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Mathematics
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Modeling, Optimization and Control of Industrial Processes
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Modeling, Optimization and Control of Industrial Processes

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "C2: Dynamical Systems".

Deadline for manuscript submissions: 15 January 2026 | Viewed by 14216

Special Issue Editor

Dr. Marjan Golob

E-Mail Website
Guest Editor
Faculty of Electrical Engineering and Computer Science, University of Maribor, Koroška cesta 46, 2000 Maribor, Slovenia
Interests: process control, system modelling, system identification; fuzzy system; industrial automation; distributed control systems; networked control systems

Special Issue Information

Dear Colleagues,

With the remarkable advances in mathematics and information technologies, smart manufacturing has become a central strategy in the transformation of industrial production. The goals of smart manufacturing are to enable production with higher quality, lower costs, lower environmental impact, and carbon neutrality. In this development process, some technologies such as digital twin, industrial internet of things, cyber-physical systems, big data, 5G, etc., will become the main technical framework in the process industry. Process industries refer to basic raw materials industries, including oil, gas, steel, building materials, petrochemicals, chemical and plastic production, food and drink processing, water and wastewater treatment plants and energy production.

This Special Issue will focus on the latest research papers on how to develop and implement new modeling, optimization, and control methods in the process industry to take advantage of the new technologies mentioned above.

Topics include, but are not limited to, the following: building mathematical models of complex dynamic systems and related simulation methods; developing theory with the formulation of new control systems; developing theory and control systems with artificial intelligence using neural networks, fuzzy systems, and machine learning; simulating control systems for dynamic objects on computers and in real time on test beds; and developing digital twins. Contributions of both theoretical and practical research are welcome.

Dr. Marjan Golob
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

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. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • process control
  • biotechnology
  • mathematical modeling and identification
  • numerical analysis and simulation
  • data-driven modeling and control
  • fuzzy systems and control
  • machine learning
  • digital twins
  • process industry

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Published Papers (7 papers)

