Topic Editors

Prof. Dr. Jan Awrejcewicz
Faculty of Mechanical Engineering, Lodz University of Technology, 90-924 Łódź, Poland
Prof. Dr. José A. Tenreiro Machado
Department of Electrical Engineering, Institute of Engineering, Polytechnic Institute of Porto, 4249-015 Porto, Portugal
Prof. Dr. José M. Vega
School of Aerospace Engineering, Universidad Politecnica de Madrid, 28040 Madrid, Spain
Prof. Dr. Hari Mohan Srivastava
Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada
Prof. Dr. Ying-Cheng Lai
School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe 5706 , AZ, USA
Dr. Hamed Farokhi
Department of Mechanical and Construction Engineering, Northumbria University, Newcastle upon Tyne NE1 8ST, UK
Dr. Roman Starosta
Institute of Applied Mechanics, Poznan University of Technology, Poznan, Poland

Dynamical Systems: Theory and Applications

Abstract submission deadline
31 October 2022
Manuscript submission deadline
31 January 2023
Viewed by
75950

Topic Information

Dear Colleagues,

The scope of this Topic Issue (TI) has an interdisciplinary character and focuses on the dissemination of ideas between various branches of pure and applied sciences, covering a range of dynamic processes, including applied mathematics, theoretical and applied mechanics, civil engineering, electrical engineering, physics, automation and control, and bioengineering.

The core interest of this TI relies on mathematical and physical modeling, numerical/analytical study and computation, as well as experimental investigation, of dynamical systems and processes in order to understand their dynamical behavior and maximize control in order to achieve the assumed goals.

From the point of view of the theoretical aspects, the following topics are welcome:

-    Asymptotic approaches;
-    Numerical algorithms and procedures;
-    Smooth versus non-smooth dynamical systems;
-    Resonances and anti-resonances;
-    Bifurcation and chaos;
-    Stability problems;
-    Novel nonlinear phenomena;
-    Nonlinear PDEs and ODEs.

From the point of view of the applications, the following issues are covered:

-    Engineering and bioengineering;
-    Airplane and rocket industries;
-    Transport (water, air, and land);
-    Sensor modeling and fabrications;
-    Mechanics;
-    Vibrations of composite structural members;
-    Vibrations of discrete mass systems;
-    Dynamics of micro-/nano-scale systems;
-    Robotics;
-    Energy harvesting;
-    Robotics and manipulators.

Scientists and engineers are kindly incited to contribute to this Topic Issue.

Prof. Dr. Jan Awrejcewicz
Prof. Dr. José A. Tenreiro Machado
Prof. Dr. José M. Vega
Prof. Dr. Hari Mohan Srivastava
Prof. Dr. Ying-Cheng Lai
Dr. Hamed Farokhi
Dr. Roman Starosta
Topic Editors

Keywords

  • engineering and bioengineering
  • airplane and rocket industries
  • transport (water, air, and land)
  • sensor modeling and fabrications
  • mechanics
  • vibrations of composite structural members
  • vibrations of discrete mass systems
  • dynamics of micro-/nano-scale systems
  • robotics
  • energy harvesting
  • robotics and manipulators
  • asymptotic approaches
  • numerical algorithms and procedures
  • smooth versus nonsmooth dynamical systems
  • resonances and anti-resonances
  • bifurcation and chaos
  • stability problems
  • novel nonlinear phenomena
  • nonlinear PDEs and ODEs

Participating Journals

Journal Name Impact Factor CiteScore Launched Year First Decision (median) APC
Applied Sciences
applsci
2.838 3.7 2011 17.4 Days 2300 CHF Submit
Mathematics
mathematics
2.592 2.9 2013 17.8 Days 1800 CHF Submit
Vibration
vibration
- - 2018 19.3 Days 1400 CHF Submit
Symmetry
symmetry
2.940 4.3 2009 13.8 Days 1800 CHF Submit
Materials
materials
3.748 4.7 2008 15.3 Days 2300 CHF Submit

Preprints is a platform dedicated to making early versions of research outputs permanently available and citable. MDPI journals allow posting on preprint servers such as Preprints.org prior to publication. For more details about reprints, please visit https://www.preprints.org.

