Special Issue "Applications of Mathematical Models in Engineering"

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

Deadline for manuscript submissions: closed (28 February 2021).

Special Issue Editors

Prof. Dr. Eva H. Dulf
E-Mail Website
Guest Editor
Faculty of Automation and Computer Science, Department of Automation, Technical University of Cluj-Napoca, Memorandumului 28, 400014 Cluj-Napoca, Romania
Interests: fractional calculus; control engineering; biochemical engineering; biomedical engineering
Special Issues and Collections in MDPI journals
Dr. Cristina I. Muresan
E-Mail Website
Guest Editor
Faculty of Automation and Computer Science, Department of Automation, Technical University of Cluj-Napoca, Memorandumului 28, 400014 Cluj-Napoca, Romania
Interests: fractional calculus; predictive control; biomedical engineering; dead-time compensation
Special Issues and Collections in MDPI journals

Special Issue Information

Dear Colleagues,

The most influential research topic in the twenty-first century seems to be mathematics, since it generates innovation in a wide range of research fields. It supports all engineering fields, but also areas such as medicine, healthcare, business, etc. The intention of this Special Issue is therefore to deal with mathematical works related to engineering and multidisciplinary problems.

Modern developments in theoretical and applied science have widely depended on knowledge of the derivatives and integrals of the fractional order appearing in engineering practices. Therefore, one goal of this Special Issue is to focus on recent achievements and future challenges on the theory and applications of fractional calculus in engineering sciences.

We invite authors to contribute original research articles addressing significant issues and contributing towards the development of new concepts, methodologies, applications, trends, and knowledge in mathematics. Review articles describing the current state-of-the-art are also welcome.

Potential topics include but are not limited to the following:

  • Fractional mathematical models;
  • Computational methods for the fractional PDEs in engineering;
  • New mathematical approaches, innovations, and challenges in biotechnologies and biomedicine;
  • Applied mathematics;
  • Engineering research based on advanced mathematical tools.

Prof. Dr. Eva-Henrietta Dulf
Dr. Cristina-Ioana Mureșan
Guest Editors

Manuscript Submission Information

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Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1600 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

  • fractional calculus
  • mathematical models
  • mathematics in control engineering
  • mathematics in biomedicine
  • mathematics in biotechnologies

Published Papers (19 papers)