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Research

18 pages, 3259 KiB  
Article
Research on Vehicle AEB Control Strategy Based on Safety Time–Safety Distance Fusion Algorithm
by Xiang Fu, Jiaqi Wan, Daibing Wu, Wei Jiang, Wang Ma and Tianqi Yang
Mathematics 2024, 12(12), 1905; https://doi.org/10.3390/math12121905 - 19 Jun 2024
Cited by 3 | Viewed by 1978
Abstract
With the increasing consumer focus on automotive safety, Autonomous Emergency Braking (AEB) systems, recognized as effective active safety technologies for collision avoidance and the mitigation of collision-related injuries, are gaining wider application in the automotive industry. To address the issues of the insufficient [...] Read more.
With the increasing consumer focus on automotive safety, Autonomous Emergency Braking (AEB) systems, recognized as effective active safety technologies for collision avoidance and the mitigation of collision-related injuries, are gaining wider application in the automotive industry. To address the issues of the insufficient working reliability of AEB systems and their unsatisfactory level of accordance with the psychological expectations of drivers, this study proposes an optimized second-order Time to Collision (TTC) safety time algorithm based on the motion state of the preceding vehicle. Additionally, the study introduces a safety distance algorithm derived from an analysis of the braking process of the main vehicle. The safety time algorithm focusing on comfort and the safety distance algorithm focusing on safety are effectively integrated in the time domain and the space domain to obtain the safety time–safety distance fusion algorithm. A MATLAB/Simulink–Carsim joint simulation platform has been established to validate the AEB control strategy in terms of safety, comfort, and system responsiveness. The simulation results show that the proposed safety time–safety distance fusion algorithm consistently achieves complete collision avoidance, indicating a higher safety level for the AEB system. Furthermore, the application of active hierarchical braking minimizes the distance error, at under 0.37 m, which meets psychological expectations of drivers and improves the comfort of the AEB system. Full article
(This article belongs to the Special Issue Modeling, Optimization and Control of Industrial Processes)
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29 pages, 8141 KiB  
Article
Synthetic Optimization of Trafficability and Roll Stability for Off-Road Vehicles Based on Wheel-Hub Drive Motors and Semi-Active Suspension
by Xiang Fu, Jiaqi Wan, Daoyuan Liu, Song Huang, Sen Wu, Zexuan Liu, Jijie Wang, Qianfeng Ruan and Tianqi Yang
Mathematics 2024, 12(12), 1871; https://doi.org/10.3390/math12121871 - 15 Jun 2024
Cited by 1 | Viewed by 1189
Abstract
Considering the requirements pertaining to the trafficability of off-road vehicles on rough roads, and since their roll stability deteriorates rapidly when turning violently or passing slant roads due to a high center of gravity (CG), an efficient anti-slip control (ASC) method with superior [...] Read more.
Considering the requirements pertaining to the trafficability of off-road vehicles on rough roads, and since their roll stability deteriorates rapidly when turning violently or passing slant roads due to a high center of gravity (CG), an efficient anti-slip control (ASC) method with superior instantaneity and robustness, in conjunction with a rollover prevention algorithm, was proposed in this study. A nonlinear 14 DOF vehicle model was initially constructed in order to explain the dynamic coupling mechanism among the lateral motion, yaw motion and roll motion of vehicles. To acquire physical state changes and friction forces of the tires in real time, corrected LuGre tire models were utilized with the aid of resolvers and inertial sensors, and an adaptive sliding mode controller (ASMC) was designed to suppress each wheel’s slip ratio. In addition, a model predictive controller (MPC) was established to forecast rollover risk and roll moment in reaction to the change in the lateral forces as well as the different ground heights of the opposite wheels. During experimentation, the mutations of tire adhesion capacity were quickly discerned and the wheel-hub drive motors (WHDM) and ASC maintained the drive efficiency under different adhesion conditions. Finally, a hardware-in-the-loop (HIL) platform made up of the vehicle dynamic model in the dSPACE software, semi-active suspension (SAS), a vehicle control unit (VCU) and driver simulator was constructed, where the prediction and moving optimization of MPC was found to enhance roll stability effectively by reducing the length of roll arm when necessary. Full article
(This article belongs to the Special Issue Modeling, Optimization and Control of Industrial Processes)
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17 pages, 4458 KiB  
Article
Development of Mathematical Models for Industrial Processes Using Dynamic Neural Networks
by Srečko Herceg, Željka Ujević Andrijić, Nikola Rimac and Nenad Bolf
Mathematics 2023, 11(21), 4518; https://doi.org/10.3390/math11214518 - 2 Nov 2023
Cited by 3 | Viewed by 2031
Abstract
Dynamic neural networks (DNNs) are a type of artificial neural network (ANN) designed to work with sequential data where context in time is important. Unlike traditional static neural networks that process data in a fixed order, dynamic neural networks use information about past [...] Read more.
Dynamic neural networks (DNNs) are a type of artificial neural network (ANN) designed to work with sequential data where context in time is important. Unlike traditional static neural networks that process data in a fixed order, dynamic neural networks use information about past inputs, which is important if the dynamic of a certain process is emphasized. They are commonly used in natural language processing, speech recognition, and time series prediction. In industrial processes, their use is interesting for the prediction of difficult-to-measure process variables. In an industrial isomerization process, it is crucial to measure the quality attributes that affect the octane number of gasoline. Process analyzers commonly used for this purpose are expensive and subject to failure. Therefore, to achieve continuous production in the event of a malfunction, mathematical models for estimating product quality attributes are imposed as a solution. In this paper, mathematical models were developed using dynamic recurrent neural networks (RNNs), i.e., their subtype of a long short-term memory (LSTM) architecture. The results of the developed models were compared with the results of several types of other data-driven models developed for an isomerization process, such as multilayer perceptron (MLP) artificial neural networks, support vector machines (SVM), and dynamic polynomial models. The obtained results are satisfactory, suggesting a good possibility of application. Full article
(This article belongs to the Special Issue Modeling, Optimization and Control of Industrial Processes)
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13 pages, 4067 KiB  
Article
New Approach for Fertiliser Size Assessment Using Contactless Scanning
by Andrius Laucka, Darius Andriukaitis, Algimantas Valinevicius, Mindaugas Zilys, Dangirutis Navikas, Leonas Balasevicius, Audrius Merfeldas, Roman Sotner, Jan Jerabek, Zhixiong Li and Jozef Ritonja
Mathematics 2023, 11(17), 3676; https://doi.org/10.3390/math11173676 - 25 Aug 2023
Viewed by 1168
Abstract
The growing population and lack of change in resources of cultivated land have led to the search for more efficient farming solutions. The recovery of soil is facilitated by using chemicals designed for the enrichment of cultivated soil. Fertilisers are made of a [...] Read more.