Published Papers (137 papers)

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Article
Adaptive Fuzzy Tracking Control of Uncertain Nonlinear Multi-Agent Systems with Unknown Control Directions and a Dead-Zone Fault
Mathematics 2022, 10(15), 2655; https://doi.org/10.3390/math10152655 - 28 Jul 2022
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)
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Article
Analysis of the Influence of a Powertrain Mounting System on a Dual-Clutch Transmission Vehicle under Typical Working Conditions
Appl. Sci. 2022, 12(15), 7439; https://doi.org/10.3390/app12157439 - 25 Jul 2022
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)
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Article
Exact Traveling Wave Solutions in a Generalized Harry Dym Type Equation
by and
Symmetry 2022, 14(7), 1480; https://doi.org/10.3390/sym14071480 - 20 Jul 2022
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)
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Article
Effect of Observation Geometry on Short-Arc Angles-Only Initial Orbit Determination
Appl. Sci. 2022, 12(14), 6966; https://doi.org/10.3390/app12146966 - 09 Jul 2022
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)
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Article
A Variable-Order Dynamic Constitutive Model for Clay Based on the Fractional Calculus
Appl. Sci. 2022, 12(13), 6416; https://doi.org/10.3390/app12136416 - 24 Jun 2022
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)
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Article
Optimization of a Non-Traditional Vibration Absorber for Vibration Suppression and Energy Harvesting
Vibration 2022, 5(3), 383-407; https://doi.org/10.3390/vibration5030022 - 22 Jun 2022
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)
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Article
Harmonic Balance Method to Analyze the Steady-State Response of a Controlled Mass-Damper-Spring Model
Symmetry 2022, 14(6), 1247; https://doi.org/10.3390/sym14061247 - 16 Jun 2022
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)
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Article
Continued Fraction Expansions of Stable Discrete-Time Systems of Difference Equations
Symmetry 2022, 14(6), 1226; https://doi.org/10.3390/sym14061226 - 13 Jun 2022
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)
Article
Efficiency Analysis of Herringbone Star Gear Train Transmission with Different Load-Sharing Conditions
Appl. Sci. 2022, 12(12), 5970; https://doi.org/10.3390/app12125970 - 11 Jun 2022
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)
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Article
Finite-Time Contractively Bounded Control of Positive Linear Systems under H Performance and Its Application to Pest Management
Mathematics 2022, 10(12), 1997; https://doi.org/10.3390/math10121997 - 09 Jun 2022
Abstract
This paper investigates the finite-time contractively bounded control issue for positive linear systems under H performance. The notion of H finite-time contractive boundedness is first extended to positive systems. Finite-time contractively bounded control is considered to ensure the H finite-time [...] Read more.
This paper investigates the finite-time contractively bounded control issue for positive linear systems under H performance. The notion of H finite-time contractive boundedness is first extended to positive systems. Finite-time contractively bounded control is considered to ensure the H 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)
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Article
On The 3D VR Simulated Rubik’s Cube Game for Smart Pads
Symmetry 2022, 14(6), 1193; https://doi.org/10.3390/sym14061193 - 09 Jun 2022
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)
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Article
Damping Optimization of Linear Vibrational Systems with a Singular Mass Matrix
Mathematics 2022, 10(11), 1854; https://doi.org/10.3390/math10111854 - 28 May 2022
Abstract
We present two novel results for small damped oscillations described by the vector differential equation Mx¨+Cx˙+Kx=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 Mx¨+Cx˙+Kx=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 ATX+XA=I, where A=A(v) is obtained from M,C(v)Rn×n, and KRn×n, which are the so-called mass, damping, and stiffness matrices, respectively, and rank(M)=n1. 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))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 ATX+XA=I, and a novel optimization process. The proposed optimization process computes the optimal damping C(v) that minimizes a function vtrace(ZX) (where Z is a chosen symmetric positive semidefinite matrix) using the approximation function g(v)=cv+av+bv, for the trace function f(v)trace(ZX(v)). Both results are illustrated with several corresponding numerical examples. Full article
(This article belongs to the Topic Dynamical Systems: Theory and Applications)
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Article
Linear Proportional-Integral-Differential-Robustified Continuous-Time Optimal Predictive Control for a Class of Nonlinear Systems
Appl. Sci. 2022, 12(11), 5446; https://doi.org/10.3390/app12115446 - 27 May 2022
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)
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Article