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Research

Article
μ-Synthesis FO-PID for Twin Rotor Aerodynamic System
Mathematics 2021, 9(19), 2504; https://doi.org/10.3390/math9192504 - 06 Oct 2021
Viewed by 276
Abstract
μ-synthesis is a NP-hard optimization problem based on the generalized Robust Control framework which manages to find a controller which fulfills both robust stability and robust performance. In order to solve such problems, nonsmooth optimization techniques are employed to find nearly-optimal parameters [...] Read more.
μ-synthesis is a NP-hard optimization problem based on the generalized Robust Control framework which manages to find a controller which fulfills both robust stability and robust performance. In order to solve such problems, nonsmooth optimization techniques are employed to find nearly-optimal parameters values. However, the free parameters available for tuning must be involved only in classical arithmetic operations, which leads to a problem for the fractional-order operator or for its integer-order approximation, exponential operations being involved. The main goal of the current article consists of presenting a possibility to integrate a fixed-structure multiple-input-multiple-output (MIMO) fractional-order proportional-integral-derivative (FO-PID) controller in the μ-synthesis optimization problem. The solution consists in a possibility to find a set of tunable parameters isomorphic with the fractional-order such that the coefficients involved in the approximation of the fractional element, along with the formulation of a fixed-structure mixed-sensitivity loop shaping μ-synthesis control problem. The proposed design procedure is applied to a twin rotor aerodynamic system (TRAS) using both MATLAB numerical simulation and practical experiments on laboratory scale equipment. Moreover, a comparison with the unstructured μ-synthesis is performed, highlighting the advantages of the proposed solution: simpler form and guaranteed robust stability and performance. Full article
(This article belongs to the Special Issue Applications of Mathematical Models in Engineering)
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Article
Adaptive Control of CO2 Production during Milk Fermentation in a Batch Bioreactor
Mathematics 2021, 9(15), 1712; https://doi.org/10.3390/math9151712 - 21 Jul 2021
Viewed by 354
Abstract
The basic characteristic of batch bioreactors is their inability to inflow or outflow the substances during the fermentation process. This follows in the simple construction and maintenance, which is the significant advantage of batch bioreactors. Unfortunately, this characteristic also results in the inability [...] Read more.
The basic characteristic of batch bioreactors is their inability to inflow or outflow the substances during the fermentation process. This follows in the simple construction and maintenance, which is the significant advantage of batch bioreactors. Unfortunately, this characteristic also results in the inability of the current industrial and laboratory batch bioreactors to control fermentation production during the process duration. In some recent studies, it was shown that changing the temperature could influence the execution of the fermentation process. The presented paper shows that this phenomenon could be used to develop the closed-loop control system for the fermentation production control in batch bioreactors. First, based on theoretical work, experiments, and numerical methods, the appropriate structure of the mathematical model was determined and parameters were identified. Next, the closed-loop control system structure for batch bioreactor was proposed, and the linear and adaptive control system based on this structure and the derived and identified model were developed. Both modeling and adaptive control system design are new and represent original contributions. As expected, due to the non-linearity of the controlled plant, the adaptive control represents a more successful approach. The simulation and experimental results were used to confirm the applicability of the proposed solution. Full article
(This article belongs to the Special Issue Applications of Mathematical Models in Engineering)
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Article
μ-Synthesis for Fractional-Order Robust Controllers
Mathematics 2021, 9(8), 911; https://doi.org/10.3390/math9080911 - 20 Apr 2021
Cited by 2 | Viewed by 575
Abstract
The current article presents a design procedure for obtaining robust multiple-input and multiple-output (MIMO) fractional-order controllers using a μ-synthesis design procedure with DK iteration. μ-synthesis uses the generalized Robust Control framework in order to find a controller which meets [...] Read more.
The current article presents a design procedure for obtaining robust multiple-input and multiple-output (MIMO) fractional-order controllers using a μ-synthesis design procedure with DK iteration. μ-synthesis uses the generalized Robust Control framework in order to find a controller which meets the stability and performance criteria for a family of plants. Because this control problem is NP-hard, it is usually solved using an approximation, the most common being the DK iteration algorithm, but, this approximation leads to high-order controllers, which are not practically feasible. If a desired structure is imposed to the controller, the corresponding K step is a non-convex problem. The novelty of the paper consists in an artificial bee colony swarm optimization approach to compute the nearly optimal controller parameters. Further, a mixed-sensitivity μ-synthesis control problem is solved with the proposed approach for a two-axis Computer Numerical Control (CNC) machine benchmark problem. The resulting controller using the described algorithm manages to ensure, with mathematical guarantee, both robust stability and robust performance, while the high-order controller obtained with the classical μ-synthesis approach in MATLAB does not offer this. Full article
