Symmetry in Dynamic Systems

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Computer".

Deadline for manuscript submissions: closed (12 January 2023) | Viewed by 25649

Special Issue Editor

Department of Automation and Robotics, Far Eastern Federal University, 690990 Vladivostok, Russia
Interests: technical diagnosis; nonlinear system theory

Special Issue Information

Dear Colleagues,

Dynamic system theory considers many different aspects such as decomposition, decoupling, observability, controllability, and so on. It is well known that in linear systems, observability and controllability are dual properties: If a linear system is observable, the dual system is controllable and vise versa. Further, the problems of filtering and cotrol in linear systems are dual as well. Some matrices characterizing these problems are related to each other, and these relations can be used in practice. In addition to this, some dualities are known in nonlinear systems.

Such dualities can be considered as a special kind of symmetry. It is interesting to find and investigate other similar dual properties of linear and nonlinear systems and demostrate their practical applications.

Prof. Dr. Zhirabok Alexey
Guest Editor

Manuscript Submission Information

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Keywords

  • Dynamic systems
  • Duality
  • Control
  • Decomposition
  • Decoupling
  • Observability
  • Controllability
  • Estimation
  • Identification

Published Papers (13 papers)

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Research

17 pages, 3194 KiB  
Article
Symmetrical Control Law for Chaotization of Platform Vibrations
by Boris Andrievsky and Iuliia Zaitceva
Symmetry 2022, 14(11), 2460; https://0-doi-org.brum.beds.ac.uk/10.3390/sym14112460 - 20 Nov 2022
Cited by 3 | Viewed by 1012
Abstract
The paper proposes an experimentally validated method of chaotization of the platform movement process based on the principle of feedback control using a symmetrical (bidirectional) controller. The significance is shown and the prospect of chaotization of platform oscillations for vibration technologies, in particular, [...] Read more.
The paper proposes an experimentally validated method of chaotization of the platform movement process based on the principle of feedback control using a symmetrical (bidirectional) controller. The significance is shown and the prospect of chaotization of platform oscillations for vibration technologies, in particular, mixing of bulk materials, is disclosed. The proposed algorithm was comprehensively experimentally studied with a laboratory vibratory setup, and the results of experiments demonstrating its efficacy are presented. Full article
(This article belongs to the Special Issue Symmetry in Dynamic Systems)
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11 pages, 400 KiB  
Article
Interval Observers for Discrete-Time Linear Systems with Uncertainties
by Oleg Sergiyenko, Alexey Zhirabok, Ibraheem Kasim Ibraheem, Alexander Zuev, Vladimir Filaretov, Ahmad Taher Azar and Ibrahim A. Hameed
Symmetry 2022, 14(10), 2131; https://0-doi-org.brum.beds.ac.uk/10.3390/sym14102131 - 13 Oct 2022
Cited by 4 | Viewed by 1261
Abstract
In this paper, we consider the problem involved when designing the interval observer for the system described by a linear discrete-time model under external disturbances and measurement noises. To solve this problem, we used the reduced order model of the initial system, which [...] Read more.
In this paper, we consider the problem involved when designing the interval observer for the system described by a linear discrete-time model under external disturbances and measurement noises. To solve this problem, we used the reduced order model of the initial system, which is insensitive or has minimal sensitivity to the disturbances. The relations involved in designing the interval observer, which has minimal dimensions and estimates the prescribed linear function of the original system state vector, were obtained. The theoretical results were illustrated by a practical example. Full article
(This article belongs to the Special Issue Symmetry in Dynamic Systems)
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12 pages, 444 KiB  
Article
UIO-Based Practical Fixed-Time Fault Estimation Observer Design of Nonlinear Systems
by Jingping Xia, Bin Jiang and Ke Zhang
Symmetry 2022, 14(8), 1618; https://0-doi-org.brum.beds.ac.uk/10.3390/sym14081618 - 06 Aug 2022
Cited by 3 | Viewed by 1192
Abstract
A practical fixed-time fault estimation observer strategy for non-linear systems using an unknown input observer scheme is investigated. The external disturbances of non-linear systems are decoupled by an unknown input observer technique; therefore, the constructed error dynamics do not include these disturbances. The [...] Read more.