Performance Evaluation of Track Curvature Sensor for Curvature Estimation in a Curved Section of Railway Tracks
Appl. Sci. 2022, 12(11), 5398; https://doi.org/10.3390/app12115398 - 26 May 2022
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)
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Article
An Efficient Numerical Model to Predict the Mechanical Response of a Railway Track in the Low-Frequency Range
Vibration 2022, 5(2), 326-343; https://doi.org/10.3390/vibration5020019 - 24 May 2022
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)
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Article
Optimal H2 Moment Matching-Based Model Reduction for Linear Systems through (Non)convex Optimization
Mathematics 2022, 10(10), 1765; https://doi.org/10.3390/math10101765 - 22 May 2022
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 H2-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 H2-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 H2-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)
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Article
Control Analysis of Stochastic Lagging Discrete Ecosystems
Symmetry 2022, 14(5), 1039; https://doi.org/10.3390/sym14051039 - 19 May 2022
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)
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Article
Hyperbolicity of First Order Quasi-Linear Equations
Symmetry 2022, 14(5), 1024; https://doi.org/10.3390/sym14051024 - 17 May 2022
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)
Article
Coupling Effect Suppressed Compact Surgical Robot with 7-Axis Multi-Joint Using Wire-Driven Method
Mathematics 2022, 10(10), 1698; https://doi.org/10.3390/math10101698 - 16 May 2022
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)
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Article
Long Time Simulation Analysis of Geometry Dynamics Model under Iteration
Appl. Sci. 2022, 12(10), 4910; https://doi.org/10.3390/app12104910 - 12 May 2022
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)
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Article
Fatigue Life Assessment of Intercity Track Viaduct Based on Vehicle–Bridge Coupled System
Mathematics 2022, 10(10), 1663; https://doi.org/10.3390/math10101663 - 12 May 2022
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)
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Article
Fuzzy-Based Adaptive Dynamic Surface Control for a Type of Uncertain Nonlinear System with Unknown Actuator Faults
Mathematics 2022, 10(10), 1624; https://doi.org/10.3390/math10101624 - 10 May 2022
Cited by 1
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)
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Article
Graph Colorings and Labelings Having Multiple Restrictive Conditions in Topological Coding
Mathematics 2022, 10(9), 1592; https://doi.org/10.3390/math10091592 - 07 May 2022
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)
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Article
Evolutionary Dynamics of Division of Labor Games for Underwater Searching Tasks
Symmetry 2022, 14(5), 941; https://doi.org/10.3390/sym14050941 - 05 May 2022
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)
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Article
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
Appl. Sci. 2022, 12(9), 4351; https://doi.org/10.3390/app12094351 - 25 Apr 2022
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)
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Article
Continuous Rotor Dynamics of Multi-Disc and Multi-Span Rotor: A Theoretical and Numerical Investigation on the Identification of Bearing Coefficients from Unbalance Responses
Appl. Sci. 2022, 12(9), 4251; https://doi.org/10.3390/app12094251 - 22 Apr 2022
Cited by 1
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)
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Article
Suppression of Harmonic Current in Magnetic Bearing–Rotor System with Redundant Structure
Appl. Sci. 2022, 12(9), 4126; https://doi.org/10.3390/app12094126 - 20 Apr 2022
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)
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Article
Third-Order Superharmonic Resonance Analysis and Control in a Nonlinear Dynamical System
Mathematics 2022, 10(8), 1282; https://doi.org/10.3390/math10081282 - 12 Apr 2022
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)
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Article
Continuous Rotor Dynamics of Multi-Disc and Multi-Span Rotors: A Theoretical and Numerical Investigation of the Identification of Rotor Unbalance from Unbalance Responses
Appl. Sci. 2022, 12(8), 3865; https://doi.org/10.3390/app12083865 - 11 Apr 2022
Cited by 2
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)
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Article
Controllability and Hyers–Ulam Stability of Differential Systems with Pure Delay
Mathematics 2022, 10(8), 1248; https://doi.org/10.3390/math10081248 - 11 Apr 2022
Cited by 2
Abstract
Dynamic systems of linear and nonlinear differential equations with pure delay are considered in this study. As an application, the representation of solutions of these systems with the help of their delayed Mittag–Leffler matrix functions is used to obtain the controllability and Hyers–Ulam [...] Read more.