(This article belongs to the Special Issue Applications of Mathematical Models in Engineering)
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Article
New Expressions to Apply the Variation Operation Strategy in Engineering Tools Using Pumps Working as Turbines
Mathematics 2021, 9(8), 860; https://doi.org/10.3390/math9080860 - 14 Apr 2021
Cited by 3 | Viewed by 499
Abstract
The improvement in energy saving aspects in water systems is currently a topic of major interest. The utilization of pumps working as turbines is a relevant strategy in water distribution networks consisting of pressurized pipes, using these machines to recover energy, generate green [...] Read more.
The improvement in energy saving aspects in water systems is currently a topic of major interest. The utilization of pumps working as turbines is a relevant strategy in water distribution networks consisting of pressurized pipes, using these machines to recover energy, generate green energy and reduce leakages in water systems. The need to develop energy studies, prior to the installation of these facilities, requires the use of simulation tools. These tools should be able to define the operation curves of the machine as a function of the flow rate. This research proposes a new strategy to develop a mathematics model for pumps working as turbines (PATs), considering the modified affinity laws. This proposed model, which can be input into hydraulic simulation tools (e.g., Epanet, WaterGems), allows estimation of the head, efficiency, and power curves of the PATs when operating at different rotational speeds. The research used 87 different curves for 15 different machines to develop the new model. This model improves the results of the previously published models, reducing the error in the estimation of the height, efficiency, and power values. The proposed model reduced the errors by between 30 and 50% compared to the rest of the models. Full article
(This article belongs to the Special Issue Applications of Mathematical Models in Engineering)
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Article
Statistical and Type II Error Assessment of a Runoff Predictive Model in Peninsula Malaysia
Mathematics 2021, 9(8), 812; https://doi.org/10.3390/math9080812 - 08 Apr 2021
Viewed by 477
Abstract
Flood related disasters continue to threaten mankind despite preventative efforts in technological advancement. Since 1954, the Soil Conservation Services (SCS) Curve Number (CN0.2) rainfall-runoff model has been widely used but reportedly produced inconsistent results in field studies worldwide. As such, this [...] Read more.
Flood related disasters continue to threaten mankind despite preventative efforts in technological advancement. Since 1954, the Soil Conservation Services (SCS) Curve Number (CN0.2) rainfall-runoff model has been widely used but reportedly produced inconsistent results in field studies worldwide. As such, this article presents methodology to reassess the validity of the model and perform model calibration with inferential statistics. A closed form equation was solved to narrow previous research gap with a derived 3D runoff difference model for type II error assessment. Under this study, the SCS runoff model is statistically insignificant (alpha = 0.01) without calibration. Curve Number CN0.2 = 72.58 for Peninsula Malaysia with a 99% confidence interval range of 67 to 76. Within these CN0.2 areas, SCS model underpredicts runoff amounts when the rainfall depth of a storm is < 70 mm. Its overprediction tendency worsens in cases involving larger storm events. For areas of 1 km2, it underpredicted runoff amount the most (2.4 million liters) at CN0.2 = 67 and the rainfall depth of 55 mm while it nearly overpredicted runoff amount by 25 million liters when the storm depth reached 430 mm in Peninsula Malaysia. The SCS model must be validated with rainfall-runoff datasets prior to its adoption for runoff prediction in any part of the world. SCS practitioners are encouraged to adopt the general formulae from this article to derive assessment models and equations for their studies. Full article
(This article belongs to the Special Issue Applications of Mathematical Models in Engineering)
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Article
Unified CACSD Toolbox for Hybrid Simulation and Robust Controller Synthesis with Applications in DC-to-DC Power Converter Control
Mathematics 2021, 9(7), 731; https://doi.org/10.3390/math9070731 - 28 Mar 2021
Cited by 3 | Viewed by 912
Abstract
The current article presents the design, implementation, validation, and use of a Computer-Aided Control System Design (CACSD) toolbox for nonlinear and hybrid system uncertainty modeling, simulation, and control using μ synthesis. Remarkable features include generalization of classical system interconnection operations to nonlinear and [...] Read more.
The current article presents the design, implementation, validation, and use of a Computer-Aided Control System Design (CACSD) toolbox for nonlinear and hybrid system uncertainty modeling, simulation, and control using μ synthesis. Remarkable features include generalization of classical system interconnection operations to nonlinear and hybrid systems, automatic computation of equilibrium points for nonlinear systems, and optimization of least conservative uncertainty bounds, with direct applicability for μ synthesis. A unified approach is presented for the step-down (buck), step-up (boost), and single-ended primary-inductor (SEPIC) converters to showcase the use and flexibility of the toolbox. Robust controllers were computed by minimization of the H norm of the augmented performance systems, encompassing a wide range of uncertainty types, and have been designed using the well-known mixed-sensitivity closed loop shaping μ synthesis method. Full article
