Advanced Mathematics and Computational Applications in Control Systems Engineering

A special issue of Mathematical and Computational Applications (ISSN 2297-8747). This special issue belongs to the section "Engineering".

Deadline for manuscript submissions: closed (31 July 2020) | Viewed by 33127

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Special Issue Editors


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Tecnológico Nacional de México / Instituto Tecnológico de Tuxtla Gutiérrez, TURIX-DYNAMICS Diagnosis and Control Group, Carretera Panamericana, Km 1080, Tuxtla Gutierrez 29050, Mexico
Interests: control applications; optimization; LMIs; Takagi–Sugeno; fault diagnosis
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Guest Editor
Tecnológico Nacional de México / Instituto Tecnológico de Hermosillo, Ave. Tecnológico y Periférico Poniente SN, Hermosillo 83170, Mexico
Interests: predictive control; optimization; LPV systems; fault detection and isolation
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Control system engineering is a multidisciplinary discipline that applies automatic control theory to design systems with desired behaviors in control environments. Automatic control theory has played a vital role in the advancement of engineering and science. It has become an important and integral part of modern industrial and manufacturing processes. Today, the requirements for control precision have become higher, and real systems have become more complex, including higher order, discrete, hybrid, time-delayed linear, nonlinear systems, and systems without a mathematical model and uncertainties.
In control engineering, in parallel to all other engineering disciplines, the impact of advanced mathematical and computational methods is rapidly increasing. Advanced mathematical methods are needed because real-world control systems need to comply with several conditions related to product quality and safety constraints that have to be taken into account in problem formulation. Conversely, the increment in mathematical complexity has an impact on the computational aspects related with numerical simulation and practical implementation of the algorithms, where a balance must also be maintained between implementation costs and the performance of the control system.
The present Special Issue aims to present the recent advances in the development and application of advanced mathematics and computational applications in control system engineering. In addition to original research papers, review papers on the state-of-the-art and future perspectives are invited.

Potential topics include (but are not limited to):

  • Linear and nonlinear systems;
  • Complex systems;
  • Observer design;
  • Control systems;
  • Fuzzy logic control systems;
  • Neuronal network control systems;
  • System identification;
  • Takagi–Sugeno systems;
  • LPV systems;
  • Fault detection and isolation;
  • Fault-tolerant control.

Dr. Francisco Ronay López-Estrada
Prof. Dr. Guillermo Valencia-Palomo
Guest Editors

Manuscript Submission Information

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

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Keywords

  • control systems
  • control applications
  • nonlinear control
  • robust control
  • real-time control implementations
  • data-based control systems
  • data-driven control systems

Published Papers (10 papers)

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Editorial

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2 pages, 169 KiB  
Editorial
Advanced Mathematics and Computational Applications in Control Systems Engineering
by Francisco-Ronay López-Estrada and Guillermo Valencia-Palomo
Math. Comput. Appl. 2021, 26(1), 20; https://doi.org/10.3390/mca26010020 - 3 Mar 2021
Viewed by 1709
Abstract
Control-systems engineering is a multidisciplinary subject that applies automatic-control theory to design systems with desired behaviors in control environments [...] Full article

