Dynamical Systems: Theory and Applications

Journal Name	Impact Factor	CiteScore	Launched Year	First Decision (median)	APC
Applied Sciences applsci	2.5	5.3	2011	17.8 Days	CHF 2400
Mathematics mathematics	2.3	4.0	2013	17.1 Days	CHF 2600
Vibration vibration	1.9	3.2	2018	22 Days	CHF 1600
Symmetry symmetry	2.2	5.4	2009	16.8 Days	CHF 2400
Materials materials	3.1	5.8	2008	15.5 Days	CHF 2600

16 pages, 670 KiB

Open AccessFeature PaperArticle

Multi-Objective LQG Design with Primal-Dual Method

by Donghwan Lee

Mathematics 2023, 11(8), 1857; https://doi.org/10.3390/math11081857 - 13 Apr 2023

Cited by 1 | Viewed by 1430

The objective of this paper is to investigate a multi-objective linear quadratic Gaussian (LQG) control problem. Specifically, we examine an optimal control problem that minimizes a quadratic cost over a finite time horizon for linear stochastic systems subject to control energy constraints. To [...] Read more.

The objective of this paper is to investigate a multi-objective linear quadratic Gaussian (LQG) control problem. Specifically, we examine an optimal control problem that minimizes a quadratic cost over a finite time horizon for linear stochastic systems subject to control energy constraints. To tackle this problem, we propose an efficient bisection line search algorithm that outperforms other approaches such as semidefinite programming in terms of computational efficiency. The primary idea behind our algorithm is to use the Lagrangian function and Karush–Kuhn–Tucker (KKT) optimality conditions to address the constrained optimization problem. The bisection line search is employed to search for the Lagrange multiplier. Furthermore, we provide numerical examples to illustrate the efficacy of our proposed methods. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

13 pages, 2879 KiB

Open AccessArticle

The Highly Accurate Interatomic Potential of CsPbBr₃ Perovskite with Temperature Dependence on the Structure and Thermal Properties

by Qianyu You, Shun Gu and Xiaofan Gou

Materials 2023, 16(5), 2043; https://doi.org/10.3390/ma16052043 - 1 Mar 2023

Cited by 5 | Viewed by 2504

Abstract

CsPbBr₃ perovskite has excellent optoelectronic properties and many important application prospects in solar cells, photodetectors, high-energy radiation detectors and other fields. For this kind of perovskite structure, to theoretically predict its macroscopic properties through molecular dynamic (MD) simulations, a highly accurate interatomic [...] Read more.

CsPbBr₃ perovskite has excellent optoelectronic properties and many important application prospects in solar cells, photodetectors, high-energy radiation detectors and other fields. For this kind of perovskite structure, to theoretically predict its macroscopic properties through molecular dynamic (MD) simulations, a highly accurate interatomic potential is first necessary. In this article, a new classical interatomic potential for CsPbBr₃ was developed within the framework of the bond-valence (BV) theory. The optimized parameters of the BV model were calculated through first-principle and intelligent optimization algorithms. Calculated lattice parameters and elastic constants for the isobaric–isothermal ensemble (NPT) by our model are in accordance with the experimental data within a reasonable error and have a higher accuracy than the traditional Born–Mayer (BM) model. In our potential model, the temperature dependence of CsPbBr₃ structural properties, such as radial distribution functions and interatomic bond lengths, was calculated. Moreover, the temperature-driven phase transition was found, and the phase transition temperature was close to the experimental value. The thermal conductivities of different crystal phases were further calculated, which agreed with the experimental data. All these comparative studies proved that the proposed atomic bond potential is highly accurate, and thus, by using this interatomic potential, the structural stability and mechanical and thermal properties of pure inorganic halide and mixed halide perovskites can be effectively predicted. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

16 pages, 915 KiB

Open AccessArticle

Finite-Time Bounded Tracking Control for a Class of Neutral Systems

by Jiang Wu, Yujie Xu, Hao Xie and Yao Zou

Mathematics 2023, 11(5), 1199; https://doi.org/10.3390/math11051199 - 28 Feb 2023

Cited by 1 | Viewed by 1006

Abstract

In this paper, we investigate finite-time bounded (FTB) tracking control for a class of neutral systems. Firstly, the dynamic equation of the tracking error signal is given based on the original neutral system. Then, we combine it with the equations of the state [...] Read more.

In this paper, we investigate finite-time bounded (FTB) tracking control for a class of neutral systems. Firstly, the dynamic equation of the tracking error signal is given based on the original neutral system. Then, we combine it with the equations of the state vector to construct an error system, where the reference signal and the disturbance signal are fused in a new vector. Next, about the error system, we study the input–output finite-time stability problem of the closed-loop system by utilizing the Lyapunov–Krasovskii functional. We also give a finite-time stability condition in the form of linear matrix inequalities (LMIs). Furthermore, the delay-dependent and delay-independent finite-time bounded tracking controllers are designed separately for the original system. Finally, a realistic example is given to show the effectiveness of the controller design method in the paper. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

15 pages, 10607 KiB

Open AccessArticle

Dynamic Behavior Analysis of I-Shaped RC Beams under Combined Blast and Impact Loads

by Jianyu Liu, Yiping Yin, Yunlei Zhao and Yuan Li

Appl. Sci. 2023, 13(3), 1943; https://doi.org/10.3390/app13031943 - 2 Feb 2023

Viewed by 2038

Abstract

The existing literature mainly focuses on the research of reinforced concrete (RC) beams under a single load such as blast or impact. In this paper, the slab–rib–slab RC beam, a new type of structure widely used in bridge structures, was taken as the [...] Read more.

The existing literature mainly focuses on the research of reinforced concrete (RC) beams under a single load such as blast or impact. In this paper, the slab–rib–slab RC beam, a new type of structure widely used in bridge structures, was taken as the research object. The explicit dynamic analysis software LS-DYNA was used to numerically analyze the dynamic response and failure behavior of I-shaped RC beams under combined blast and impact loads. For this reason, an effective numerical analysis model was obtained by carrying out experiments on I-shaped RC beams under contact explosion. The key factors affecting the dynamic response of the structure under combined loads were numerically analyzed. Numerical results showed that different load application sequences have important effects on the dynamic response of the structure. When the impact load was first applied to the structure, more severe concrete damage and deformation occured in the depth direction of the beam. However, when the blast load was first applied to the structure, the concrete at the lower flange was damaged in the span direction of the beam due to tension, and no large-scale concrete spallation occurred in the depth direction. This was mainly due to the different mechanisms of blast and impact loads. In addition, the vulnerability of the I-shaped RC beams varied with some structural parameters, including span, depth, and configuration of reinforcement. At the same time, the results showed that the structure is more sensitive to changes in structural parameters when it is first subjected to impact loads. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

12 pages, 643 KiB

Open AccessArticle

Compound-Combination Synchronization for Fractional Hyperchaotic Models with Different Orders

by Gamal M. Mahmoud, Asma Althemairi, Tarek M. Abed-Elhameed and Ahmed A. Farghaly

Symmetry 2023, 15(2), 279; https://doi.org/10.3390/sym15020279 - 19 Jan 2023

Cited by 4 | Viewed by 1026

Abstract

In this paper, we introduce a new type of synchronization for the fractional order (FO) hyperchaotic models with different orders called compound-combination synchronization (CCS). Using the tracking control method, a theorem to calculate the analytical controllers which achieve our proposed synchronization is described [...] Read more.

In this paper, we introduce a new type of synchronization for the fractional order (FO) hyperchaotic models with different orders called compound-combination synchronization (CCS). Using the tracking control method, a theorem to calculate the analytical controllers which achieve our proposed synchronization is described and proved. We introduce, also, the FO hyperchaotic complex Lü, Chen, and Lorenz models with complex periodic forcing. The symmetry property is found in the FO hyperchaotic complex Lü, Chen, and Lorenz models. These hyperchaotic models are found in many areas of applied sciences, such as physics and secure communication. These FO hyperchaotic models are used as an example for our proposed synchronization. The numerical simulations show a good agreement with the analytical results. The complexity and existence of additional variables mean that it is safer and interesting to transmit and receive signals in communication theory. The proposed scheme of synchronization is considered a generalization of many types in the literature and other examples can be found in similar studies. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

23 pages, 1240 KiB

Open AccessArticle

Observer-Based PID Control Protocol of Positive Multi-Agent Systems

by Xiaogang Yang, Mengxing Huang, Yuanyuan Wu and Siling Feng

Mathematics 2023, 11(2), 419; https://doi.org/10.3390/math11020419 - 12 Jan 2023

Cited by 7 | Viewed by 2107

Abstract

This paper proposes the observer-based proportional-integral-derivative control of positive multi-agent systems. First, a positive observer is constructed for the considered multi-agent systems in terms of a matrix decomposition approach. Then, a novel proportional-integral-derivative protocol framework is proposed based on an improved observer. By [...] Read more.