Dynamic systems of linear and nonlinear differential equations with pure delay are considered in this study. As an application, the representation of solutions of these systems with the help of their delayed Mittag–Leffler matrix functions is used to obtain the controllability and Hyers–Ulam stability results. By introducing a delay Gramian matrix, we establish some sufficient and necessary conditions for the controllability of linear delay differential systems. In addition, by applying Krasnoselskii’s fixed point theorem, we establish some sufficient conditions of controllability and Hyers–Ulam stability of nonlinear delay differential systems. Our results improve, extend, and complement some existing ones. Finally, two examples are given to illustrate the main results. Full article
(This article belongs to the Topic Dynamical Systems: Theory and Applications)
Article
Numerical Assessment of Dipole Interaction with the Single-Phase Nanofluid Flow in an Enclosure: A Pseudo-Transient Approach
Materials 2022, 15(8), 2761; https://doi.org/10.3390/ma15082761 - 09 Apr 2022
Abstract
Nanofluids substantially enhance the physical and thermal characteristics of the base or conducting fluids specifically when interacting with the magnetic field. Several engineering processes like geothermal energy extraction, metal casting, nuclear reactor coolers, nuclear fusion, magnetohydrodynamics flow meters, petrochemicals, and pumps incorporate magnetic [...] Read more.
Nanofluids substantially enhance the physical and thermal characteristics of the base or conducting fluids specifically when interacting with the magnetic field. Several engineering processes like geothermal energy extraction, metal casting, nuclear reactor coolers, nuclear fusion, magnetohydrodynamics flow meters, petrochemicals, and pumps incorporate magnetic field interaction with the nanofluids. On the other hand, an enhancement in heat transfer due to nanofluids is essentially required in various thermal systems. The goal of this study is to figure out that how much a magnetic field affects nanofluid flow in an enclosure because of a dipole. The nanofluid is characterized using a single-phase model, and the governing partial differential equations are computed numerically. A Pseudo time based numerical algorithm is developed to numerically solve the problem. It can be deduced that the Reynolds number and the magnetic parameter have a low effect on the Nusselt number and skin friction. The Nusselt number rises near the dipole location because of an increase in the magnetic parameter Mn and the Reynolds number Re. The imposed magnetic field alters the region of high temperature nearby the dipole, while newly generated vortices rotate in alternate directions. Furthermore, nanoparticle volume fraction causes a slight change in the skin friction while it marginally reduces the Nusselt number. Full article
(This article belongs to the Topic Dynamical Systems: Theory and Applications)
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Article
Adaptive, Observer-Based Synchronization of Different Chaotic Systems
Appl. Sci. 2022, 12(7), 3394; https://doi.org/10.3390/app12073394 - 27 Mar 2022
Abstract
In this study, the problem of master–slave synchronization of two different chaotic systems is considered and solved under a novel set of assumptions. The mathematical model of each of them contains unknown, constant parameters. Only a single output of the master system is [...] Read more.
In this study, the problem of master–slave synchronization of two different chaotic systems is considered and solved under a novel set of assumptions. The mathematical model of each of them contains unknown, constant parameters. Only a single output of the master system is available, and only a single input of the slave system is a control input. The proposed, novel approach is based on the active cooperation of the adaptive observer of the master system and adaptive controller of the slave. The tuning function technique is included in the observer–controller design to avoid overparameterization. Complexity explosion and unacceptable increases in adaptive parameters are prevented by proper adaptive techniques application. Due to the selected observer type, the derivation is restricted to the defined class of master systems—output-nonlinear parametric (ONP) systems. Linear transformation of several popular chaotic systems (e.g., Arneodo, Arneodo–Coullet, Genesio–Tesi, Lur’e) into the ONP form is discussed. The stability of the whole, closed-loop system is derived using Lyapunov techniques and examples of implementation (synchronization of Arneodo and 3D jerk systems) are provided. Full article
(This article belongs to the Topic Dynamical Systems: Theory and Applications)
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Article
Robust Nonlinear Non-Referenced Inertial Frame Multi-Stage PID Controller for Symmetrical Structured UAV
Symmetry 2022, 14(4), 689; https://doi.org/10.3390/sym14040689 - 26 Mar 2022
Abstract
The design and implementation of a multi-stage PID (MS-PID) controller for non-inertial referenced UAVs are highly complex. Symmetrical multirotor UAVs are unstable systems, and it is thought that the kinematics of the symmetrical UAV rotor, such as the quadrotor and hexacopter resembles the [...] Read more.