Research

Jump to: Editorial

20 pages, 4911 KiB  
Article
Sensorless Speed Tracking of a Brushless DC Motor Using a Neural Network
by Oscar-David Ramírez-Cárdenas and Felipe Trujillo-Romero
Math. Comput. Appl. 2020, 25(3), 57; https://doi.org/10.3390/mca25030057 - 4 Sep 2020
Cited by 12 | Viewed by 3650
Abstract
In this work, the sensorless speed control of a brushless direct current motor utilizing a neural network is presented. This control is done using a two-layer neural network that uses the backpropagation algorithm for training. The values provided by a Proportional, Integral, and [...] Read more.
In this work, the sensorless speed control of a brushless direct current motor utilizing a neural network is presented. This control is done using a two-layer neural network that uses the backpropagation algorithm for training. The values provided by a Proportional, Integral, and Derivative (PID) control to this type of motor are used to train the network. From this PID control, the velocity values and their corresponding signal control (u) are recovered for different values of load pairs. Five different values of load pairs were used to consider the entire working range of the motor to be controlled. After carrying out the training, it was observed that the proposed network could hold constant load pairs, as well as variables. Several tests were carried out at the simulation level, which showed that control based on neural networks is robust. Finally, it is worth mentioning that this control strategy can be realized without the need for a speed sensor. Full article
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12 pages, 1697 KiB  
Article
Simultaneous Optimal Estimation of Roughness and Minor Loss Coefficients in a Pipeline
by Ildeberto Santos-Ruiz, Francisco-Ronay López-Estrada, Vicenç Puig and Guillermo Valencia-Palomo
Math. Comput. Appl. 2020, 25(3), 56; https://doi.org/10.3390/mca25030056 - 1 Sep 2020
Cited by 9 | Viewed by 4411
Abstract
This paper presents a proposal to estimate simultaneously, through nonlinear optimization, the roughness and head loss coefficients in a non-straight pipeline. With the proposed technique, the calculation of friction is optimized by minimizing the fitting error in the Colebrook–White equation for an operating [...] Read more.
This paper presents a proposal to estimate simultaneously, through nonlinear optimization, the roughness and head loss coefficients in a non-straight pipeline. With the proposed technique, the calculation of friction is optimized by minimizing the fitting error in the Colebrook–White equation for an operating interval of the pipeline from the flow and pressure measurements at the pipe ends. The proposed method has been implemented in MATLAB and validated in a serpentine-shaped experimental pipeline by contrasting the theoretical friction for the estimated coefficients obtained from the Darcy–Weisbach equation for a set of steady-state measurements. Full article
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24 pages, 2893 KiB  
Article
Analysis and Comparison of Fuzzy Models and Observers for DC-DC Converters Applied to a Distillation Column Heating Actuator
by Mario Heras-Cervantes, Adriana del Carmen Téllez-Anguiano, Juan Anzurez-Marín and Elisa Espinosa-Juárez
Math. Comput. Appl. 2020, 25(3), 55; https://doi.org/10.3390/mca25030055 - 28 Aug 2020
Cited by 2 | Viewed by 1924
Abstract
In this paper, as an introduction, the nonlinear model of a distillation column is presented in order to understand the fundamental paper that the column heating actuator has in the distillation process dynamics as well as in the quality and safety of the [...] Read more.
In this paper, as an introduction, the nonlinear model of a distillation column is presented in order to understand the fundamental paper that the column heating actuator has in the distillation process dynamics as well as in the quality and safety of the process. In order to facilitate the implementation control strategies to maintain the heating power regulated in the distillation process, it is necessary to represent adequately the heating power actuator behavior; therefore, three different models (switching, nonlinear and fuzzy Takagi–Sugeno) of a DC-DC Buck-Boost power converter, selected to regulate the electric power regarding the heating power, are presented and compared. Considering that the online measurements of the two main variables of the converter, the inductor current and the capacitor voltage, are not always available, two different fuzzy observers (with and without sliding modes) are developed to allow monitoring the physical variables in the converter. The observers response is compared to determine which has a better performance. The role of the observer in estimating the state variables with the purpose of using them in the sensors fault diagnosis, using the analytical redundancy concept, likewise, from the estimation of these variables other non-measurable can be determined; for example, the caloric power. The stability analysis and observers gains are obtained by linear matrix inequalities (LMIs). The observers are validated by MATLAB® simulations to verify the observers convergence and analyze their response under system disturbances. Full article
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13 pages, 47242 KiB  
Article
Design of a Nonhomogeneous Nonlinear Synchronizer and Its Implementation in Reconfigurable Hardware