This paper proposes the observer-based proportional-integral-derivative control of positive multi-agent systems. First, a positive observer is constructed for the considered multi-agent systems in terms of a matrix decomposition approach. Then, a novel proportional-integral-derivative protocol framework is proposed based on an improved observer. By using copositive Lyapunov function, the positivity and consensus of the multi-agent systems are achieved. The corresponding observer and control protocol gain matrices are designed in terms of linear programming. Moreover, the proposed design is developed for heterogeneous positive multi-agent systems. The main contributions of this paper include the following: (i) A positive observer is constructed to estimate the states of positive multi-agent systems; (ii) A novel observer-based proportional-integral-derivative protocol is designed to handle the consensus problem of positive multi-agent systems; and (iii) The presented conditions are solvable in terms of linear programming and the gain matrices can be constructed based on a matrix decomposition technology. Finally, two illustrative examples are provided to verify the effectiveness of the design. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

23 pages, 1850 KiB

Open AccessArticle

Constrained Nonsingular Terminal Sliding Mode Attitude Control for Spacecraft: A Funnel Control Approach

by Nguyen Xuan-Mung, Mehdi Golestani and Sung Kyung Hong

Mathematics 2023, 11(1), 247; https://doi.org/10.3390/math11010247 - 3 Jan 2023

Cited by 8 | Viewed by 1840

Abstract

This paper presents an adaptive constrained attitude control for uncertain spacecraft. Inspired by the concept of nonsingular terminal sliding mode control and funnel control for nonlinear systems, a novel adaptive attitude control is introduced which contains a time-varying gain to handle the constraints [...] Read more.

This paper presents an adaptive constrained attitude control for uncertain spacecraft. Inspired by the concept of nonsingular terminal sliding mode control and funnel control for nonlinear systems, a novel adaptive attitude control is introduced which contains a time-varying gain to handle the constraints imposed on the spacecraft attitude. Indeed, when the attitude trajectory approaches the boundary of the constraint set, the control effort as well as the time-varying gain will increase in order to preclude the trajectory from intersecting the boundary. Then, it is analytically proved that the system trajectories converge to an arbitrary small region around the origin within a fixed time where the smallest upper bound of the convergence time is determined as an independent parameter in the controller. Further, the proposed control scheme is nonsingular without having to use any piecewise continuous function which simplifies stability analysis. These properties distinguish the proposed control scheme from the existing finite/fixed-time attitude controls. Finally, several simulation results confirm the robustness and performance of the proposed control framework. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

22 pages, 5267 KiB

Open AccessArticle

Adaptive Fuzzy Command Filtered Finite-Time Tracking Control for Uncertain Nonlinear Multi-Agent Systems with Unknown Input Saturation and Unknown Control Directions

by Xiongfeng Deng, Yiqing Huang and Lisheng Wei

Mathematics 2022, 10(24), 4656; https://doi.org/10.3390/math10244656 - 8 Dec 2022

Cited by 4 | Viewed by 1264

Abstract

This paper investigates the finite-time consensus tracking control problem of uncertain nonlinear multi-agent systems with unknown input saturation and unknown control directions. An adaptive fuzzy finite-time consensus control law is proposed by combining the fuzzy logic system, command filter, and finite-time control theory. [...] Read more.

This paper investigates the finite-time consensus tracking control problem of uncertain nonlinear multi-agent systems with unknown input saturation and unknown control directions. An adaptive fuzzy finite-time consensus control law is proposed by combining the fuzzy logic system, command filter, and finite-time control theory. Using the fuzzy logic systems, the uncertain nonlinear dynamics are approximated. Considering the command filter and backstepping control technique, the problem of the so-called “explosion of complexity” in the design of virtual control laws and adaptive updating laws is avoided. Meanwhile, the Nussbaum gain function method is applied to handle the unknown control directions and unknown input saturation problems. Based on the finite-time control theory and Lyapunov stability theory, it was found that all signals in the closed-loop system remained semi-global practical finite-time stable, and the tracking error could converge to a sufficiently small neighborhood of the origin in the finite time. In the end, simulation results were provided to verify the validity of the designed control law. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

16 pages, 650 KiB

Open AccessArticle

Tolerance Modelling of Vibrations of a Sandwich Plate with Honeycomb Core

by Jakub Marczak

Materials 2022, 15(21), 7611; https://doi.org/10.3390/ma15217611 - 29 Oct 2022

Cited by 2 | Viewed by 1165

Abstract

Sandwich structures are commonly used in many branches of modern engineering, such as aerospace or naval constructions. In this work, a vibration analysis of such structures is performed with the use of an anlytical model based on a zig-zag hypothesis. Due to the [...] Read more.

Sandwich structures are commonly used in many branches of modern engineering, such as aerospace or naval constructions. In this work, a vibration analysis of such structures is performed with the use of an anlytical model based on a zig-zag hypothesis. Due to the assumed periodic microstructure, which may occure in any layer of the structure, the initial governing equations describing its dynamic behaviour may contain periodic, non-continuous coefficients. The main aim of the presented paper is to show an analytical solution to the issue of the vibration analysis of the mentioned structures. With the use of the tolerance averaging technique, the initial governing equations are transformed to the form with constant coefficients, which is convenient to solve using well-known mathematical methods. The derived model is a versatile solution for any type of periodically inhomogeneous sandwich plate, including sandwich plates with a honeycomb core. Eventually, in the calculation example, the application of the derived averaged model in the analysis of vibrations of such structures is presented and discussed. The convergence of results of the tolerance model and FEM analysis proves the correctness and superiority of the proposed solution. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

10 pages, 459 KiB

Open AccessArticle

On the Dynamics of New 4D and 6D Hyperchaotic Systems

by Samia Rezzag and Fuchen Zhang

Mathematics 2022, 10(19), 3668; https://doi.org/10.3390/math10193668 - 6 Oct 2022

Cited by 2 | Viewed by 1514

Abstract

One of the most interesting problems is the investigation of the boundaries of chaotic or hyperchaotic systems. In addition to estimating the Lyapunov and Hausdorff dimensions, it can be applied in chaos control and chaos synchronization. In this paper, by means of the [...] Read more.

One of the most interesting problems is the investigation of the boundaries of chaotic or hyperchaotic systems. In addition to estimating the Lyapunov and Hausdorff dimensions, it can be applied in chaos control and chaos synchronization. In this paper, by means of the analytical optimization, comparison principle, and generalized Lyapunov function theory, we find the ultimate bound set for a new six-dimensional hyperchaotic system and the globally exponentially attractive set for a new four-dimensional Lorenz- type hyperchaotic system. The novelty of this paper is that it not only shows the 4D hyperchaotic system is globally confined but also presents a collection of global trapping regions of this system. Furthermore, it demonstrates that the trajectories of the 4D hyperchaotic system move at an exponential rate from outside the trapping zone to its inside. Finally, some numerical simulations are shown to demonstrate the efficacy of the findings. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

28 pages, 8684 KiB

Open AccessArticle

Design and Development of a Mathematical Model for an Industrial Process, in a System Dynamics Environment

by Jorge Manuel Barrios Sánchez, Roberto Baeza Serrato and Marco Bianchetti

Appl. Sci. 2022, 12(19), 9855; https://doi.org/10.3390/app12199855 - 30 Sep 2022

Cited by 2 | Viewed by 2984

Abstract

This research proposes a methodology based on control engineering, transforming the simulation model of system dynamics into a mathematical model expressed as a system transfer function. The differential equations of a time domain present in the Forrester diagram are transformed into a frequency [...] Read more.

This research proposes a methodology based on control engineering, transforming the simulation model of system dynamics into a mathematical model expressed as a system transfer function. The differential equations of a time domain present in the Forrester diagram are transformed into a frequency domain based on the Laplace transform. The conventional control engineering technique is used to present and reduce the dynamic system in a block diagram as a mechanism for determining the structure of the system. The direct path equation and the feedback equation are determined to obtain mathematical models that explain the trajectory of the behavior of each state variable through a transfer function in response to the different inputs of the system. The research proposal is based on presenting an alternative of analytical validation for more robust decision-making to systems dynamics models, based on the explanation of the system structure through a transfer function and its analysis of stability and external controllability for the system dynamics model under study. The results are visually analyzed in a root diagram. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

15 pages, 4984 KiB

Open AccessArticle

Estimation of Resonance Frequency for Systems with Contact Using Linear Dynamics Methods

by Maciej Wnuk and Artur Iluk

Appl. Sci. 2022, 12(18), 9344; https://doi.org/10.3390/app12189344 - 18 Sep 2022

Viewed by 1970

Abstract

Limitations in determining the resonance frequency for large models, taking into account non-linearity in the form of contact, initiated work on the creation of a simplified method of estimating these resonance frequencies. The trend in this field is the use of time-domain methods [...] Read more.