A practical fixed-time fault estimation observer strategy for non-linear systems using an unknown input observer scheme is investigated. The external disturbances of non-linear systems are decoupled by an unknown input observer technique; therefore, the constructed error dynamics do not include these disturbances. The fixed-time fault estimation observer is then constructed. Moreover, a non-linear fault estimator with two power functions is proposed to improve the convergence speed of fault estimation. Finally, simulation results of a non-linear Lorenz chaotic system are provided to demonstrate the feasibility of the presented strategy. Full article
(This article belongs to the Special Issue Symmetry in Dynamic Systems)
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9 pages, 1011 KiB  
Article
Models of Dynamic Systems in Diagnostic Tasks
by Egor Lukoyanov, Nikolai Kolesov, Alexander Gruzlikov and Marina Tolmacheva
Symmetry 2022, 14(7), 1433; https://0-doi-org.brum.beds.ac.uk/10.3390/sym14071433 - 12 Jul 2022
Viewed by 1138
Abstract
Models of dynamic systems are considered with regard to the tasks of diagnosing real-time complex information processing and control systems. The problem of diagnosing is one of the most important in the practice of development technical systems. It is important to note that [...] Read more.
Models of dynamic systems are considered with regard to the tasks of diagnosing real-time complex information processing and control systems. The problem of diagnosing is one of the most important in the practice of development technical systems. It is important to note that symmetry principles are used in this work, in particular, to formulate the basic approach to diagnosing complex systems. This approach assumes that the components of a system are allocated to the levels based on inclusion relations. In this case, level-based diagnostic tools with their own models can be synthesized, and the relations between them are characterized by the symmetry feature. Problems of both functional and test-based diagnostic methods are discussed. Particular diagnostic methods may also involve symmetry principles since, in a certain sense, they operate with symmetric notions of observability and controllability of a dynamic system. The implementation of the proposed methods is illustrated by an example of their application to a navigation system of an autonomous underwater vehicle. Full article
(This article belongs to the Special Issue Symmetry in Dynamic Systems)
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20 pages, 355 KiB  
Article
Quadratic Stabilization of Linear Uncertain Positive Discrete-Time Systems
by Dušan Krokavec and Anna Filasová
Symmetry 2021, 13(9), 1725; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13091725 - 17 Sep 2021
Cited by 6 | Viewed by 1532
Abstract
The paper provides extended methods for control linear positive discrete-time systems that are subject to parameter uncertainties, reflecting structural system parameter constraints and positive system properties when solving the problem of system quadratic stability. By using an extension of the Lyapunov approach, system [...] Read more.
The paper provides extended methods for control linear positive discrete-time systems that are subject to parameter uncertainties, reflecting structural system parameter constraints and positive system properties when solving the problem of system quadratic stability. By using an extension of the Lyapunov approach, system quadratic stability is presented to become apparent in pre-existing positivity constraints in the design of feedback control. The approach prefers constraints representation in the form of linear matrix inequalities, reflects the diagonal stabilization principle in order to apply to positive systems the idea of matrix parameter positivity, applies observer-based linear state control to assert closed-loop system quadratic stability and projects design conditions, allowing minimization of an undesirable impact on matching parameter uncertainties. The method is utilised in numerical examples to illustrate the technique when applying the above strategy. Full article
(This article belongs to the Special Issue Symmetry in Dynamic Systems)
13 pages, 25001 KiB  
Article
Thermal Noise Decoupling of Micro-Newton Thrust Measured in a Torsion Balance
by Linxiao Cong, Jianchao Mu, Qian Liu, Hao Wang, Linlin Wang, Yonggui Li and Congfeng Qiao
Symmetry 2021, 13(8), 1357; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13081357 - 27 Jul 2021
Cited by 4 | Viewed by 2496
Abstract