by Jesus R. Pulido-Luna, Jorge A. López-Rentería and Nohe R. Cazarez-Castro
Math. Comput. Appl. 2020, 25(3), 51; https://doi.org/10.3390/mca25030051 - 14 Aug 2020
Cited by 5 | Viewed by 2307
Abstract
In this work, a generalization of a synchronization methodology applied to a pair of chaotic systems with heterogeneous dynamics is given. The proposed control law is designed using the error state feedback and Lyapunov theory to guarantee asymptotic stability. The control law is [...] Read more.
In this work, a generalization of a synchronization methodology applied to a pair of chaotic systems with heterogeneous dynamics is given. The proposed control law is designed using the error state feedback and Lyapunov theory to guarantee asymptotic stability. The control law is used to synchronize two systems with different number of scrolls in their dynamics and defined in a different number of pieces. The proposed control law is implemented in an FPGA in order to test performance of the synchronization schemes. Full article
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12 pages, 467 KiB  
Article
Robust qLPV Tracking Fault-Tolerant Control of a 3 DOF Mechanical Crane
by Francisco-Ronay López-Estrada, Oscar Santos-Estudillo, Guillermo Valencia-Palomo, Samuel Gómez-Peñate and Carlos Hernández-Gutiérrez
Math. Comput. Appl. 2020, 25(3), 48; https://doi.org/10.3390/mca25030048 - 28 Jul 2020
Cited by 12 | Viewed by 2875
Abstract
The main aim of this paper is to propose a robust fault-tolerant control for a three degree of freedom (DOF) mechanical crane by using a convex quasi-Linear Parameter Varying (qLPV) approach for modeling the crane and a passive fault-tolerant scheme. The control objective [...] Read more.
The main aim of this paper is to propose a robust fault-tolerant control for a three degree of freedom (DOF) mechanical crane by using a convex quasi-Linear Parameter Varying (qLPV) approach for modeling the crane and a passive fault-tolerant scheme. The control objective is to minimize the load oscillations while the desired path is tracked. The convex qLPV model is obtained by considering the nonlinear sector approach, which can represent exactly the nonlinear system under the bounded nonlinear terms. To improve the system safety, tolerance to partial actuator faults is considered. Performance requirements of the tracking control system are specified in an H criteria that guarantees robustness against measurement noise, and partial faults. As a result, a set of Linear Matrix Inequalities is derived to compute the controller gains. Numerical experiments on a realistic 3 DOF crane model confirm the applicability of the control scheme. Full article
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16 pages, 614 KiB  
Article
A Fractional High-Gain Nonlinear Observer Design—Application for Rivers Environmental Monitoring Model
by Abraham Efraim Rodriguez-Mata, Yaneth Bustos-Terrones, Victor Gonzalez-Huitrón, Pablo Antonio Lopéz-Peréz, Omar Hernández-González and Leonel Ernesto Amabilis-Sosa
Math. Comput. Appl. 2020, 25(3), 44; https://doi.org/10.3390/mca25030044 - 16 Jul 2020
Cited by 6 | Viewed by 2231
Abstract
The deterioration of current environmental water sources has led to the need to find ways to monitor water quality conditions. In this paper, we propose the use of Streeter–Phelps contaminant distribution models and state estimation techniques (observer) to be able to estimate variables [...] Read more.
The deterioration of current environmental water sources has led to the need to find ways to monitor water quality conditions. In this paper, we propose the use of Streeter–Phelps contaminant distribution models and state estimation techniques (observer) to be able to estimate variables that are very difficult to measure in rivers with online sensors, such as Biochemical Oxygen Demand (BOD). We propose the design of a novel Fractional Order High Gain Observer (FOHO) and consider the use of Lyapunov convergence functions to demonstrate stability, as it is compared to classical extended Luenberger Observer published in the literature, to study the convergence in BOD estimation in rivers. The proposed methodology was used to estimated Dissolved oxygen (DO) and BOD monitoring of River Culiacan, Sinaloa, Mexico. The use of fractional order in high-gain observers has a very effective effect on BOD estimation performance, as shown by our numerical studies. The theoretical results have shown that robust observer design can help solve problems in estimating complex variables. Full article
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26 pages, 4053 KiB  
Article
Hybrid State Constraint Adaptive Disturbance Rejection Controller for a Mobile Worm Bio-Inspired Robot
by Vania Lara-Ortiz, Ivan Salgado, David Cruz-Ortiz, Alejandro Guarneros, Misael Magos-Sanchez and Isaac Chairez
Math. Comput. Appl. 2020, 25(1), 13; https://doi.org/10.3390/mca25010013 - 4 Mar 2020
Cited by 7 | Viewed by 3407
Abstract
This study presents the design of a hybrid active disturbance rejection controller (H-ADRC) which regulates the gait cycle of a worm bio-inspired robotic device (WBRD). The WBRD is designed as a full actuated six rigid link robotic manipulator. The controller considers the state [...] Read more.