Limitations in determining the resonance frequency for large models, taking into account non-linearity in the form of contact, initiated work on the creation of a simplified method of estimating these resonance frequencies. The trend in this field is the use of time-domain methods with full contact, or frequency-domain methods which take into account nonlinearity for specific cases. For simplification, classical modal analysis is often used, with boundary conditions taken into account or freeform vibrations, with neglected contact, or with tied contact areas, as though the contact was always closed. The presented approximation method is based on both types of such analysis and compensates for the error of both of the solutions. The method was elaborated with nonlinear dynamics simulations in the time domain. This work presents experimental verification of the method for a simple beam, and for more complex geometry—the satellite antenna panel. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

10 pages, 7510 KiB

Open AccessArticle

On the Efficiency Enhancement of an Actively Tunable MEMS Energy Harvesting Device

by Mortaza Aliasghary, Saber Azizi, Hadi Madinei and Hamed Haddad Khodaparast

Vibration 2022, 5(3), 603-612; https://doi.org/10.3390/vibration5030035 - 6 Sep 2022

Cited by 4 | Viewed by 1914

Abstract

In this paper, we propose an active control method to adjust the resonance frequency of a capacitive energy harvester. To this end, the resonance frequency of the harvester is tuned using an electrostatic force, which is actively controlled by a voltage source. The [...] Read more.

In this paper, we propose an active control method to adjust the resonance frequency of a capacitive energy harvester. To this end, the resonance frequency of the harvester is tuned using an electrostatic force, which is actively controlled by a voltage source. The spring softening effect of the electrostatic force is used to accommodate the dominant frequency of the ambient mechanical vibration within the bandwidth of the resonance region. A single degree of freedom is considered, and the nonlinear equation of motion is numerically integrated over time. Using a conventional proportional–integral–derivative (PID) control mechanism, the results demonstrated that our controller could shift the resonance frequency leftward on the frequency domain and, as a result, improve the efficiency of the energy harvester, provided that the excitation frequency is lower than the resonance frequency of the energy harvester. Application of the PID controller in the resonance zone resulted in pull-in instability, adversely affecting the harvester’s performance. To tackle this problem, we embedded a saturation mechanism in the path of the control signal to prevent a sudden change in motion amplitude. Outside the pull-in band, the saturation of the control signal resulted in the reduction of harvested power compared to the non-saturated signal; this is a promising improvement in the design and analysis of energy harvesting devices. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

15 pages, 2493 KiB

Open AccessArticle

Parametric Instability of Functionally Graded Porous Cylindrical Panels under the Effect of Static and Time-Dependent Axial Loads

by Salah M. Zaidan and Hamad M. Hasan

Vibration 2022, 5(3), 570-584; https://doi.org/10.3390/vibration5030033 - 2 Sep 2022

Cited by 2 | Viewed by 1630

Abstract

This work presents an analytical study of the parametric instability of cylindrical panels containing functionally graded porous exposed to static and dynamic periodic axial loads under simply supported boundary conditions. Based on Hamilton’s principle, the governing equation of motion by using first-order shear [...] Read more.

This work presents an analytical study of the parametric instability of cylindrical panels containing functionally graded porous exposed to static and dynamic periodic axial loads under simply supported boundary conditions. Based on Hamilton’s principle, the governing equation of motion by using first-order shear deformation theory (FSDT) has been obtained. By applying the Galerkin technique, an excitation frequency expression is derived, which helps identify areas of instability of functionally graded porous cylindrical panels. Numerical simulations are used to validate the analytical results. Eventually, the impacts of the porosity coefficient, porosity distribution method, static and dynamic periodic axial loads, panel angle, circumferential wave number, and cylindrical panel characteristics on the region of instability are displayed in the section of results and discussions. The findings show that when the porosity is further from the surface, the more stable the structure is. Furthermore, a small angle of the cylindrical panels gives a better dynamic response than a large angle. In addition, increased static and dynamic loads lead to an expansion of areas of instability. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

9 pages, 1229 KiB

Open AccessArticle

Highly Efficient Numerical Integrator for the Circular Restricted Three-Body Problem

by Xiongbiao Tu, Qiao Wang and Yifa Tang

Symmetry 2022, 14(9), 1769; https://doi.org/10.3390/sym14091769 - 25 Aug 2022

Cited by 1 | Viewed by 1505

Abstract

The dynamic equation of a mass point in the circular restricted three-body problem is governed by Coriolis and centrifugal force, in addition to a co-rotating potential relative to the frame. In this paper, we provide an explicit, symmetric integrator for this problem. Such [...] Read more.

The dynamic equation of a mass point in the circular restricted three-body problem is governed by Coriolis and centrifugal force, in addition to a co-rotating potential relative to the frame. In this paper, we provide an explicit, symmetric integrator for this problem. Such an integrator is more efficient than the symplectic Euler method and the Gauss Runge–Kutta method as regards this problem. In addition, we proved the integrator is symplectic by the discrete Hamilton’s principle. Several groups of numerical experiments demonstrated the precision and high efficiency of the integrator in the examples of the quadratic potential and the bounded orbits in the circular restricted three-body problem. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

19 pages, 4086 KiB

Open AccessArticle

Adaptive Fuzzy Tracking Control of Uncertain Nonlinear Multi-Agent Systems with Unknown Control Directions and a Dead-Zone Fault

by Xiongfeng Deng and Xiyu Zhang

Mathematics 2022, 10(15), 2655; https://doi.org/10.3390/math10152655 - 28 Jul 2022

Cited by 6 | Viewed by 1630

Abstract

In this paper, a class of uncertain nonlinear multi-agent systems with unknown control directions and a dead-zone fault is addressed, where unknown control gains exist in each subsystem. In terms of the approximation characteristic of a fuzzy logic system, it is used to [...] Read more.

In this paper, a class of uncertain nonlinear multi-agent systems with unknown control directions and a dead-zone fault is addressed, where unknown control gains exist in each subsystem. In terms of the approximation characteristic of a fuzzy logic system, it is used to approximate uncertain nonlinear dynamics, and then the relevant adaptive control laws are designed. Considering the presence of unknown control directions and a dead-zone fault, the Nussbaum gain function technique is introduced to design the intermediate control law and the adaptive fuzzy control law. A theoretical analysis shows that the tracking control problem of the given multi-agent systems can be effectively solved through the application of the proposed adaptive fuzzy control law and the tracking errors can converge to a small neighborhood of zero through an adjustment of the relevant parameters. Finally, the effectiveness of the theoretical analysis results is verified by two simulation cases. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

19 pages, 24852 KiB

Open AccessArticle

Analysis of the Influence of a Powertrain Mounting System on a Dual-Clutch Transmission Vehicle under Typical Working Conditions

by Zheng Guo, Datong Qin, Antai Li, Jihao Feng and Yonggang Liu

Appl. Sci. 2022, 12(15), 7439; https://doi.org/10.3390/app12157439 - 25 Jul 2022

Cited by 2 | Viewed by 1809

Abstract

The unsuitably designed powertrain mount may cause jittering and shrugging during the starting and shifting processes of the vehicle, which seriously affects the comfort of using the vehicle. However, the influence of mounts on vehicles has been neglected in previous studies. In view [...] Read more.