The space gravitational wave detection and drag free control requires the micro-thruster to have ultra-low thrust noise within 0.1 mHz–0.1 Hz, which brings a great challenge to calibration on the ground because it is impossible to shield any spurious couplings due to the [...] Read more.
The space gravitational wave detection and drag free control requires the micro-thruster to have ultra-low thrust noise within 0.1 mHz–0.1 Hz, which brings a great challenge to calibration on the ground because it is impossible to shield any spurious couplings due to the asymmetry of torsion balance. Most thrusters dissipate heat during the test, making the rotation axis tilt and components undergo thermal drift, which is hysteretic and asymmetric for micro-Newton thrust measurement. With reference to LISA’s research and coming up with ideas inspired from proportional-integral-derivative (PID) control and multi-timescale (MTS), this paper proposes to expand the state space of temperature to be applied on the thrust prediction based on fine tree regression (FTR) and to subtract the thermal noise filtered by transfer function fitted with z-domain vector fitting (ZDVF). The results show that thrust variation of diurnal asymmetry in temperature is decoupled from 24 μN/Hz1/2 to 4.9 μN/Hz1/2 at 0.11 mHz. Additionally, 1 μN square wave modulation of electrostatic force is extracted from the ambiguous thermal drift background of positive temperature coefficient (PTC) heater. The PID-FTR validation is performed with experimental data in thermal noise decoupling, which can guide the design of thermal control and be extended to other physical quantities for noise decoupling. Full article
(This article belongs to the Special Issue Symmetry in Dynamic Systems)
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21 pages, 8666 KiB  
Article
Rub-Impact Dynamics of Shrouded Blades under Bending-Torsion Coupling Vibration
by Shangwen He, Kunli Si, Bingbing He, Zhaorui Yang and Ying Wang
Symmetry 2021, 13(6), 1073; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13061073 - 16 Jun 2021
Cited by 4 | Viewed by 1849
Abstract
Shroud devices which are typical cyclic symmetric structures are widely used to reduce the vibration of turbine blades in aero engines. Asymmetric rub-impact of adjacent shrouds or aerodynamic excitation forces can excite the bending-torsion coupling vibration of shrouded blades, which will lead to [...] Read more.
Shroud devices which are typical cyclic symmetric structures are widely used to reduce the vibration of turbine blades in aero engines. Asymmetric rub-impact of adjacent shrouds or aerodynamic excitation forces can excite the bending-torsion coupling vibration of shrouded blades, which will lead to complex contact motions. The aim of this paper is to study the rub-impact dynamic characteristics of bending-torsion coupling vibration of shrouded blades using a numerical method. The contact-separation transition mechanism under complex motions is studied, the corresponding boundary conditions are set up, and the influence of moments of contact forces and aerodynamic excitation forces on the motion of the blade is considered. A three-degree-of-freedom mass-spring model including two mass blocks with the same size and shape is established to simulate the bending-torsion coupling vibration, and the dynamic equations of shrouded blades under different contact conditions are derived. An algorithm based on the fourth-order Runge–Kutta method is presented for simulations. Variation laws of the forced response characteristics of shrouded blades under different parameters are studied, on the basis of which the method to evaluate the vibration reduction characteristics of the shrouded blade system when the motion of the blade is chaotic is discussed. Then, the vibration reduction law of shrouded blades under bending-torsion coupling vibration is obtained. Full article
(This article belongs to the Special Issue Symmetry in Dynamic Systems)
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23 pages, 10781 KiB  
Article
A Prediction Method with Altering Equivalent Stiffness for Damping Evaluation of Shrouded Bladed Disk Dynamic Systems
by Shimin Gao, Yanrong Wang, Zhiwei Sun and Siyuan Chen
Symmetry 2021, 13(3), 413; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13030413 - 04 Mar 2021
Cited by 3 | Viewed by 1611
Abstract
In turbomachinery bladed disks are typical cyclic symmetric structures where high-cycle fatigue of the blades can easily occur. Increasing the shroud structure is an effective blade vibration reduction method using the dry friction of the shroud contact surface to dissipate vibration energy. During [...] Read more.
