Advances and Trends in Mathematical Modelling, Control and Identification of Vibrating Systems

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

Deadline for manuscript submissions: closed (31 December 2021) | Viewed by 13197

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Departamento de Energía, Universidad Autónoma Metropolitana, Unidad Azcapotzalco, Mexico City 02200, Mexico
Interests: vibration control; system identification; rotating machinery; mechatronics; automatic control of energy conversion systems
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Faculty of Engineering, Universidad Panamericana Sede Guadalajara, Zapopan CP 45010, Mexico
Interests: power electronics; DC-DC converters; optimization of power electronics systems; modelling and control of power converters
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Department of Electrical Engineering (Guadalajara), Center for Research and Advanced Studies of the National Polytechnic Institute, Mexico City CP 45019, Mexico
Interests: analysis and control of electric power systems; applications of power electronics in electrical networks; optimization
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Department of Aviation Academy, Centre for Applied Research on Education, Amsterdam University of Applied Sciences, 1097 DZ Amsterdam, Netherlands
Interests: mathematical optimization; data analysis; machine learning; aviation and airport operations

Special Issue Information

Dear Colleagues,

It is well known that vibrations can be found in many dynamic engineering systems. Mathematics plays a significant role in the analysis, design, and control of vibrating systems. This Special Issue aims at introducing novel results on mathematical modelling, system identification, damage detection and control of vibrations for a wide range of applications of mechanical, electric, electronic, and civil engineering systems. In this context, important advances on both theoretical and experimental studies are welcome. Potential topics include but are not limited to mathematical modelling, vibration control, system identification, vehicle suspensions, dynamic vibration absorbers, rotordynamics, modern energy conversion systems, modal analysis, engineering structures, finite element analysis, numerical methods, and other engineering applications and theoretical developments in which the presence of oscillations constitutes a relevant issue.

Prof. Dr. Francisco Beltran-Carbajal
Dr. Julio Cesar Rosas-Caro
Dr. Juan M Ramirez
Dr. Roberto Salvador Félix Patrón
Guest Editors

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Keywords

  • mathematical modelling
  • vibration control
  • system identification
  • engineering structures
  • renewable energy conversion systems
  • rotordynamics
  • vibration absorbers

Published Papers (6 papers)