The unsuitably designed powertrain mount may cause jittering and shrugging during the starting and shifting processes of the vehicle, which seriously affects the comfort of using the vehicle. However, the influence of mounts on vehicles has been neglected in previous studies. In view of the above problems, this study establishes a DCT vehicle coupling dynamic model, considering six degrees of freedom of the powertrain mount and the engine dynamic torque, nonlinear characteristics of a dual-mass flywheel, time-varying stiffness of gear systems, and other factors. Furthermore, the effect of mounts on the longitudinal dynamic characteristics of the vehicle is studied during the starting, shifting, and tip-in/tip-out process. The results show that under typical working conditions, the mount and its stiffness and damping affect the fluctuation frequency and amplitude of the jerk. When the torque of the vehicle transmission system changes greatly, such as under starting and tip-in/tip-out conditions, the mount has a great impact on the dynamic performance of the vehicle. Simultaneously, the engine torque fluctuation can act on the vehicle through the mount, which has an impact on the jerk of the vehicle. A comparison with vehicle test results reveals that the DCT coupling dynamic model can reflect the law of the effect of the mount on the vehicle performance and verify the rationality of the model. Under typical working conditions, when the influence of the mount is not considered in the vehicle dynamic’s modeling, there is a large error of the jerk between the simulation results and the actual situation. The results provide a reference for optimizing the parameters of the mount and improving the dynamic characteristics of DCT vehicles. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

10 pages, 2324 KiB

Open AccessArticle

Exact Traveling Wave Solutions in a Generalized Harry Dym Type Equation

by Rong Wu and Yan Zhou

Symmetry 2022, 14(7), 1480; https://doi.org/10.3390/sym14071480 - 20 Jul 2022

Cited by 3 | Viewed by 1729

Abstract

The traveling wave solutions of a generalized HD type equation are investigated in this study. The traveling wave system is a singular system of the first class with given parameter conditions. From the standpoint of dynamical systems, the bifurcations of traveling wave solutions [...] Read more.

The traveling wave solutions of a generalized HD type equation are investigated in this study. The traveling wave system is a singular system of the first class with given parameter conditions. From the standpoint of dynamical systems, the bifurcations of traveling wave solutions in parameter space are examined. It is demonstrated that solitary wave solutions, periodic peakons, pseudo-peakons, and compacton solutions exist. All conceivable exact explicit parametric representations of various solutions are presented. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

12 pages, 3590 KiB

Open AccessArticle

Effect of Observation Geometry on Short-Arc Angles-Only Initial Orbit Determination

by Zhao Feng, Changxiang Yan, Yanfeng Qiao, Anlin Xu and Haihong Wang

Appl. Sci. 2022, 12(14), 6966; https://doi.org/10.3390/app12146966 - 9 Jul 2022

Cited by 2 | Viewed by 1472

Abstract

Space-based optical sensors are attracting increasing research attention as they can measure the angle of space targets over large areas, facilitating low-cost, wide-area space target surveillance. Studying the effect of observation geometry on short-arc angles-only initial orbit determination is important for analysing the [...] Read more.

Space-based optical sensors are attracting increasing research attention as they can measure the angle of space targets over large areas, facilitating low-cost, wide-area space target surveillance. Studying the effect of observation geometry on short-arc angles-only initial orbit determination is important for analysing the surveillance capability of systems that use optics as the main means for surveilling different areas of space. In this paper, the initial orbit is calculated based on the unit vector method (UVM); the geometric dilution of precision (GDOP)—derived under the condition that the approximate Lagrangian coefficient and distance are constant—is used as the parameter for the uncertainty distribution of the target orbit solution. A suitable coordinate system transformation is conducted and all possible observation geometry relationships between the target and the sensor are expressed in terms of the angle between orbital planes and the right ascension of the target and sensor in the transformed coordinate system. Simulation experiments show that the GDOP is approximately equal to that obtained statistically through Monte Carlo simulation experiments. The accuracy of the initial orbit solution is poor when the target and optical sensor are at the same right ascension and declination, or in the same orbital plane. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

20 pages, 4209 KiB

Open AccessArticle

A Variable-Order Dynamic Constitutive Model for Clay Based on the Fractional Calculus

by Bo-Lang Zhang, Kai-Sheng Chen, Xing Hu and Kun Zhang

Appl. Sci. 2022, 12(13), 6416; https://doi.org/10.3390/app12136416 - 24 Jun 2022

Cited by 3 | Viewed by 1467

Abstract

To accurately describe the deformation characteristics of clay under long-term cyclic load, based on fractional calculus theory, elastoplastic theory and the basic element model, a variable-order fractional dynamic model designed to predict accumulative strain of clay was exhibited. Firstly, the cyclic load was [...] Read more.

To accurately describe the deformation characteristics of clay under long-term cyclic load, based on fractional calculus theory, elastoplastic theory and the basic element model, a variable-order fractional dynamic model designed to predict accumulative strain of clay was exhibited. Firstly, the cyclic load was separated into static and alternating load in accordance with cyclic load characteristics, and the strain of clay under static and alternating load was analyzed. Then, on the basis of the variable-order Abel dashpot model, rheological theory and elastoplastic theory, the expressions of the rheological constitutive model and strain response were both obtained. Finally, in combination with the undrained dynamic triaxial testing of Zhan Jiang clay and Tian Jin soft clay, a series of analyses was carried out on the effectiveness and parameter sensitivity of the model when subjected to long-term cyclic loading. By comparing the dynamic constitutive model with pre-existing models, the superiority of the dynamic constitutive model is revealed. The results show that the dynamic constitutive model can characterize properly the deformation characteristics of clay under the action of long-term cyclic loading, especially in its accelerating stage. The parameter sensitivity of the model exhibits a growing trend with the increment of loading duration. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

25 pages, 14122 KiB

Open AccessArticle

Optimization of a Non-Traditional Vibration Absorber for Vibration Suppression and Energy Harvesting

by Miao Yuan, Youzuo Jin, Kefu Liu and Ayan Sadhu

Vibration 2022, 5(3), 383-407; https://doi.org/10.3390/vibration5030022 - 22 Jun 2022

Cited by 2 | Viewed by 2187

Abstract

This paper investigates the optimization of a non-traditional vibration absorber for simultaneous vibration suppression and energy harvesting. Unlike a traditional vibration absorber, the non-traditional vibration absorber has its damper connected between the absorber mass and the base. An electromagnetic energy harvester is used [...] Read more.

This paper investigates the optimization of a non-traditional vibration absorber for simultaneous vibration suppression and energy harvesting. Unlike a traditional vibration absorber, the non-traditional vibration absorber has its damper connected between the absorber mass and the base. An electromagnetic energy harvester is used as a tunable absorber damper. This non-traditional vibration absorber is attached to a primary system that is subjected to random base excitation. An analytical study is conducted by assuming that the base excitation is white noise. In terms of vibration suppression, the objective of the optimization is to minimize the power dissipated by the primary damper and maximize the power dissipated by the absorber damper. It is found that when the primary system is undamped, the power dissipated by the absorber damper remains a constant that is related to the mass ratio. The higher the mass ratio, the higher the power dissipated. When the primary system is damped, the minimization of the power dissipated by the primary damping is equivalent to the maximization of the power dissipated by the absorber damper. The existence of the optimum solutions depends on both the mass ratio and the primary damping ratio. In terms of energy harvesting, the objective of optimization is to maximize the power harvested by the load resistor. It is found that for a given mass ratio and primary damping ratio, the optimum frequency tuning ratio required to maximize vibration suppression is slightly higher than that required to maximize the harvested power. The trade-off issue between vibration suppression and energy harvesting is investigated. An apparatus is developed to allow frequency tuning and damping tuning. Both the numerical simulation and experimental study with band-limited white noise validate the general trends revealed in the analytical study. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

18 pages, 12924 KiB

Open AccessArticle

Harmonic Balance Method to Analyze the Steady-State Response of a Controlled Mass-Damper-Spring Model

by Ali Kandil, Y. S. Hamed and Jan Awrejcewicz

Symmetry 2022, 14(6), 1247; https://doi.org/10.3390/sym14061247 - 16 Jun 2022

Cited by 6 | Viewed by 2816

Abstract

This research is concerned with extracting the approximate solutions of a controlled mass-damper-spring model via the harmonic balance method. The stability of these solutions was checked with the aid of Floquet theory. A nonlinear saturation controller (NSC), a linear variable differential transformer (LVDT) [...] Read more.

This research is concerned with extracting the approximate solutions of a controlled mass-damper-spring model via the harmonic balance method. The stability of these solutions was checked with the aid of Floquet theory. A nonlinear saturation controller (NSC), a linear variable differential transformer (LVDT) and a servo-controlled linear actuator (SCLA), were applied to suppress the undesired oscillations of the harmonically-excited car. 2D and 3D graphical plots are included based upon the equations resulting from the harmonic balance method. Moreover, a numerical simulation was established using the fourth order Rung–Kutta technique in order to confirm the overall controlled behavior of the studied model. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

10 pages, 244 KiB

Open AccessArticle

Continued Fraction Expansions of Stable Discrete-Time Systems of Difference Equations

by Ziad Zahreddine

Symmetry 2022, 14(6), 1226; https://doi.org/10.3390/sym14061226 - 13 Jun 2022

Cited by 1 | Viewed by 1422

Abstract

We provide a systematic procedure for generating the coefficients of the continued fraction expansion of the test function associated with the characteristic polynomial of a stable system of difference equations. We illustrate the feasibility of the procedure, and we provide an application on [...] Read more.