In turbomachinery bladed disks are typical cyclic symmetric structures where high-cycle fatigue of the blades can easily occur. Increasing the shroud structure is an effective blade vibration reduction method using the dry friction of the shroud contact surface to dissipate vibration energy. During one vibration cycle of the blade, the contact surface of the shroud may have one or several states of stick, slip, and separation due to the different amplitude of blade, which affects not only the damping, but also the stiffness of the system. This paper proposes a method to analyze the damping characteristics of blades with shroud considering the change of equivalent contact stiffness of the shroud by using the finite element method. With a 2D contact model, this method calculates the equivalent damping and obtains the damping characteristic curve to evaluate the damping of shroud. During the design phase, the objective is that when resonance occurs, the shroud can provide the optimal damping ratio under the allowable vibration stress of the blade. The parameter sensitivity of the damping characteristic for one bladed disk with parallel shroud is investigated. It is shown that vibration phase angle, contact stiffness, contact force, friction coefficient significantly influence the damping characteristics. Full article
(This article belongs to the Special Issue Symmetry in Dynamic Systems)
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11 pages, 898 KiB  
Article
Dynamic Response of the Newton Voigt–Kelvin Modelled Linear Viscoelastic Systems at Harmonic Actions
by Cornelia Dobrescu
Symmetry 2020, 12(9), 1571; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12091571 - 22 Sep 2020
Cited by 6 | Viewed by 1721
Abstract
The variety of viscoelastic systems and structures, for the most part, is studied analytically, with significant results. As a result of analytical, numerical and experimental research, which was conducted on a larger variety of linear viscoelastic systems and structures. We analyzed the dynamic [...] Read more.
The variety of viscoelastic systems and structures, for the most part, is studied analytically, with significant results. As a result of analytical, numerical and experimental research, which was conducted on a larger variety of linear viscoelastic systems and structures. We analyzed the dynamic behavior for the viscoelastic composite materials, anti-vibration viscous-elastic systems consisting of discrete physical devices, road structures consisting of natural soil structures with mineral aggregates and asphalt mixes, and mixed mechanic systems of insulation of the industrial vibrations consisting of elastic and viscous devices. In this context, the compound rheological model can be schematized as being V(E|V) type of the Newton Voigt–Kelvin model with inertial excited mass, applicable to linear viscoelastic materials. Full article
(This article belongs to the Special Issue Symmetry in Dynamic Systems)
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9 pages, 219 KiB  
Article
The Problem of Invariance in Nonlinear Discrete-Time Dynamic Systems
by Alexey Zhirabok
Symmetry 2020, 12(8), 1241; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12081241 - 28 Jul 2020
Cited by 2 | Viewed by 1307
Abstract
The paper considers the problem of invariance with respect to the unknown input for discrete-time nonlinear dynamic systems. To solve the problem, the algebraic approaches, called algebra of functions and logic–dynamic approach, are used. Such approaches assume that description of the system may [...] Read more.
The paper considers the problem of invariance with respect to the unknown input for discrete-time nonlinear dynamic systems. To solve the problem, the algebraic approaches, called algebra of functions and logic–dynamic approach, are used. Such approaches assume that description of the system may contain non-differentiable functions. Necessary and sufficient conditions of solvability the problem are obtained. Moreover, procedures which find the appropriate functions and matrices are developed. Some applications of such invariance in fault detection and isolation, disturbance decoupling problem, and fault-tolerant control are considered. Full article
(This article belongs to the Special Issue Symmetry in Dynamic Systems)
20 pages, 1271 KiB  
Article
Rational Transfer Function Model for a Double-Pipe Parallel-Flow Heat Exchanger
by Krzysztof Bartecki
Symmetry 2020, 12(8), 1212; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12081212 - 23 Jul 2020
Cited by 1 | Viewed by 2310
Abstract
Transfer functions of typical heat exchangers, resulting from their partial differential equations, usually contain irrational functions which quite accurately describe the spatio-temporal nature of the processes occurring therein. However, such an accurate but complex mathematical representation is often not convenient from the practical [...] Read more.