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Research

21 pages, 4238 KiB  
Article
An Algebraic Approach for Identification of Rotordynamic Parameters in Bearings with Linearized Force Coefficients
by José Gabriel Mendoza-Larios, Eduardo Barredo, Manuel Arias-Montiel, Luis Alberto Baltazar-Tadeo, Saulo Jesús Landa-Damas, Ricardo Tapia-Herrera and Jorge Colín-Ocampo
Mathematics 2021, 9(21), 2747; https://doi.org/10.3390/math9212747 - 29 Oct 2021
Cited by 3 | Viewed by 1550
Abstract
In this work, a novel methodology for the identification of stiffness and damping rotordynamic coefficients in a rotor-bearing system is proposed. The mathematical model for the identification process is based on the algebraic identification technique applied to a finite element (FE) model of [...] Read more.
In this work, a novel methodology for the identification of stiffness and damping rotordynamic coefficients in a rotor-bearing system is proposed. The mathematical model for the identification process is based on the algebraic identification technique applied to a finite element (FE) model of a rotor-bearing system with multiple degree-of-freedom (DOF). This model considers the effects of rotational inertia, gyroscopic moments, shear deformations, external damping and linear forces attributable to stiffness and damping parameters of the supports. The proposed identifier only requires the system’s vibration response as input data. The performance of the proposed identifier is evaluated and analyzed for both schemes, constant and variable rotational speed of the rotor-bearing system, and numerical results are obtained. In the presented results, it can be observed that the proposed identifier accurately determines the stiffness and damping parameters of the bearings in less than 0.06 s. Moreover, the identification procedure rapidly converges to the estimated values in both tested conditions, constant and variable rotational speed. Full article
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17 pages, 1597 KiB  
Article
Active Suspension Control Using an MPC-LQR-LPV Controller with Attraction Sets and Quadratic Stability Conditions
by Daniel Rodriguez-Guevara, Antonio Favela-Contreras, Francisco Beltran-Carbajal, David Sotelo and Carlos Sotelo
Mathematics 2021, 9(20), 2533; https://doi.org/10.3390/math9202533 - 09 Oct 2021
Cited by 18 | Viewed by 3040
Abstract
The control of an automotive suspension system by means of a hydraulic actuator is a complex nonlinear control problem. In this work, a linear parameter varying (LPV) model is proposed to reduce the complexity of the system while preserving the nonlinear behavior. In [...] Read more.
The control of an automotive suspension system by means of a hydraulic actuator is a complex nonlinear control problem. In this work, a linear parameter varying (LPV) model is proposed to reduce the complexity of the system while preserving the nonlinear behavior. In terms of control, a dual controller consisting of a model predictive control (MPC) and a Linear Quadratic Regulator (LQR) is implemented. To ensure stability, quadratic stability conditions are imposed in terms of Linear Matrix Inequalities (LMI). Simulation results for quarter-car model over several disturbances are tested in both frequency and time domain to show the effectiveness of the proposed algorithm. Full article
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28 pages, 1825 KiB  
Article
Adaptive Robust Motion Control of Quadrotor Systems Using Artificial Neural Networks and Particle Swarm Optimization
by Hugo Yañez-Badillo, Francisco Beltran-Carbajal, Ruben Tapia-Olvera, Antonio Favela-Contreras, Carlos Sotelo and David Sotelo
Mathematics 2021, 9(19), 2367; https://doi.org/10.3390/math9192367 - 24 Sep 2021
Cited by 16 | Viewed by 2078
Abstract
Most of the mechanical dynamic systems are subjected to parametric uncertainty, unmodeled dynamics, and undesired external vibrating disturbances while are motion controlled. In this regard, new adaptive and robust, advanced control theories have been developed to efficiently regulate the motion trajectories of these [...] Read more.
Most of the mechanical dynamic systems are subjected to parametric uncertainty, unmodeled dynamics, and undesired external vibrating disturbances while are motion controlled. In this regard, new adaptive and robust, advanced control theories have been developed to efficiently regulate the motion trajectories of these dynamic systems while dealing with several kinds of variable disturbances. In this work, a novel adaptive robust neural control design approach for efficient motion trajectory tracking control tasks for a considerably disturbed non-linear under-actuated quadrotor system is introduced. Self-adaptive disturbance signal modeling based on Taylor-series expansions to handle dynamic uncertainty is adopted. Dynamic compensators of planned motion tracking errors are then used for designing a baseline controller with adaptive capabilities provided by three layers B-spline artificial neural networks (Bs-ANN). In the presented adaptive robust control scheme, measurements of position signals are only required. Moreover, real-time accurate estimation of time-varying disturbances and time derivatives of error signals are unnecessary. Integral reconstructors of velocity error signals are properly integrated in the output error signal feedback control scheme. In addition, the appropriate combination of several mathematical tools, such as particle swarm optimization (PSO), Bézier polynomials, artificial neural networks, and Taylor-series expansions, are advantageously exploited in the proposed control design perspective. In this fashion, the present contribution introduces a new adaptive desired motion tracking control solution based on B-spline neural networks, along with dynamic tracking error compensators for quadrotor non-linear systems. Several numeric experiments were performed to assess and highlight the effectiveness of the adaptive robust motion tracking control for a quadrotor unmanned aerial vehicle while subjected to undesired vibrating disturbances. Experiments include important scenarios that commonly face the quadrotors as path and trajectory tracking, take-off and landing, variations of the quadrotor nominal mass and basic navigation. Obtained results evidence a satisfactory quadrotor motion control while acceptable attenuation levels of vibrating disturbances are exhibited. Full article