We provide a systematic procedure for generating the coefficients of the continued fraction expansion of the test function associated with the characteristic polynomial of a stable system of difference equations. We illustrate the feasibility of the procedure, and we provide an application on the stability of two-dimensional digital filters. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

12 pages, 3692 KiB

Open AccessArticle

Efficiency Analysis of Herringbone Star Gear Train Transmission with Different Load-Sharing Conditions

by Dong Li, Shuyan Wang, Dongliang Li and Yong Yang

Appl. Sci. 2022, 12(12), 5970; https://doi.org/10.3390/app12125970 - 11 Jun 2022

Cited by 4 | Viewed by 1939

Abstract

A slight improvement in the transmission efficiency of the herringbone star gear train in a GTF has a great impact on the fuel economy of the engine. Here, the influencing factors of gear train efficiency were studied from the perspective of gear train [...] Read more.

A slight improvement in the transmission efficiency of the herringbone star gear train in a GTF has a great impact on the fuel economy of the engine. Here, the influencing factors of gear train efficiency were studied from the perspective of gear train composition, and the efficiency calculation model of the split star gear train, including the load-sharing coefficient, was established. Based on the efficiency calculation model, the mechanical relationship affecting the load distribution of the split star gear train, and the influence of installation error on the power split of the gear train, were studied. The effects of torque and installation error on the load coefficient of the gear train were studied using dynamic analysis software, and the efficiency of the gear train under multiple working conditions was verified and analyzed. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

13 pages, 418 KiB

Open AccessArticle

Finite-Time Contractively Bounded Control of Positive Linear Systems under H_∞ Performance and Its Application to Pest Management

by Liang Zhu, Baolong Zhu, Zhiguo Yan and Guolin Hu

Mathematics 2022, 10(12), 1997; https://doi.org/10.3390/math10121997 - 9 Jun 2022

Cited by 1 | Viewed by 1404

Abstract

This paper investigates the finite-time contractively bounded control issue for positive linear systems under

H_{\infty}

performance. The notion of

H_{\infty}

finite-time contractive boundedness is first extended to positive systems. Finite-time contractively bounded control is considered to ensure the

H_{\infty}

finite-time [...] Read more.

This paper investigates the finite-time contractively bounded control issue for positive linear systems under

H_{\infty}

performance. The notion of

H_{\infty}

finite-time contractive boundedness is first extended to positive systems. Finite-time contractively bounded control is considered to ensure the

H_{\infty}

finite-time contractive boundedness of the considered positive systems. A state feedback finite-time contractively bounded controller design method is proposed. The corresponding sufficient condition for the existence of the desired controller is derived by using the Lyapunov function method and the matrix inequality technique. Moreover, a computable scheme for solving the controller gain is established by employing the cone complementary linearization approach. Finally, a numerical example and an application example about pest management are used to validate the effectiveness of proposed conditions. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

11 pages, 1991 KiB

Open AccessArticle

On The 3D VR Simulated Rubik’s Cube Game for Smart Pads

by Wen-Te Chang

Symmetry 2022, 14(6), 1193; https://doi.org/10.3390/sym14061193 - 9 Jun 2022

Viewed by 2255

Abstract

In this study, interface designs of a VR 3D-simulated Rubik’s Cube game were developed and evaluated. A 2 × 2 × 2 mixed-design ANOVA was executed, with age (younger adult/older adult), interface (arrow/intuitive), and task complexity (easy, a single symmetrical task/difficult, a bio-symmetrical [...] Read more.

In this study, interface designs of a VR 3D-simulated Rubik’s Cube game were developed and evaluated. A 2 × 2 × 2 mixed-design ANOVA was executed, with age (younger adult/older adult), interface (arrow/intuitive), and task complexity (easy, a single symmetrical task/difficult, a bio-symmetrical task) experimental design. The first three factors were between-subject designs while the latter was a within-subject design. The dependent variable was the percentage of the task performance and wayfinding questionnaire. The collected experimental data were analyzed by regression method to clarify the correlation among age, interface, task complexity, and wayfinding strategy. There were 96 subjects in the experiment, including 48 younger adults (aged from 18~22) and 48 older adults (aged from 60~85). The experimental results and statistical analysis showed that the task difficulty had a significant effect on task performance in the 3D VR Rubik’s Cube game. For the smart pad, the arrow interface was significantly more effective than the intuitive interface. The theoretical model regression analysis of the task complexity, interface, and wayfinding strategy was shown to be significant. Results showed that users may be affected either positively or negatively by the wayfinding strategy, as a higher score on familiarity indicates better VR game task performance, whereas for the usual spatial behavior wayfinding strategy, the opposite result was found for memory. These results can be used to assess VR game interface designs, taking into consideration age difference, task complexity, experiential self-report on 3D VR games, and including VR rotation navigational Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

21 pages, 429 KiB

Open AccessArticle

Damping Optimization of Linear Vibrational Systems with a Singular Mass Matrix

by Ninoslav Truhar and Maja Petrač

Mathematics 2022, 10(11), 1854; https://doi.org/10.3390/math10111854 - 28 May 2022

Viewed by 1845

Abstract

We present two novel results for small damped oscillations described by the vector differential equation

M \ddot{x} + C \dot{x} + K x = 0

, where the mass matrix M can be singular, but standard deflation techniques cannot be applied. [...] Read more.

We present two novel results for small damped oscillations described by the vector differential equation

M \ddot{x} + C \dot{x} + K x = 0

, where the mass matrix M can be singular, but standard deflation techniques cannot be applied. The first result is a novel formula for the solution X of the Lyapunov equation

A^{T} X + X A = - I

, where

A = A (v)

is obtained from

M, C (v) \in R^{n \times n}

, and

K \in R^{n \times n}

, which are the so-called mass, damping, and stiffness matrices, respectively, and

rank (M) = n - 1

. Here,

C (v)

is positive semidefinite with

rank (C (v)) = 1

. Using the obtained formula, we propose a very efficient way to compute the optimal damping matrix. The second result was obtained for a different structure, where we assume that

dim (N (M)) \geq 1

and internal damping exists (usually a small percentage of the critical damping). For this structure, we introduce a novel linearization, i.e., a novel construction of the matrix A in the Lyapunov equation

A^{T} X + X A = - I

, and a novel optimization process. The proposed optimization process computes the optimal damping

C (v)

that minimizes a function

v \mapsto trace (Z X)

(where Z is a chosen symmetric positive semidefinite matrix) using the approximation function

g (v) = c_{v} + \frac{a}{v} + b v

, for the trace function

f (v) ≐ trace (Z X (v))

. Both results are illustrated with several corresponding numerical examples. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

15 pages, 3265 KiB

Open AccessArticle

Linear Proportional-Integral-Differential-Robustified Continuous-Time Optimal Predictive Control for a Class of Nonlinear Systems

by Guilin Wu, Haisong Ang and Qingxi Li

Appl. Sci. 2022, 12(11), 5446; https://doi.org/10.3390/app12115446 - 27 May 2022

Viewed by 1555

Abstract

This paper presents a novel robust optimal predictive control approach for a class of nonlinear continuous-time systems perturbed by unknown disturbances. First, a new error state with a linear proportional-integral-differential (PID) structure considering current, accumulative, and derivative tracking errors is defined. Second, prediction [...] Read more.

This paper presents a novel robust optimal predictive control approach for a class of nonlinear continuous-time systems perturbed by unknown disturbances. First, a new error state with a linear proportional-integral-differential (PID) structure considering current, accumulative, and derivative tracking errors is defined. Second, prediction of the error state within the predictive periods is expressed by the error state and its high-order derivatives according to the Taylor series expansion. Last, the proposed control law as well as the main result of this paper are derived by minimizing the prediction of the error state. Numerical validation for designing a missile autopilot shows that, due to minimizing the accumulative tracking error included in the PID-structuralized new error state, the proposed approach can generate smaller steady-state tracking errors than two commonly applied continuous-time optimal predictive control approaches whether the disturbances encountered by the missile are constant or time-varying. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

15 pages, 4152 KiB

Open AccessArticle

Performance Evaluation of Track Curvature Sensor for Curvature Estimation in a Curved Section of Railway Tracks

by Hyun Moo Hur, Yu Jeong Shin, Jung Won Seo and Kyung Ho Moon

Appl. Sci. 2022, 12(11), 5398; https://doi.org/10.3390/app12115398 - 26 May 2022

Cited by 1 | Viewed by 1699

Abstract

Active railway vehicles such as tilting trains and active steering bogies are being developed to improve the curve running performance of railway vehicles. In this case, a technology for sensing a curve and extracting curve information such as a curvature in real time [...] Read more.