(This article belongs to the Special Issue Applications of Mathematical Models in Engineering)
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Article
Robust Fractional-Order Control Using a Decoupled Pitch and Roll Actuation Strategy for the I-Support Soft Robot
Mathematics 2021, 9(7), 702; https://doi.org/10.3390/math9070702 - 24 Mar 2021
Cited by 1 | Viewed by 500
Abstract
Tip control is a current open issue in soft robotics; therefore, it has received a good amount of attention in recent years. The desirable soft characteristics of these robots turn a well-solved problem in classic robotics, like the end-effector kinematics and dynamics, into [...] Read more.
Tip control is a current open issue in soft robotics; therefore, it has received a good amount of attention in recent years. The desirable soft characteristics of these robots turn a well-solved problem in classic robotics, like the end-effector kinematics and dynamics, into a challenging problem. The high redundancy condition of these robots hinders classical solutions, resulting in controllers with very high computational costs. In this paper, a simplification is proposed in the actuation setup of the I-Support soft robot, allowing the use of simple strategies for tip inclination control. In order to verify the proposed approach, inclination step input and trajectory-tracking experiments were performed on a single module of the I-Support robot, resulting in zero output error in all cases, including those where the system was exposed to disturbances. The comparative results of the proposed controllers, a proportional integral derivative (PID) and a fractional order robust (FOPI) controller, validate the feasibility of the proposed approach, showing a clear advantage in the use of the fractional robust controller for the tip inclination control of the I-Support robot compared to the integer order controller. Full article
(This article belongs to the Special Issue Applications of Mathematical Models in Engineering)
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Article
Tuning Rules for Active Disturbance Rejection Controllers via Multiobjective Optimization—A Guide for Parameters Computation Based on Robustness
Mathematics 2021, 9(5), 517; https://doi.org/10.3390/math9050517 - 02 Mar 2021
Cited by 1 | Viewed by 534
Abstract
A set of tuning rules for Linear Active Disturbance Rejection Controller (LADRC) with three different levels of compromise between disturbance rejection and robustness is presented. The tuning rules are the result of a Multiobjective Optimization Design (MOOD) procedure followed by curve fitting and [...] Read more.
A set of tuning rules for Linear Active Disturbance Rejection Controller (LADRC) with three different levels of compromise between disturbance rejection and robustness is presented. The tuning rules are the result of a Multiobjective Optimization Design (MOOD) procedure followed by curve fitting and are intended as a tool for designers who seek to implement LADRC by considering the load disturbance response of processes whose behavior is approximated by a general first-order system with delay. The validation of the proposed tuning rules is done through illustrative examples and the control of a nonlinear thermal process. Compared to classical PID (Proportional-Integral-Derivative) and other LADRC tuning methods, the derived functions offer an improvement in either disturbance rejection, robustness or both design objectives. Full article
(This article belongs to the Special Issue Applications of Mathematical Models in Engineering)
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Article
Study on the Intelligent Modeling of the Blade Aerodynamic Force in Compressors Based on Machine Learning
Mathematics 2021, 9(5), 476; https://doi.org/10.3390/math9050476 - 25 Feb 2021
Viewed by 467
Abstract
In order to obtain the aerodynamic loads of the vibrating blades efficiently, the eXterme Gradient Boosting (XGBoost) algorithm in machine learning was adopted to establish a three-dimensional unsteady aerodynamic force reduction model. First, the database for the unsteady aerodynamic response during the blade [...] Read more.
In order to obtain the aerodynamic loads of the vibrating blades efficiently, the eXterme Gradient Boosting (XGBoost) algorithm in machine learning was adopted to establish a three-dimensional unsteady aerodynamic force reduction model. First, the database for the unsteady aerodynamic response during the blade vibration was acquired through the numerical simulation of flow field. Then the obtained data set was trained by the XGBoost algorithm to set up the intelligent model of unsteady aerodynamic force for the three-dimensional blade. Afterwards, the aerodynamic load could be gained at any spatial location during blade vibration. To evaluate and verify the reliability of the intelligent model for the blade aerodynamic load, the prediction results of the machine learning model were compared with the results of Computation Fluid Dynamics (CFD). The determination coefficient R2 and the Root Mean Square Error (RMSE) were introduced as the model evaluation indicators. The results show that the prediction results based on the machine learning model are in good agreement with the CFD results, and the calculation efficiency is significantly improved. The results also indicate that the aerodynamic intelligent model based on the machine learning method is worthy of further study in evaluating the blade vibration stability. Full article