The design and implementation of a multi-stage PID (MS-PID) controller for non-inertial referenced UAVs are highly complex. Symmetrical multirotor UAVs are unstable systems, and it is thought that the kinematics of the symmetrical UAV rotor, such as the quadrotor and hexacopter resembles the kinematics of an inverted pendulum. Several researchers have investigated the structure and design of PID controllers for high-order systems during the last decade. The designs were always concerned with the enhanced response, robustness, model reduction and performance of PID controllers. An accurate tuning process of such a controller depends on the engineer’s experience level. This is due to the number of variables and hyperparameters tuned during the process. An adaptive genetic algorithm (AGA) is utilized to optimize the MS-PID controllers for controlling the quadrotor in this study. The proposed method optimizes the offline-planned approach, providing several possibilities for adapting the controllers with various paths and or varying weather conditions. The MS-PID parameters are optimized in parallel, as every PID controller affects the other controller’s behavior and performance. Furthermore, the proposed AGA generates new chromosomes for “new solutions” by randomly developing new solutions close to the previous best values, which will prevent any local minima solution. This study intends to investigate the design and development of a highly tuned robust multi-stage PID controller for a symmetrical multirotor UAV. The work presents a model for a non-referenced inertial frame multirotor UAV (quadcopter). Once the model is defined, a robust multi-stage PID controller for the non-inertial referenced frame symmetrical multirotor UAV is designed, tuned, and tested. A genetic algorithm (GA) will be used to tune the MS-PID controller. Finally, the performance comparison between the proposed and conventional methods is presented. The results show that the proposed method provides stability improvement, better transient response, and power consumption. Full article
(This article belongs to the Topic Dynamical Systems: Theory and Applications)
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Article
1/3 Order Subharmonic Resonance Control of a Mass-Damper-Spring Model via Cubic-Position Negative-Velocity Feedback
Symmetry 2022, 14(4), 685; https://doi.org/10.3390/sym14040685 - 25 Mar 2022
Cited by 1
Abstract
A cubic-position negative-velocity (CPNV) feedback controller is proposed in this research in order to suppress the nontrivial oscillations of the 1/3 order subharmonic resonance of a mass-damper-spring model. Based on the Krylov–Bogoliubov (KB) averaging method, the model’s equation of motion is [...] Read more.
A cubic-position negative-velocity (CPNV) feedback controller is proposed in this research in order to suppress the nontrivial oscillations of the 1/3 order subharmonic resonance of a mass-damper-spring model. Based on the Krylov–Bogoliubov (KB) averaging method, the model’s equation of motion is approximately solved and tested for stability. The nontrivial solutions region is plotted to determine where these solutions occur and try to quench them. The controller parameters can play crucial roles in eliminating such regions, keeping only the trivial solutions, and improving the transient response of the car’s oscillations. Different response curves and relations are included in this study to provide the reader a wide overview of the control process. Full article
(This article belongs to the Topic Dynamical Systems: Theory and Applications)
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Article
Symmetric Properties of Routh–Hurwitz and Schur–Cohn Stability Criteria
Symmetry 2022, 14(3), 603; https://doi.org/10.3390/sym14030603 - 18 Mar 2022
Cited by 1
Abstract
It is often noticed in the literature that some key results on the stability of discrete-time systems of difference equations are obtained from their corresponding results on the stability of continuous-time systems of differential equations using suitable conformal mappings or bilinear transformations. Such [...] Read more.
It is often noticed in the literature that some key results on the stability of discrete-time systems of difference equations are obtained from their corresponding results on the stability of continuous-time systems of differential equations using suitable conformal mappings or bilinear transformations. Such observations lead to the search for a unified approach to the study of root distribution for real and complex polynomials, with respect to the left-half plane for continuous-time systems (Routh–Hurwitz stability) and with respect to the unit disc for discrete-time systems (Schur–Cohn stability). This paper is a further contribution toward this objective. We present, in a systematic way, the similarities, and yet, the differences between these two types of stability, and we highlight the symmetry that exists between them. We also illustrate how results on the stability of continuous-time systems are conveyed to the stability of discrete-time systems through the proposed techniques. It should be mentioned that the results on Schur–Cohn stability are known to be harder to obtain than Routh–Hurwitz stability ones, giving more credibility to the proposed approach. Full article
(This article belongs to the Topic Dynamical Systems: Theory and Applications)
Article
Runtime Software Architecture-Based Reliability Prediction for Self-Adaptive Systems