Active railway vehicles such as tilting trains and active steering bogies are being developed to improve the curve running performance of railway vehicles. In this case, a technology for sensing a curve and extracting curve information such as a curvature in real time is required. The existing railway curve detection technology has the disadvantage of requiring many calibration processes through test driving and being affected by running speed. In order to overcome these disadvantages, this paper proposes a very simple and efficient curvature estimation method. A curvature sensor prototype was manufactured and a test run was performed on the test track. As a test result compared with the track inspection data, the minimum deviation was 0.8%, the maximum deviation was 4.0% and the average deviation was 2.8%, showing good curvature measurement performance. It was also confirmed that the effect of the running speed was very small and the accuracy was high in the small curve with a large curvature. Therefore, the developed curvature measurement sensor is expected to be used very practically in the field of curvature detection and curvature extraction to control the vehicle in the curve section. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

18 pages, 7141 KiB

Open AccessArticle

An Efficient Numerical Model to Predict the Mechanical Response of a Railway Track in the Low-Frequency Range

by Maryam El Moueddeb, François Louf, Pierre-Alain Boucard, Franck Dadié, Gilles Saussine and Danilo Sorrentino

Vibration 2022, 5(2), 326-343; https://doi.org/10.3390/vibration5020019 - 24 May 2022

Cited by 4 | Viewed by 2607

Abstract

With railway interoperability, new trains are allowed to move on the French railway network. These trains may present different designs from standard trains. This work aims to complete the current approach for vehicle admission on the railway network, which is defined in technical [...] Read more.

With railway interoperability, new trains are allowed to move on the French railway network. These trains may present different designs from standard trains. This work aims to complete the current approach for vehicle admission on the railway network, which is defined in technical baselines. Historically, computation rules for traffic conditions are based on simplified analytical works, which are considerably qualitative. They have evolved through feedback and experimental campaigns to comply with the track structure evolution. An efficient methodology based on numerical simulation is needed to evaluate railway vehicle admission to answer this issue. A perspective to update these computation rules is to evaluate the structural fatigue in the rail. That is to say, fatigue is caused by bending and shear stresses. The complexity of the railway system has led to an investigation at first of the vertical response of the railway track and quantifying its contribution to the rail’s stress response. In that sense, this paper investigates the vertical track response to a moving railway vehicle at low frequencies. For this purpose, a lightweight numerical model for the track, a multi-body model for the vehicle, and a random vertical track irregularity are proposed. More explicitly, the track model consists of a two-layer discrete support model in which the rail is considered as a beam and sleepers are point masses. The rail pads and ballast layer are modelled as spring/damper couples. Numerical results show a negligible effect of track inertia forces due to high track stiffness and damping. Nevertheless, this assumption is valid for normal rail stresses but not for ballast loading, especially in the case of sleeper voids or unsupported sleepers. Hence, the prediction of the mechanical stress state in the rail for fatigue issues is achieved through a static track model where the equivalent loading is obtained from a dynamic study of a simplified vehicle model. A statistical analysis shows that the variability of the vertical track irregularity does not influence the output variabilities like the maximum in time and space of the normal and shear stress. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

19 pages, 416 KiB

Open AccessArticle

Optimal H₂ Moment Matching-Based Model Reduction for Linear Systems through (Non)convex Optimization

by Ion Necoara and Tudor-Corneliu Ionescu

Mathematics 2022, 10(10), 1765; https://doi.org/10.3390/math10101765 - 22 May 2022

Viewed by 1844

Abstract

In this paper, we compute a (local) optimal reduced order model that matches a prescribed set of moments of a stable linear time-invariant system of high dimension. We fix the interpolation points and parametrize the models achieving moment-matching in a set of free [...] Read more.

In this paper, we compute a (local) optimal reduced order model that matches a prescribed set of moments of a stable linear time-invariant system of high dimension. We fix the interpolation points and parametrize the models achieving moment-matching in a set of free parameters. Based on the parametrization and using the

H_{2}

-norm of the approximation error as the objective function, we derive a nonconvex optimization problem, i.e., we search for the optimal free parameters to determine the model yielding the minimal

H_{2}

-norm of the approximation error. Furthermore, we provide the necessary first-order optimality conditions in terms of the controllability and the observability Gramians of a minimal realization of the error system. We then propose two gradient-type algorithms to compute the (local) optimal models, with mathematical guarantees on the convergence. We also derive convex semidefinite programming relaxations for the nonconvex Problem, under the assumption that the error system admits block-diagonal Gramians, and derive sufficient conditions to guarantee the block diagonalization. The solutions resulting at each step of the proposed algorithms guarantee the achievement of the imposed moment matching conditions. The second gradient-based algorithm exhibits the additional property that, when stopped, yields a stable approximation with a reduced

H_{2}

-error norm. We illustrate the theory on a CD-player and on a discretized heat equation. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

12 pages, 9840 KiB

Open AccessArticle

Control Analysis of Stochastic Lagging Discrete Ecosystems

by Jinyi Zhang

Symmetry 2022, 14(5), 1039; https://doi.org/10.3390/sym14051039 - 19 May 2022

Cited by 3 | Viewed by 1143

Abstract

In this paper, control analysis of a stochastic lagging discrete ecosystem is investigated. Two-dimensional stochastic hysteresis discrete ecosystem equilibrium points with symmetry are discussed, and the dynamical behavior of equilibrium points with symmetry and their control analysis is discussed. Using the orthogonal polynomial [...] Read more.

In this paper, control analysis of a stochastic lagging discrete ecosystem is investigated. Two-dimensional stochastic hysteresis discrete ecosystem equilibrium points with symmetry are discussed, and the dynamical behavior of equilibrium points with symmetry and their control analysis is discussed. Using the orthogonal polynomial approximation theory, the stochastic lagged discrete ecosystems are approximately transformed as its equivalent deterministic ecosystem. Based on the stability and bifurcation theory of deterministic discrete systems, through mathematical analysis, asymptotic stability and Hopf bifurcation are existent in the ecosystem, constructing control functions, controlling the behavior of the system dynamics. Finally, the effects of different random strengths on the bifurcation control and asymptotic stability control are verified by numerical simulations, which validate the correctness and effectiveness of the main results of this paper. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

13 pages, 310 KiB

Open AccessArticle

Hyperbolicity of First Order Quasi-Linear Equations

by Vladimir Vasilyev and Yuri Virchenko

Symmetry 2022, 14(5), 1024; https://doi.org/10.3390/sym14051024 - 17 May 2022

Viewed by 1316

Abstract

The theorem about equivalence of the strong hyperbolicity concept and the Friedrichs hyperbolicity concept for partial quasi-linear differential equations of the first order is proved. On the basis of this theorem, the necessary and sufficient conditions of hyperbolicity are found in terms of [...] Read more.

The theorem about equivalence of the strong hyperbolicity concept and the Friedrichs hyperbolicity concept for partial quasi-linear differential equations of the first order is proved. On the basis of this theorem, the necessary and sufficient conditions of hyperbolicity are found in terms of the matrix of the corresponding linearized first order equations system. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

17 pages, 5456 KiB

Open AccessArticle

Coupling Effect Suppressed Compact Surgical Robot with 7-Axis Multi-Joint Using Wire-Driven Method

by Kicheol Yoon, Sung-Min Cho and Kwang Gi Kim

Mathematics 2022, 10(10), 1698; https://doi.org/10.3390/math10101698 - 16 May 2022

Cited by 5 | Viewed by 2798

Abstract

Currently, the most prevalent surgical treatment method is laparoscopic surgery. Robotic surgery has many advantages over laparoscopic surgery. Therefore, robotic surgery technology is currently constantly evolving. The advantages of robotic surgery are that it can minimize incision, bleeding, and sequelae. Other advantages of [...] Read more.