Transfer functions of typical heat exchangers, resulting from their partial differential equations, usually contain irrational functions which quite accurately describe the spatio-temporal nature of the processes occurring therein. However, such an accurate but complex mathematical representation is often not convenient from the practical point of view, and some approximation of the original model would be more useful. This paper discusses approximate rational transfer functions for a typical thick-walled double-pipe heat exchanger working in the parallel-flow configuration. Using the method of lines with the backward difference scheme, the original symmetric hyperbolic partial differential equations describing the heat transfer phenomena are transformed into a set of ordinary differential equations and expressed in the form of N subsystems representing spatial sections of the exchanger. Each section is described by a rational transfer function matrix and their cascade interconnection results in the overall approximation model expressed by a matrix of rational transfer functions of high order. Based on the rational transfer function representation, the frequency and steady-state responses of the approximate model are evaluated and compared with those resulting from its original irrational transfer function model. The presented results show better approximation quality for the “crossover” input–output channels where the in-domain heat conduction effects prevail as compared to the “straightforward” channels, where the transport delay associated with the heat convection dominates. Full article
(This article belongs to the Special Issue Symmetry in Dynamic Systems)
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13 pages, 347 KiB  
Article
Switching Perfect Control Algorithm
by Marek Krok, Wojciech P. Hunek and Tomasz Feliks
Symmetry 2020, 12(5), 816; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12050816 - 15 May 2020
Cited by 6 | Viewed by 1814
Abstract
The application of the switching control framework to the perfect control algorithm is presented in this paper. Employing the nonunique matrix inverses, the different closed-loop properties are obtained and further enhanced with possible switching methodology implementation. Simulation examples performed in the MATLAB/Simulink environment [...] Read more.
The application of the switching control framework to the perfect control algorithm is presented in this paper. Employing the nonunique matrix inverses, the different closed-loop properties are obtained and further enhanced with possible switching methodology implementation. Simulation examples performed in the MATLAB/Simulink environment clearly show that the new framework can lead to benefits in terms of the control energy, speed, and robustness of the perfect control law. The possibility of transferring the new obtained results to the symmetrical nonlinear plants seems to be immediate. Full article
(This article belongs to the Special Issue Symmetry in Dynamic Systems)
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19 pages, 878 KiB  
Article
Trajectory Planning for Mechanical Systems Based on Time-Reversal Symmetry
by Stepan Ozana, Tomas Docekal, Aleksandra Kawala-Sterniuk, Jakub Mozaryn, Milos Schlegel and Akshaya Raj
Symmetry 2020, 12(5), 792; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12050792 - 08 May 2020
Cited by 4 | Viewed by 4803
Abstract
The generation of feasible trajectories poses an eminent task in the field of control design in mechanical systems. The paper demonstrates innovative approach in trajectory planning for mechanical systems via time-reversal symmetry. It also presents two case studies: mass-spring-damper and inverted pendulum on [...] Read more.
The generation of feasible trajectories poses an eminent task in the field of control design in mechanical systems. The paper demonstrates innovative approach in trajectory planning for mechanical systems via time-reversal symmetry. It also presents two case studies: mass-spring-damper and inverted pendulum on the cart. As real systems break the time-reversal symmetry, the authors of this work propose a unique method in order to overcome this drawback. It computes a feed-forward reference control signal and state trajectories. The proposed solution enables compensation for the effects of couplings, which break the time-symmetry by a special proposed measure. The method suppresses the overall open-loop accumulated error and produces high-quality favorable control and state trajectories. Furthermore, the existence of the designed control signal and state trajectories is guaranteed if the equations of the motion have a solution in the direct flow of time. Full article
(This article belongs to the Special Issue Symmetry in Dynamic Systems)
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