Symmetry 2022, 14(3), 589; https://doi.org/10.3390/sym14030589 - 16 Mar 2022
Abstract
Modern software systems need to autonomously adapt their behavior at runtime in order to maintain their utility in response to continuous environmental changes. Most studies on models at runtime focus on providing suitable techniques to manage the complexity of software at runtime but [...] Read more.
Modern software systems need to autonomously adapt their behavior at runtime in order to maintain their utility in response to continuous environmental changes. Most studies on models at runtime focus on providing suitable techniques to manage the complexity of software at runtime but neglect reliability caused by adaptation activities. Therefore, adaptive behaviors may lead to a decrease in reliability, which may result in severe financial loss or life damage. Runtime software architecture (RSA) is an abstract of a running system, which describes the elements of the current system, the states of these elements and the relation between the elements and their states at runtime. The main difference between RSA and software architecture at design time (DSA) is that RSA has a causal connection with the running system, whereas DSA does not. However, RSA and DSA have both symmetry and asymmetry in software architecture. To ensure that architecture-centric software can provide reliable services after adaptation adjustment, a method is proposed to analyze the impact of changes caused by adaptation strategy on the overall software reliability, which will be predicted at the runtime architecture model layer. Based on a Java platform, through non-intrusive monitoring, an RSA behavioral model is obtained followed by runtime reliability analysis model. Following this, reliability prediction results are obtained through a discrete-time Markov chain (DTMC). Finally, an experiment is conducted to verify the feasibility of the proposed method. Full article
(This article belongs to the Topic Dynamical Systems: Theory and Applications)
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Article
Event-Triggered Cooperative Predictive Control for Networked Multi-Agent Systems with Random Delays and Packet Dropouts
Symmetry 2022, 14(3), 541; https://doi.org/10.3390/sym14030541 - 07 Mar 2022
Abstract
This paper addresses the cooperative output tracking control problem for a class of leader-following linear heterogeneous networked multi-agent systems subject to random network delays and packet dropouts in the feedback and forward channels of each agent. A state observer is established at the [...] Read more.
This paper addresses the cooperative output tracking control problem for a class of leader-following linear heterogeneous networked multi-agent systems subject to random network delays and packet dropouts in the feedback and forward channels of each agent. A state observer is established at the plant side of each agent, and an event-triggering transmission mechanism is introduced to decide which state estimate is transmitted to the corresponding controller so as to save the network resources of the feedback channel. To further compensate for the negative effects of those random communication constraints and the event trigger, a cooperative predictive control scheme with proportional and integral actions is proposed. Then, a necessary and sufficient condition is derived for the stability of the resulting closed-loop system. Finally, simulation results are given to show the effectiveness of the proposed scheme. Full article
(This article belongs to the Topic Dynamical Systems: Theory and Applications)
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Article
Finite-Time Synchronization Analysis for BAM Neural Networks with Time-Varying Delays by Applying the Maximum-Value Approach with New Inequalities
Mathematics 2022, 10(5), 835; https://doi.org/10.3390/math10050835 - 06 Mar 2022
Cited by 2
Abstract
In this paper, we consider the finite-time synchronization for drive-response BAM neural networks with time-varying delays. Instead of using the finite-time stability theorem and integral inequality method, by using the maximum-value method, two new criteria are obtained to ensure the finite-time synchronization for [...] Read more.
In this paper, we consider the finite-time synchronization for drive-response BAM neural networks with time-varying delays. Instead of using the finite-time stability theorem and integral inequality method, by using the maximum-value method, two new criteria are obtained to ensure the finite-time synchronization for the considered drive-response systems. The inequalities in our paper, applied to obtaining the maximum-valued and designing the novel controllers, are different from those in existing papers. Full article
(This article belongs to the Topic Dynamical Systems: Theory and Applications)
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Article
Infinite–Dimensional Bifurcations in Spatially Distributed Delay Logistic Equation
Mathematics 2022, 10(5), 775; https://doi.org/10.3390/math10050775 - 28 Feb 2022
Abstract
This paper investigates the questions about the local dynamics in the neighborhood of the equilibrium state for the spatially distributed delay logistic equation with diffusion. The critical cases in the stability problem are singled out. The equations for their invariant manifolds that determine [...] Read more.