(This article belongs to the Special Issue Applications of Mathematical Models in Engineering)
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Article
Flow towards a Stagnation Region of a Vertical Plate in a Hybrid Nanofluid: Assisting and Opposing Flows
Mathematics 2021, 9(4), 448; https://doi.org/10.3390/math9040448 - 23 Feb 2021
Cited by 1 | Viewed by 453
Abstract
This study investigates a hybrid nanofluid flow towards a stagnation region of a vertical plate with radiation effects. The hybrid nanofluid consists of copper (Cu) and alumina (Al2O3) nanoparticles which are added into water to form Cu-Al2O [...] Read more.
This study investigates a hybrid nanofluid flow towards a stagnation region of a vertical plate with radiation effects. The hybrid nanofluid consists of copper (Cu) and alumina (Al2O3) nanoparticles which are added into water to form Cu-Al2O3/water nanofluid. The stagnation point flow describes the fluid motion in the stagnation region of a solid surface. In this study, both buoyancy assisting and opposing flows are considered. The similarity equations are obtained using a similarity transformation and numerical results are obtained via the boundary value problem solver (bvp4c) in MATLAB software. Findings discovered that dual solutions exist for both opposing and assisting flows. The heat transfer rate is intensified with the thermal radiation (49.63%) and the hybrid nanoparticles (32.37%). Full article
(This article belongs to the Special Issue Applications of Mathematical Models in Engineering)
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Article
Improving the Gridshells’ Regularity by Using Evolutionary Techniques
Mathematics 2021, 9(4), 440; https://doi.org/10.3390/math9040440 - 23 Feb 2021
Cited by 1 | Viewed by 410
Abstract
Designing and optimizing gridshell structures have been very attractive problems in the last decades. In this work, two indexes are introduced as “length ratio” and “shape ratio” to measure the regularity of a gridshell and are compared to the existing indexes in the [...] Read more.
Designing and optimizing gridshell structures have been very attractive problems in the last decades. In this work, two indexes are introduced as “length ratio” and “shape ratio” to measure the regularity of a gridshell and are compared to the existing indexes in the literature. Two evolutionary techniques, genetic algorithm (GA) and particle swarm optimization (PSO) method, are utilized to improve the gridshells’ regularity by using the indexes. An approach is presented to generate the initial gridshells for a given surface in MATLAB. The two methods are implemented in MATLAB and compared on three benchmarks with different Gaussian curvatures. For each grid, both triangular and quadrangular meshes are generated. Experimental results show that the regularity of some gridshell is improved more than 50%, the regularity of quadrangular gridshells can be improved more than the regularity of triangular gridshells on the same surfaces, and there may be some relationship between Gaussian curvature of a surface and the improvement percentage of generated gridshells on it. Moreover, it is seen that PSO technique outperforms GA technique slightly in almost all the considered test problems. Finally, the Dolan–Moré performance profile is produced to compare the two methods according to running times. Full article
(This article belongs to the Special Issue Applications of Mathematical Models in Engineering)
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Article
Mathematical Calculation of Stray Losses in Transformer Tanks with a Stainless Steel Insert
Mathematics 2021, 9(2), 184; https://doi.org/10.3390/math9020184 - 18 Jan 2021
Viewed by 585
Abstract
At present it is claimed that all electrical energy systems operate with high values of efficiency and reliability. In electric power systems (EPS), electrical power and distribution transformers are responsible for transferring the electrical energy from power stations up to the load centers. [...] Read more.
At present it is claimed that all electrical energy systems operate with high values of efficiency and reliability. In electric power systems (EPS), electrical power and distribution transformers are responsible for transferring the electrical energy from power stations up to the load centers. Consequently, it is mandatory to design transformers that possess the highest efficiency and reliability possible. Considerable power losses and hotspots may exist in the bushing region of a transformer, where conductors pass through the tank. Most transformer tanks are made of low-carbon steel, for economical reasons, causing the induction of high eddy currents in the bushing regions. Using a non-magnetic insert in the transformer tank can reduce the eddy currents in the region and as a consequence avoid overheating. In this work, analytical formulations were developed to calculate the magnetic field distribution and the stray losses in the transformer region where bushings are mounted, considering a stainless steel insert (SSI) in the transformer tank. Previously, this problem had only been tackled with numerical models. Several cases were analyzed considering different non-magnetic insert sizes. Additionally, a numerical study using a two dimensional (2D) finite element (FE) axisymmetric model was carried out in order to validate the analytical results. The solved cases show a great concordance between models, obtaining relative errors between the solutions of less than two percent. Full article