Currently, the most prevalent surgical treatment method is laparoscopic surgery. Robotic surgery has many advantages over laparoscopic surgery. Therefore, robotic surgery technology is currently constantly evolving. The advantages of robotic surgery are that it can minimize incision, bleeding, and sequelae. Other advantages of robotic surgery are that it can reduce hospitalization, recovery period, and side effects. The appeal of robotic surgery is that it requires fewer surgical personnel compared to laparoscopic surgery. This paper proposes an ultra-compact 7-axis vertical multi-joint robot that employs the wire-driven method for minimally invasive surgery. The proposed robot analyzes the degree of freedom and motion coupling for control. The robot joint is composed of a total of seven joints, and among them, the 7-axis joint operates the forceps. At this time, the forceps joint (#7 axis) can only operate open and close functions, while the link is bent and rotatable, regardless of position change. This phenomenon can be analyzed by Forward Kinematics. Also, when the DOF rotates, the passing wires become twisted, and the wire is generated through length change and coupling phenomenon. The maximum rotation angle of DOF is 90° and the rotating passing wire is wound by the rotation of the wire pulley. If the DOF is rotated to the full range of 120°, the second DOF will be rotated to 90°, and at this time, the coupling phenomenon caused by the first DOF rotation can be eliminated. The length change and the robot joint angle change related to the motor drive, based on the surgical robot control using the wire-driven method, are correlated, and the values for the position and direction of the end effector of the robot can be obtained through a forward kinematic analysis. The coupling problem occurring in the wire connecting the robot driving part can be solved through a kinematic analysis. Therefore, it was possible to test the position of the slave robot and the performance of the surgical forceps movement using the master system. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

24 pages, 19922 KiB

Open AccessArticle

Long Time Simulation Analysis of Geometry Dynamics Model under Iteration

by Weiwei Sun, Long Bai, Xinsheng Ge and Lili Xia

Appl. Sci. 2022, 12(10), 4910; https://doi.org/10.3390/app12104910 - 12 May 2022

Cited by 1 | Viewed by 1373

Abstract

Geometry modeling methods can conserve the geometry characters of a system, which helps the dynamic equations more concisely and is good for long simulations. Reduced attitude, Lie group and Lie algebra are three different expressions of geometry. Models for the dynamics of a [...] Read more.

Geometry modeling methods can conserve the geometry characters of a system, which helps the dynamic equations more concisely and is good for long simulations. Reduced attitude, Lie group and Lie algebra are three different expressions of geometry. Models for the dynamics of a planer pendulum and a 3D pendulum were built with these three geometry expressions. According to the variation method, the dynamics models as ordinary differential equations were transformed into nonlinear equations which are solved by Newton iteration. The simulation results show that Lie group and Lie algebra calculations can conserve the geometric structure, but have different long-time behavior. The complete Lie group expression has the best long simulation behavior and has the lowest sensitivity to the time step in both planer and 3D pendulum simulations, because it saves the complete geometry of the system in the dynamics model. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

18 pages, 3414 KiB

Open AccessArticle

Fatigue Life Assessment of Intercity Track Viaduct Based on Vehicle–Bridge Coupled System

by Chenxing Cui, Fan Feng, Xiandong Meng and Xiang Liu

Mathematics 2022, 10(10), 1663; https://doi.org/10.3390/math10101663 - 12 May 2022

Cited by 5 | Viewed by 1530

Abstract

During the long-term operation of an urban railway viaduct, it is subjected to multiple cyclic loads caused by the movement of a vehicle. As a result, the fatigue life of the bridge should be fully considered during the design process. Furthermore, the bridge [...] Read more.

During the long-term operation of an urban railway viaduct, it is subjected to multiple cyclic loads caused by the movement of a vehicle. As a result, the fatigue life of the bridge should be fully considered during the design process. Furthermore, the bridge structure will be subject to environmental corrosion for an extended period of time, resulting in concrete carbonization and reinforcement corrosion, which aggravates the bridge structure’s fatigue damage. To compensate for the disadvantage of the traditional static analysis method’s inability to consider vehicle speed, a vehicle–bridge system coupled model is established, material corrosion is considered, railway bridge damage under vehicle load is analyzed, and the service life of common 30 m and 25 m span bridges is calculated. The results show that ignoring corrosion will understate the bridge damage, and vehicle speed has a significant impact on bridge fatigue life. Finally, the recommended operating speeds for 30 m span and 25 m span bridges are provided. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

21 pages, 4076 KiB

Open AccessArticle

Fuzzy-Based Adaptive Dynamic Surface Control for a Type of Uncertain Nonlinear System with Unknown Actuator Faults

by Xiongfeng Deng and Jiakai Wang

Mathematics 2022, 10(10), 1624; https://doi.org/10.3390/math10101624 - 10 May 2022

Cited by 4 | Viewed by 1653

Abstract

In this paper, the adaptive control problem of a type of uncertain nonlinear system is addressed. The system discussed includes unknown nonlinear functions, uncertain nonlinear dynamics, and unknown actuator faults. Based on the fuzzy logic systems and dynamic surface control technique, an adaptive [...] Read more.

In this paper, the adaptive control problem of a type of uncertain nonlinear system is addressed. The system discussed includes unknown nonlinear functions, uncertain nonlinear dynamics, and unknown actuator faults. Based on the fuzzy logic systems and dynamic surface control technique, an adaptive fuzzy control law is designed to solve the tracking control problem. In control law design, fuzzy logic systems are utilized to approximate uncertain nonlinear functions, and with the help of the dynamic surface control technique, the problem of the “explosion of complexity” can be overcome. Through stability analysis, it is confirmed that all of the signals in the closed-loop system are semi-global bounded, and the convergence of the tracking error to the specified small neighborhood of the origin can be ensured by adjusting the control law parameters. Finally, the effectiveness of the proposed control law is verified by simulation examples. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

9 pages, 704 KiB

Open AccessArticle

Graph Colorings and Labelings Having Multiple Restrictive Conditions in Topological Coding

by Xiaohui Zhang, Chengfu Ye, Shumin Zhang and Bing Yao

Mathematics 2022, 10(9), 1592; https://doi.org/10.3390/math10091592 - 7 May 2022

Cited by 3 | Viewed by 1679

Abstract

With the fast development of networks, one has to focus on the security of information running in real networks. A technology that might be able to resist attacks equipped with AI techniques and quantum computers is the so-called topological graphic password of topological [...] Read more.

With the fast development of networks, one has to focus on the security of information running in real networks. A technology that might be able to resist attacks equipped with AI techniques and quantum computers is the so-called topological graphic password of topological coding. In order to further study topological coding, we use the multiple constraints of graph colorings and labelings to propose 6C-labeling, 6C-complementary labeling, and its reciprocal-inverse labeling, since they can be applied to build up topological coding. We show some connections between 6C-labeling and other graph labelings/colorings and show graphs admitting twin-type 6C-labelings, as well as the construction of graphs admitting twin-type 6C-labelings. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

13 pages, 665 KiB

Open AccessArticle

Evolutionary Dynamics of Division of Labor Games for Underwater Searching Tasks

by Minglei Xiong and Guangming Xie

Symmetry 2022, 14(5), 941; https://doi.org/10.3390/sym14050941 - 5 May 2022

Cited by 3 | Viewed by 1618

Abstract

Division of labor in self-organized groups is a problem of both theoretical significance and application value. Many application problems in the real world require efficient task allocation. We propose a model combining bio-inspiration and evolutionary game theory. This research model theoretically analyzes the [...] Read more.

Division of labor in self-organized groups is a problem of both theoretical significance and application value. Many application problems in the real world require efficient task allocation. We propose a model combining bio-inspiration and evolutionary game theory. This research model theoretically analyzes the problem of target search in unknown areas for multi-robot systems. If the robot’s operating area is underwater, the problem becomes more complicated due to its information sharing restrictions. Additionally, it drives strategy updates and calculates the fixed probability of relevant strategies, using evolutionary game theory and the commonly used Fermi function. Our study estimates the fixed probability under arbitrary selection intensity and the fixed probability and time under weak selection for the two-player game model. In the multi-player game, we get these results for weak selection, which is conducive to the coexistence of the two strategies. Moreover, the conducted simulations confirm our analysis. These results help to understand and design effective mechanisms in which self-organizing collective dynamics appears in the form of maximizing the benefits of multi-agent systems in the case of the asymmetric game. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

41 pages, 10969 KiB

Open AccessArticle

Continuous Rotor Dynamics of Multi-Disc and Multi-Span Rotor: A Theoretical and Numerical Investigation on the Continuous Model and Analytical Solution for Unbalance Responses

by Aiming Wang, Yujie Bi, Yun Xia, Xiaohan Cheng, Jie Yang and Guoying Meng

Appl. Sci. 2022, 12(9), 4351; https://doi.org/10.3390/app12094351 - 25 Apr 2022

Cited by 1 | Viewed by 1618

Abstract

Continuous rotor dynamics remains stagnant. In this paper, aim at multi-span and multi-disc rotor-bearing system, the continuous rotor dynamic analysis method (CRDAM) is proposed. The force acting on the shaft by the rotating eccentric disc is simulated as a point force. The counterforce [...] Read more.