This paper investigates the questions about the local dynamics in the neighborhood of the equilibrium state for the spatially distributed delay logistic equation with diffusion. The critical cases in the stability problem are singled out. The equations for their invariant manifolds that determine the structure of the solutions in the equilibrium state neighborhood are constructed. The dominant bulk of this paper is devoted to the consideration of the most interesting and important cases of either the translation (advection) coefficient is large enough or the diffusion coefficient is small enough. Both of this cases convert the original problem to a singularly perturbed one. It is shown that under these conditions the critical cases are infinite–dimensional in the problems of the equilibrium state stability for the singularly perturbed problems. This means that infinitely many roots of the characteristic equations of the corresponding linearized boundary value problems tend to the imaginary axis as the small parameter tends to zero. Thus, we are talking about infinite–dimensional bifurcations. Standard approaches to the study of the local dynamics based on the application of the invariant integral manifolds methods and normal forms methods are not applicable. Therefore, special methods of infinite–dimensional normalization have been developed which allow one to construct special nonlinear boundary value problems called quasinormal forms. Their nonlocal dynamics determine the behavior of the initial boundary value problem solutions in the neighborhood of the equilibrium state. The bifurcation features arising in the case of different boundary conditions are illustrated. Full article
(This article belongs to the Topic Dynamical Systems: Theory and Applications)
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Article
Adaptive Sliding Mode Attitude Control of Quadrotor UAVs Based on the Delta Operator Framework
Symmetry 2022, 14(3), 498; https://doi.org/10.3390/sym14030498 - 28 Feb 2022
Cited by 2
Abstract
In this paper, a novel adaptive sliding-mode control algorithm is proposed for the attitude control of quadrotor unmanned aerial vehicles (UAVs) under the delta operator framework. First, the delta operator technique is used to discretize the attitude control systems of a quadrotor UAV. [...] Read more.
In this paper, a novel adaptive sliding-mode control algorithm is proposed for the attitude control of quadrotor unmanned aerial vehicles (UAVs) under the delta operator framework. First, the delta operator technique is used to discretize the attitude control systems of a quadrotor UAV. Then, based on the linear matrix inequality technique, a linear sliding surface is designed to ensure the asymptotical stability of the quadrotor UAV attitude control system during the sliding motion process. Second, by the estimated external disturbance using a radical basis function (RBF) neural network, an adaptive sliding-mode attitude controller is designed such that the states of the quadrotor UAV attitude systems can be driven towards the desired sliding surface, and thus the attitude control objective of the qudarotor UAV is achieved. Compared with the traditional adaptive sliding-mode control algorithm, the proposed adaptive sliding-mode control algorithm can effectively realize the attitude control of a quadrotor UAV subject to strong disturbances and couplings. Finally, comparisons of the simulation results verify the effectiveness and superiority of the control algorithm proposed in this paper. Full article
(This article belongs to the Topic Dynamical Systems: Theory and Applications)
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Article
Hydrocode Investigations of Terminal Astroballistics Problems during the Hypothetical Future Planetary Defense System’s Space Mission
Materials 2022, 15(5), 1752; https://doi.org/10.3390/ma15051752 - 25 Feb 2022
Abstract
The article is devoted to the preliminary concept of the Future Planetary Defense System (FPDS) emphasizing astroballistics. This paper is intended to support international efforts to improve the planetary security of Earth. The work covers three areas of knowledge: astronautics, astrodynamics, and astroballistics. [...] Read more.
The article is devoted to the preliminary concept of the Future Planetary Defense System (FPDS) emphasizing astroballistics. This paper is intended to support international efforts to improve the planetary security of Earth. The work covers three areas of knowledge: astronautics, astrodynamics, and astroballistics. The most important part of the presented article is dynamic, contact combat modeling against small, deformable celestial bodies. For these purposes, the original, proprietary hydrocode of the free particle method (HEFPM-G) with gravity was used. The main aim of combat is to redirect potentially hazardous objects (PHOs) to orbits safe for Earth or destroy them. This concept’s first task is to find, prepare, and use dynamic three-dimensional models of the motion of celestial bodies and spacecraft or human-crewed spaceships in the solar system’s relativistic frame. The second task is to prepare the FPDS’ architecture and computer simulation space missions’ initial concepts in the internal part of the solar system. The third and main task covers simulating, using hydrocodes, and selected methods of fighting 100 m diameter rock material asteroids. Full article