This study presents the design of a hybrid active disturbance rejection controller (H-ADRC) which regulates the gait cycle of a worm bio-inspired robotic device (WBRD). The WBRD is designed as a full actuated six rigid link robotic manipulator. The controller considers the state restrictions in the device articulations; this means the maximum and minimum angular ranges, to avoid any possible damage to the structure. The controller uses an active compensation method to estimate the unknown dynamics of the WBRD by means of an extended state observer. The sequence of movements for the gait cycle of a WBRD is represented as a class of hybrid system by alternative reference frameworks placed at the first and the last link. The stability analysis employs a class of Hybrid Barrier Lyapunov Function to ensure the fulfillment of the angular restrictions in the robotic device. The proposed controller is evaluated using a numerical simulation system based on the virtual version of the WBRD. Moreover, experimental results confirmed that the H-ADRC may endorse the realization of the proposed gait cycle despite the presence of perturbations and modeling uncertainties. The H-ADRC is compared against a proportional derivative (PD) controller and a proportional-integral-derivative (PID) controller. The H-ADRC shows a superior performance as a consequence of the estimation provided by the homogeneous extended state observer. Full article
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14 pages, 2286 KiB  
Article
Adaptive Control of Resistance Spot Welding Based on a Dynamic Resistance Model
by Ziyad Kas and Manohar Das
Math. Comput. Appl. 2019, 24(4), 86; https://doi.org/10.3390/mca24040086 - 28 Sep 2019
Cited by 4 | Viewed by 4417
Abstract
Resistance spot welding is a process commonly used for joining a stack of two or three metal sheets at desired spots. Such welds are accomplished by holding the metallic workpieces together by applying pressure through the tips of a pair of electrodes and [...] Read more.
Resistance spot welding is a process commonly used for joining a stack of two or three metal sheets at desired spots. Such welds are accomplished by holding the metallic workpieces together by applying pressure through the tips of a pair of electrodes and then passing a strong electric current for a short duration. This kind of welding process often suffers from two common drawbacks, namely, inconsistent weld quality and inadequate nugget size. In order to address these problems, a new theoretical approach of controlling resistance spot welding processes is proposed in this paper. The proposed controller is based on a simplified dynamical model of the resistance spot welding process and employs the principle of adaptive one-step-ahead control. It is essentially an adaptive tracking controller that estimates the unknown process parameters and adjusts the welding voltage continuously to make sure that the nugget resistance tracks a desired reference resistance profile. The modeling and controller design methodologies are discussed in detail. Also, the results of a simulation study to evaluate the performance of the proposed controller are presented. The proposed control scheme is expected to reduce energy consumption and produce consistent welds. Full article
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27 pages, 4429 KiB  
Article
Direct Power Control Optimization for Doubly Fed Induction Generator Based Wind Turbine Systems
by Mohammed Mazen Alhato and Soufiene Bouallègue
Math. Comput. Appl. 2019, 24(3), 77; https://doi.org/10.3390/mca24030077 - 26 Aug 2019
Cited by 37 | Viewed by 5194
Abstract
This study presents an intelligent metaheuristics-based design procedure for the Proportional-Integral (PI) controllers tuning in the direct power control scheme for 1.5 MW Doubly Fed Induction Generator (DFIG) based Wind Turbine (WT) systems. The PI controllers’ gains tuning is formulated as a constrained [...] Read more.
This study presents an intelligent metaheuristics-based design procedure for the Proportional-Integral (PI) controllers tuning in the direct power control scheme for 1.5 MW Doubly Fed Induction Generator (DFIG) based Wind Turbine (WT) systems. The PI controllers’ gains tuning is formulated as a constrained optimization problem under nonlinear and non-smooth operational constraints. Such a formulated tuning problem is efficiently solved by means of the proposed Thermal Exchange Optimization (TEO) algorithm. To evaluate the effectiveness of the introduced TEO metaheuristic, an empirical comparison study with the homologous particle swarm optimization, genetic algorithm, harmony search algorithm, water cycle algorithm, and grasshopper optimization algorithm is achieved. The proposed TEO algorithm is ensured to perform several desired operational characteristics of DFIG for the active/reactive power and DC-link voltage simultaneously. This is performed by solving a multi-objective function optimization problem through a weighted-sum approach. The proposed control strategy is investigated in MATLAB/environment and the results proved the capabilities of the proposed control system in tracking and control under different scenarios. Moreover, a statistical analysis using non-parametric Friedman and Bonferroni–Dunn’s tests demonstrates that the TEO algorithm gives very competitive results in solving global optimization problems in comparison to the other reported metaheuristic algorithms. Full article
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