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21 pages, 1355 KiB  
Article
Power Grid Dynamic Performance Enhancement via STATCOM Data-Driven Control
by David Rivera, Daniel Guillen, Jonathan C. Mayo-Maldonado, Jesus E. Valdez-Resendiz and Gerardo Escobar
Mathematics 2021, 9(19), 2361; https://doi.org/10.3390/math9192361 - 23 Sep 2021
Cited by 3 | Viewed by 2076
Abstract
This work proposes a data-driven approach to controlling the alternating current (AC) voltage via a static synchronous compensator (STATCOM). This device offers a fast dynamic response injecting reactive power to compensate the voltage profile, not only during load variations but also depending on [...] Read more.
This work proposes a data-driven approach to controlling the alternating current (AC) voltage via a static synchronous compensator (STATCOM). This device offers a fast dynamic response injecting reactive power to compensate the voltage profile, not only during load variations but also depending on the operating point established by the grid. The proposed control scheme is designed to improve the dynamic grid performance according to the defined operating point into the grid. The mathematical fundamentals of the proposed control strategy are described according to a (model-free) data-driven-based controller. The robustness of the proposed scheme is proven with several tests carried out using Matlab/Simulink software. The analysis is performed with the well-known test power system of two areas, demonstrating that the proposed controller can enhance the dynamic performance under transient scenarios. As the main strength of the present work with respect to the current state-of-the-art, we highlight the fact that no prior knowledge of the system is required for the controller implementation, that is, a model or a system representation. The synthesis of the controller is obtained in a pure numerical way from data, while it can simultaneously ensure stability in a rigorous way, by satisfying Lyapunov conditions. Full article
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12 pages, 920 KiB  
Article
A Novel Exact Plate Theory for Bending Vibrations Based on the Partial Differential Operator Theory
by Chuanping Zhou, Maofa Wang, Xiao Han, Huanhuan Xue, Jing Ni and Weihua Zhou
Mathematics 2021, 9(16), 1920; https://doi.org/10.3390/math9161920 - 12 Aug 2021
Viewed by 1500
Abstract
Thick wall structures are usually applied at a highly reduced frequency. It is crucial to study the refined dynamic modeling of a thick plate, as it is directly related to the dynamic mechanical characteristics of an engineering structure or device, elastic wave scattering [...] Read more.
Thick wall structures are usually applied at a highly reduced frequency. It is crucial to study the refined dynamic modeling of a thick plate, as it is directly related to the dynamic mechanical characteristics of an engineering structure or device, elastic wave scattering and dynamic stress concentration, and motion stability and dynamic control of a distributed parameter system. In this paper, based on the partial differential operator theory, an exact elasto-dynamics theory without assumptions for bending vibrations is presented by using the formal solution proposed by Boussinesq–Galerkin, and its dynamic equations are obtained under appropriate gauge conditions. The exact plate theory is then compared with other theories of plates. Since the derivation of the dynamic equation is conducted without any prior assumption, the proposed dynamic equation of plates is more exact and can be applied to a wider frequency range and greater thickness. Full article
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18 pages, 1983 KiB  
Article
A Novel Methodology for Adaptive Coordination of Multiple Controllers in Electrical Grids
by Ruben Tapia-Olvera, Francisco Beltran-Carbajal, Antonio Valderrabano-Gonzalez and Omar Aguilar-Mejia
Mathematics 2021, 9(13), 1474; https://doi.org/10.3390/math9131474 - 23 Jun 2021
Cited by 1 | Viewed by 1656
Abstract
This proposal is aimed to overcome the problem that arises when diverse regulation devices and controlling strategies are involved in electric power systems regulation design. When new devices are included in electric power system after the topology and regulation goals were defined, a [...] Read more.
This proposal is aimed to overcome the problem that arises when diverse regulation devices and controlling strategies are involved in electric power systems regulation design. When new devices are included in electric power system after the topology and regulation goals were defined, a new design stage is generally needed to obtain the desired outputs. Moreover, if the initial design is based on a linearized model around an equilibrium point, the new conditions might degrade the whole performance of the system. Our proposal demonstrates that the power system performance can be guaranteed with one design stage when an adequate adaptive scheme is updating some critic controllers’ gains. For large-scale power systems, this feature is illustrated with the use of time domain simulations, showing the dynamic behavior of the significant variables. The transient response is enhanced in terms of maximum overshoot and settling time. This is demonstrated using the deviation between the behavior of some important variables with StatCom, but without or with PSS. A B-Spline neural networks algorithm is used to define the best controllers’ gains to efficiently attenuate low frequency oscillations when a short circuit event is presented. This strategy avoids the parameters and power system model dependency; only a dataset of typical variable measurements is required to achieve the expected behavior. The inclusion of PSS and StatCom with positive interaction, enhances the dynamic performance of the system while illustrating the ability of the strategy in adding different controllers in only one design stage. Full article
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