simultaneous determination of controller + filter parameters, the design uses the multiple real dominant poles method. The excellent control loop performance in a noisy environment and the specific advantages and disadvantages of the resulting equivalences are discussed. The results show that none of them is globally optimal. Each of them is advantageous only for certain noise levels and the desired degree of their filtering. Full article
(This article belongs to the Special Issue Advances in Study of Time-Delay Systems and Their Applications)
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19 pages, 476 KiB  
Article
New Stability Conditions for a Class of Nonlinear Discrete-Time Systems with Time-Varying Delay
by Sami Elmadssia and Karim Saadaoui
Mathematics 2020, 8(9), 1531; https://doi.org/10.3390/math8091531 - 08 Sep 2020
Cited by 2 | Viewed by 2041
Abstract
In this paper, the stability problem of discrete time delay systems is investigated. The class of systems under consideration is represented by delayed difference equations and models nonlinear discrete time systems with time varying delay. It is transformed into an arrow from matrix [...] Read more.
In this paper, the stability problem of discrete time delay systems is investigated. The class of systems under consideration is represented by delayed difference equations and models nonlinear discrete time systems with time varying delay. It is transformed into an arrow from matrix representation which allows the use of aggregation techniques and M-matrix properties to determine novel sufficient stability conditions. The originalities of our findings are shown in their explicit representation, using system’s parameters, as well as in their easiness to be employed. The obtained results demonstrate also that checking stability of nonlinear discrete time systems with time varying delay can be reduced to an M-matrix test. Next, it is shown how to use our method in designing a state feedback controller that stabilizes a discrete time Lure system with time varying delay and sector bounded nonlinearity. Finally, several examples are provided to show the effectiveness of the introduced technique. Full article
(This article belongs to the Special Issue Advances in Study of Time-Delay Systems and Their Applications)
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14 pages, 278 KiB  
Article
Partial Eigenvalue Assignment for Gyroscopic Second-Order Systems with Time Delay
by Hao Liu, Ranran Li and Yingying Ding
Mathematics 2020, 8(8), 1235; https://doi.org/10.3390/math8081235 - 27 Jul 2020
Cited by 3 | Viewed by 1575
Abstract
In this paper, the partial eigenvalue assignment problem of gyroscopic second-order systems with time delay is considered. We propose a multi-step method for solving this problem in which the undesired eigenvalues are moved to desired values and the remaining eigenvalues are required to [...] Read more.
In this paper, the partial eigenvalue assignment problem of gyroscopic second-order systems with time delay is considered. We propose a multi-step method for solving this problem in which the undesired eigenvalues are moved to desired values and the remaining eigenvalues are required to remain unchanged. Using the matrix vectorization and Hadamard product, we transform this problem into a linear systems of lower order, and analysis the computational costs of our method. Numerical results exhibit the efficiency of our method. Full article
(This article belongs to the Special Issue Advances in Study of Time-Delay Systems and Their Applications)
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19 pages, 1583 KiB  
Article
Stability Analysis of Multi-Discrete Delay Milling with Helix Effects Using a General Order Full-Discretization Method Updated with a Generalized Integral Quadrature
by Chigbogu Ozoegwu and Peter Eberhard
Mathematics 2020, 8(6), 1003; https://doi.org/10.3390/math8061003 - 18 Jun 2020
Cited by 10 | Viewed by 1867
Abstract
A tensor-based general order full-discretization method is enhanced with the capacity to handle multiple discrete delays and helix effects leading to a unique automated algorithm in the stability analysis of milling process chatter. The automated algorithm is then exploited in investigating the effects [...] Read more.
A tensor-based general order full-discretization method is enhanced with the capacity to handle multiple discrete delays and helix effects leading to a unique automated algorithm in the stability analysis of milling process chatter. The automated algorithm is then exploited in investigating the effects of interpolation order of chatter states and helix-induced terms on the convergence of milling stability lobes. The enhanced capacity to handle the distributed helix effects is based on a general order formulation of the Newton-Coates integral quadrature method. Application to benchmark milling models showed that high order methods are necessary for convergence of the low speed domain of stability lobes while all the numerically stable orders converge in the high speed domain where the ultra-high order methods are prone to numerical instability. Also, composite numerical integration of the helix-induced integrand beyond the usual zero-th order method leads to higher accuracy of stability lobes especially in the low speed domain. Full article
(This article belongs to the Special Issue Advances in Study of Time-Delay Systems and Their Applications)
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