Continuous rotor dynamics remains stagnant. In this paper, aim at multi-span and multi-disc rotor-bearing system, the continuous rotor dynamic analysis method (CRDAM) is proposed. The force acting on the shaft by the rotating eccentric disc is simulated as a point force. The counterforce of bearing is also considered as a point force. The shaft is considered free-ended. A continuous rotor dynamic model is obtained and an analytical solution is proposed to express the unbalance response as function of the position, unbalance, support stiffness and damping. The proposed method is validated by numerical experiments in which unbalance responses obtained by it are compared with that obtained by the two classical methods the finite element method (FEM) and Ricatti method. The results indicate that the proposed method is applicable to calculating unbalance response of multi-disc and multi-span rotor. Moreover, it is closer to FEM than Ricatti and can be applied to actual high speed rotors. Among the three methods, the calculating speed of Ricatti is the fastest, CRDAM is the second fastest and FEM is the slowest. The proposed method, which solves the forward problems of the continuous rotor dynamics for the multi-disc and multi-span rotors, can provide theoretical basis for further studies on inverse problems such as identification of rotor unbalance and bearing stiffness and damping coefficients without test runs and external excitations. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

40 pages, 4359 KiB

Open AccessArticle

Continuous Rotor Dynamics of Multi-Disc and Multi-Span Rotor: A Theoretical and Numerical Investigation on the Identification of Bearing Coefficients from Unbalance Responses

by Aiming Wang, Yujie Bi, Xiaohan Cheng, Jie Yang, Guoying Meng, Yun Xia and Yu Feng

Appl. Sci. 2022, 12(9), 4251; https://doi.org/10.3390/app12094251 - 22 Apr 2022

Cited by 1 | Viewed by 1331

Abstract

Identification of bearings’ stiffness and damping coefficients, which strongly affects the dynamic characteristics of rotors, is another inverse problem of Rotor Dynamics. In this paper, aiming at multi-disc and multi-span rotors, two novel algorithms are proposed for identifying each bearing’s coefficients based on [...] Read more.

Identification of bearings’ stiffness and damping coefficients, which strongly affects the dynamic characteristics of rotors, is another inverse problem of Rotor Dynamics. In this paper, aiming at multi-disc and multi-span rotors, two novel algorithms are proposed for identifying each bearing’s coefficients based on the continuous rotor dynamic analysis method. A linear functional relationship between the main complex coefficients and the cross-coupled complex coefficients is obtained, which eliminates the coupling between the coefficients and the rotor unbalance in the forward problem. Then, Algorithm I is proposed. However, it is only suitable for rolling-bearing. To solve the problem, changing the rotating speed slightly is proposed to solve the difficulty that another set of equations cannot be developed because the slope of the proposed linear function is constant when the rotating speed is maintained at a fixed speed. Then, Algorithm II, which can be applied to both rolling-bearing and oil-journal bearing, is provided. Numerical investigations are conducted to study the two methods. It is indicated that there should be a measuring point, called an adjustment point, near each bearing, whose coefficients should be identified, to obtain high identification accuracy. Moreover, the identification accuracy of the two algorithms is strongly related to sensor resolution. When the measuring errors of all the required unbalance responses are zero or the same, the identification errors are almost equal to zero. In conclusion, the proposed algorithms provide a method for monitoring the stiffness and damping coefficients of all bearings in a multi-disc and multi-span rotor under operation conditions to predict rotor dynamic behavior for the safe and steady running of rotating machines. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

21 pages, 5534 KiB

Open AccessArticle

Suppression of Harmonic Current in Magnetic Bearing–Rotor System with Redundant Structure

by Baixin Cheng, Xin Cheng, Shao Song, Rougang Zhou and Shuai Deng

Appl. Sci. 2022, 12(9), 4126; https://doi.org/10.3390/app12094126 - 20 Apr 2022

Viewed by 1463

Abstract

The magnetic bearing–rotor system has the advantages of no mechanical friction and active vibration control. A magnetic bearing with redundant structures provides an effective method to apply fault-tolerant control to the magnetic bearing–rotor system. In this paper, in order to improve the robustness [...] Read more.

The magnetic bearing–rotor system has the advantages of no mechanical friction and active vibration control. A magnetic bearing with redundant structures provides an effective method to apply fault-tolerant control to the magnetic bearing–rotor system. In this paper, in order to improve the robustness of a rotor suspended by a magnetic bearing with redundant structures, the harmonic current suppression approach is proposed. Firstly, the generation mechanism of harmonic current in the magnetic bearing–rotor system is analyzed. Secondly, on the basis of the current distribution theory of magnetic bearing with redundant structures, the linearization model of electromagnetic force is established. Then, the eight-pole symmetrical radial magnetic bearing is taken as the research object, and the control system model with a multi-excitation disturbance source is established under the condition of no coil failure. Lastly, considering the periodicity of disturbance signals, a repetitive controller that is suitable for magnetic bearing with redundant structures is proposed in this paper, Moreover, in order to verify the effectiveness of the proposed control strategy, we inserted the repetitive controller into the original controller applied to the magnetically levitated rotor with redundant structures, and the corresponding simulation was carried out. The results demonstrate that the repetitive control method proposed in this paper can effectively suppress the harmonic current and improve the suspension accuracy of the rotor supported by the magnetic bearing with redundant structures. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

17 pages, 6004 KiB

Open AccessArticle

Third-Order Superharmonic Resonance Analysis and Control in a Nonlinear Dynamical System

by Ali Kandil, Yasser S. Hamed, Mohamed S. Mohamed, Jan Awrejcewicz and Maksymilian Bednarek

Mathematics 2022, 10(8), 1282; https://doi.org/10.3390/math10081282 - 12 Apr 2022

Cited by 3 | Viewed by 1957

Abstract

The present work discusses the dynamical analysis of the superharmonic resonance in a mass-damper-spring model controlled by a cubic-position negative-velocity feedback (CPNV) controller. Thanks to the harmonic balance technique, the approximate solution of the studied model can be extracted and then checked for [...] Read more.

The present work discusses the dynamical analysis of the superharmonic resonance in a mass-damper-spring model controlled by a cubic-position negative-velocity feedback (CPNV) controller. Thanks to the harmonic balance technique, the approximate solution of the studied model can be extracted and then checked for stability using Floquet exponents. The cubic-position control gain is adjusted in order to suppress the model’s steady oscillations. In addition, the negative-velocity control gain is adjusted in order to shrink the period of the transient oscillations. Several plots are included to relate the car’s oscillatory amplitude with the model’s different parameters pre- and post-control so that we can determine the optimum conditions for running the model safely. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

42 pages, 8448 KiB

Open AccessArticle

Continuous Rotor Dynamics of Multi-Disc and Multi-Span Rotors: A Theoretical and Numerical Investigation of the Identification of Rotor Unbalance from Unbalance Responses

by Aiming Wang, Yujie Bi, Yu Feng, Jie Yang, Xiaohan Cheng and Guoying Meng

Appl. Sci. 2022, 12(8), 3865; https://doi.org/10.3390/app12083865 - 11 Apr 2022

Cited by 4 | Viewed by 1705

Abstract

Rotor unbalance identification plays a critical role in balancing rotors. In this paper, concerned with multi-disc and multi-span rotor-bearing systems, two novel algorithms called the Single Direction Algorithm (SDA) and the Two Orthogonal Direction Algorithm (TODA) are proposed for identifying rotor unbalance from [...] Read more.

Rotor unbalance identification plays a critical role in balancing rotors. In this paper, concerned with multi-disc and multi-span rotor-bearing systems, two novel algorithms called the Single Direction Algorithm (SDA) and the Two Orthogonal Direction Algorithm (TODA) are proposed for identifying rotor unbalance from unbalance responses. A matrix method is proposed to solve the problem of the equations being non-linear transcendental, there being too many unknown variables in the equations, and rotor unbalances and bearing coefficients being coupled together. The unbalance responses at all the eccentric discs are necessary for identifying their unbalances. Numerical simulations are conducted to validate the proposed methods. Moreover, an adjustment point is found, and a proper sensor resolution is suggested to achieve high identification accuracy by means of numerical studies. In addition, the identification accuracy of SDA is better than TODA, and SDA is more practical and suitable for medium-speed and high-speed rotors. The proposed algorithms have the flexibility to incorporate any number of bearings and discs and provide a technique for monitoring rotor unbalance without test runs or external exciters. Full article

(This article belongs to the Topic Dynamical Systems: Theory and Applications)

► Show Figures

Figure 1

Topic Menu

Topic Editors

Dynamical Systems: Theory and Applications

Topic Information

Keywords

Participating Journals

Published Papers (152 papers)