(This article belongs to the Topic Dynamical Systems: Theory and Applications)
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Article
A Quasi-3D Refined Theory for the Vibration of Functionally Graded Plates Resting on Visco-Winkler-Pasternak Foundations
Mathematics 2022, 10(5), 716; https://doi.org/10.3390/math10050716 - 24 Feb 2022
Cited by 2
Abstract
This article establishes the vibrational behavior of functionally graded plates embedded in a viscoelastic medium. The quasi-3D elasticity equations are used for this purpose. The three-parameter Visco-Winkler-Pasternak model is employed to give the interaction between the viscoelastic foundation and the presented plate. Hamilton’s [...] Read more.
This article establishes the vibrational behavior of functionally graded plates embedded in a viscoelastic medium. The quasi-3D elasticity equations are used for this purpose. The three-parameter Visco-Winkler-Pasternak model is employed to give the interaction between the viscoelastic foundation and the presented plate. Hamilton’s principle is applied to derive the governing dynamic equations. Many validation examples are presented. Additional benchmark results are tabulated for future comparisons. The effects of various parameters like geometrical, material properties, and viscoelastic foundations on the vibrational frequencies of homogeneous and functionally graded plates are investigated. The frequencies increase as all parameters increase except the functionally graded power-law index for which its increase causes a decrease in the frequency value. Full article
(This article belongs to the Topic Dynamical Systems: Theory and Applications)
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Article
(αF,αF¯)-Information Fusion Generated by Information Segmentation and Its Intelligent Retrieval
Mathematics 2022, 10(5), 713; https://doi.org/10.3390/math10050713 - 24 Feb 2022
Abstract
Making use of the mathematical model with dynamic features and attribute disjunctive characteristics, the new concepts of αF-information segmentation, αF¯-information segmentation, (αF,αF¯)-information segmentation and their attribute characteristics are given, and [...] Read more.
Making use of the mathematical model with dynamic features and attribute disjunctive characteristics, the new concepts of αF-information segmentation, αF¯-information segmentation, (αF,αF¯)-information segmentation and their attribute characteristics are given, and the intelligent acquisition of matrix reasoning and information segmentation is given, as well as the information segmentation theorem. Moreover, the equivalence between information segmentation and information fusion is discussed, and the information fusion intelligent acquisition intelligent retrieval algorithm is given. Based on these theoretical results, the intelligent information fusion retrieval algorithm and its simple application in health big data are presented. In conclusion, the results presented in this paper are entirely based on new ideas. Full article
(This article belongs to the Topic Dynamical Systems: Theory and Applications)
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Article
Dynamic Analysis of Quasi-Zero Stiffness Pneumatic Vibration Isolator
Appl. Sci. 2022, 12(5), 2378; https://doi.org/10.3390/app12052378 - 24 Feb 2022
Abstract
This paper focuses on analyzing the dynamic response of an innovated quasi-zero stiffness pneumatic vibration isolator (QZSPVI) using two mechanisms, including wedge and semicircle cam. Different from other studies relating quasi-zero stiffness isolation system, the pneumatic cylinder in this paper works as an [...] Read more.
This paper focuses on analyzing the dynamic response of an innovated quasi-zero stiffness pneumatic vibration isolator (QZSPVI) using two mechanisms, including wedge and semicircle cam. Different from other studies relating quasi-zero stiffness isolation system, the pneumatic cylinder in this paper works as an air spring in order to easily adjust the dynamic stiffness of the proposed system according to the change of the isolated load through regulating the pressure. Firstly, the dynamic stiffness of the QZSPVI will be analyzed. Then, the condition for which the minimum dynamic stiffness is quasi-zero around the equilibrium position is also determined. The fundamental resonance response of the QZSPVI subjected to the externally harmonic force is analyzed through multi-scale method and the numerical simulations are verified. Secondly, due to exiting relative sliding frictional phenomenon between the cylinder and piston, instead of an experiment, another key content of this work is to identify the friction force model of the cylinder through virtual prototyping model. From this identified result, the complex dynamic response of the QZSPVI and coexistence of multiple solutions will be discovered by realizing the direct integration of the original dynamic equation through using the 5th-order Runge–Kutta algorithm. The analysis and simulation results clearly show the advantages of the proposed model against the equivalent pneumatic vibration isolator (EPVI), which only employs the wedge mechanism. This research will offer a useful insight into design and QZSPVI in practice. Full article
(This article belongs to the Topic Dynamical Systems: Theory and Applications)
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