The growing population and lack of change in resources of cultivated land have led to the search for more efficient farming solutions. The recovery of soil is facilitated by using chemicals designed for the enrichment of cultivated soil. Fertilisers are made of a combination of various substances that determine not only the chemical but also the shape characteristics of the fertiliser pellets. The effect of the quality of fertilisation on yield size is related to even distribution. Shape and size are closely related to the quality of the fertilisation process. The intense control of the production process would not be possible without automatised and quick measurements within the production line. Constant control is necessary to ensure that the products meet quality standards. The contactless assessment of pellet sizes allows a quick reaction to changes in production quality and reduces the costs arising from the reprocessing of defective pellets. The results of the assessment of pellet volume using their two-dimensional image are presented in this publication. Pellets must be analysed according to their most characteristic position, which can provide valuable information about their properties. The aim is to determine the placement positions of the equipment based on calculations and to compare the results with those of gold-standard equipment. Correctly calibrated equipment ensures that the measurement results match the results of the control equipment of fertiliser producers. Reliable non-contact measurements can reduce the reaction time to production changes. Full article
(This article belongs to the Special Issue Modeling, Optimization and Control of Industrial Processes)
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25 pages, 7117 KiB  
Article
Active Fault-Tolerant Control Applied to a Pressure Swing Adsorption Process for the Production of Bio-Hydrogen
by Gerardo Ortiz Torres, Jesse Yoe Rumbo Morales, Moises Ramos Martinez, Jorge Salvador Valdez-Martínez, Manuela Calixto-Rodriguez, Estela Sarmiento-Bustos, Carlos Alberto Torres Cantero and Hector Miguel Buenabad-Arias
Mathematics 2023, 11(5), 1129; https://doi.org/10.3390/math11051129 - 24 Feb 2023
Cited by 15 | Viewed by 2933
Abstract
Pressure swing adsorption (PSA) technology is used in various applications. PSA is a cost-effective process with the ability to produce high-purity bio-hydrogen (99.99%) with high recovery rates. In this article, a PSA process for the production of bio-hydrogen is proposed; it uses two [...] Read more.
Pressure swing adsorption (PSA) technology is used in various applications. PSA is a cost-effective process with the ability to produce high-purity bio-hydrogen (99.99%) with high recovery rates. In this article, a PSA process for the production of bio-hydrogen is proposed; it uses two columns packed with type 5A zeolite, and it has a four-step configuration (adsorption, depressurization, purge, and repressurization) for bio-hydrogen production and regeneration of the beds. The aim of this work is to design and use an active fault-tolerant control (FTC) controller to raise and maintain a stable purity of 0.9999 in molar fraction (99.99%), even with the occurrence of actuator faults. To validate the robustness and performance of the proposed discrete FTC, it has been compared with a discrete PID (proportional–integral–derivative) controller in the presence of actuator faults and trajectory changes. Both controllers achieve to maintain stable purity by reducing the effect of faults; however, the discrete PID controller is not robust to multiple faults since the desired purity is lost and fails to meet international standards to be used as bio-fuel. On the other hand, the FTC scheme reduces the effects of individual and multiple faults by striving to maintain a purity of 0.9999 in molar fraction and complying with international standards to be used as bio-fuel. Full article
(This article belongs to the Special Issue Modeling, Optimization and Control of Industrial Processes)
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22 pages, 5990 KiB  
Article
NARX Deep Convolutional Fuzzy System for Modelling Nonlinear Dynamic Processes
by Marjan Golob
Mathematics 2023, 11(2), 304; https://doi.org/10.3390/math11020304 - 6 Jan 2023
Cited by 2 | Viewed by 1668
Abstract
This paper presents a new approach for modelling nonlinear dynamic processes (NDP). It is based on a nonlinear autoregressive with exogenous (NARX) inputs model structure and a deep convolutional fuzzy system (DCFS). The DCFS is a hierarchical fuzzy structure, which can overcome the [...] Read more.
This paper presents a new approach for modelling nonlinear dynamic processes (NDP). It is based on a nonlinear autoregressive with exogenous (NARX) inputs model structure and a deep convolutional fuzzy system (DCFS). The DCFS is a hierarchical fuzzy structure, which can overcome the deficiency of general fuzzy systems when facing high dimensional data. For relieving the curse of dimensionality, as well as improving approximation performance of fuzzy models, we propose combining the NARX with the DCFS to provide a good approximation of the complex nonlinear dynamic behavior and a fast-training algorithm with ensured convergence. There are three NARX DCFS structures proposed, and the appropriate training algorithm is adapted. Evaluations were performed on a popular benchmark—Box and Jenkin’s gas furnace data set and the four nonlinear dynamic test systems. The experiments show that the proposed NARX DCFS method can be successfully used to identify nonlinear dynamic systems based on external dynamics structures and nonlinear static approximators. Full article
(This article belongs to the Special Issue Modeling, Optimization and Control of Industrial Processes)
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15 pages, 3625 KiB  
Article
Optimized Fuzzy Logic Control System for Diver’s Automatic Buoyancy Control Device
by Nenad Muškinja, Matej Rižnar and Marjan Golob
Mathematics 2023, 11(1), 22; https://doi.org/10.3390/math11010022 - 21 Dec 2022
Viewed by 2002
Abstract
In this article, the design of a fuzzy logic control system (FLCS) in combination with multi-objective optimization for diver’s buoyancy control device (BCD) is presented. To either change or maintain the depth, the diver manually controls two pneumatic valves that are mounted on [...] Read more.
In this article, the design of a fuzzy logic control system (FLCS) in combination with multi-objective optimization for diver’s buoyancy control device (BCD) is presented. To either change or maintain the depth, the diver manually controls two pneumatic valves that are mounted on the inflatable diving jacket. This task can be very difficult, especially in specific diving circumstances such as poor visibility, safety stop procedures or critical life functions of the diver. The implemented BCD hardware automatically controls the diver’s depth by inflating or deflating the diver’s jacket with two electro-pneumatic valves. The FLCS in combination with the multi-objective optimization was used to minimize control error and simultaneously ensure minimal air supply consumption of the BCD. The diver’s vertical velocity is also critical, especially while the diver is ascending during the decompression procedure; therefore, a combination of depth and vertical velocity control was configured as a cascaded controller setup with outer proportional depth and inner FLCS vertical velocity control loops. The optimization of the FLCS parameters was achieved with differential evolution global optimum search algorithm. The results obtained were compared with the optimized cascaded position and velocity PID controller in simulations. Full article
(This article belongs to the Special Issue Modeling, Optimization and Control of Industrial Processes)
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