(This article belongs to the Special Issue Applications of Mathematical Models in Engineering)
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Article
Determination of Aircraft Cruise Altitude with Minimum Fuel Consumption and Time-to-Climb: An Approach with Terminal Residual Analysis
Mathematics 2021, 9(2), 147; https://doi.org/10.3390/math9020147 - 11 Jan 2021
Cited by 1 | Viewed by 631
Abstract
A pandemic situation of COVID-19 has made a cost-minimization strategy one of the utmost priorities for commercial airliners. A relevant scheme may involve the minimization of both the fuel- and time-related costs, and the climb trajectories of both objectives were optimized to determine [...] Read more.
A pandemic situation of COVID-19 has made a cost-minimization strategy one of the utmost priorities for commercial airliners. A relevant scheme may involve the minimization of both the fuel- and time-related costs, and the climb trajectories of both objectives were optimized to determine the optimum aircraft cruise altitude. The Hermite-Simpson method among the direct collocation methods was employed to discretize the problem domain. Novel approaches of terminal residual analysis (TRA), and a modified version, m-σ TRA, were proposed to determine the goals. The multi-objective cruise altitude (MOCA) was different by 2.5%, compared to the one statistically calculated from the commercial airliner data. The present methods, TRA and m-σ TRA were powerful tools in finding a solution to this complex problem. The value σ also worked as a transition criterion between a single- and multi-objective climb path to the cruise altitude. The exemplary MOCA was determined to be 10.91 and 11.97 km at σ = 1.1 and 2.0, respectively. The cost index (CI) varied during a flight, a more realistic approach than the one with constant CI. With validated results in this study, TRA and m-σ TRA may also be effective solutions to determine the multi-objective solutions in other complex fields. Full article
(This article belongs to the Special Issue Applications of Mathematical Models in Engineering)
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Article
Mathematical Approach to Improve the Thermoeconomics of a Humidification Dehumidification Solar Desalination System
Mathematics 2021, 9(1), 33; https://doi.org/10.3390/math9010033 - 25 Dec 2020
Cited by 1 | Viewed by 1078
Abstract
Water desalination presents a need to address the growing water-energy nexus. In this work, a literature survey is carried out, along an application of a mathematical model is presented to enhance the freshwater productivity rate of a solar-assisted humidification-dehumidification (HDH) type of desalination [...] Read more.
Water desalination presents a need to address the growing water-energy nexus. In this work, a literature survey is carried out, along an application of a mathematical model is presented to enhance the freshwater productivity rate of a solar-assisted humidification-dehumidification (HDH) type of desalination system. The prime novelty of this work is to recover the waste heat by reusing the feedwater at the exit of the condenser in the brackish water storage tank and to carry out the analysis of its effectiveness in terms of the system’s yearly thermoeconomics. The developed mathematical model for each of the components of the plant is solved through an iterative procedure. In a parametric study, the influence of mass flow rates (MFRs) of inlet air, saline water, feedwater, and air temperature on the freshwater productivity is shown with and without the waste heat recovery from the condensing coil. It is reported that the production rate of water is increased to a maximum of 15% by recovering the waste heat. Furthermore, yearly analysis has shown that the production rate of water is increased to a maximum of 16% for June in the location of Taxila, Pakistan. An analysis is also carried out on the economics of the proposed modification, which shows that the cost per litre of the desalinated water is reduced by ~13%. It is concluded that the water productivity of an HDH solar desalination plant can be significantly increased by recovering the waste heat from the condensing coil. Full article
(This article belongs to the Special Issue Applications of Mathematical Models in Engineering)
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Article
A Novel Comparative Statistical and Experimental Modeling of Pressure Field in Free Jumps along the Apron of USBR Type I and II Dissipation Basins
Mathematics 2020, 8(12), 2155; https://doi.org/10.3390/math8122155 - 03 Dec 2020
Cited by 1 | Viewed by 460
Abstract
Dissipation basins are usually constructed downstream of spillways to dissipate energy, causing large pressure fluctuations underneath hydraulic jumps. Little systematic experimental investigation seems available for the pressure parameters on the bed of the US Department of the Interior, Bureau of Reclamation (USBR) Type [...] Read more.
Dissipation basins are usually constructed downstream of spillways to dissipate energy, causing large pressure fluctuations underneath hydraulic jumps. Little systematic experimental investigation seems available for the pressure parameters on the bed of the US Department of the Interior, Bureau of Reclamation (USBR) Type II dissipation basins in the literature. We present the results of laboratory-scale experiments, focusing on the statistical modeling of the pressure field at the centerline of the apron along the USBR Type I and II basins. The accuracy of the pressure transducers was ±0.5%. The presence of accessories within basinII reduced the maximum pressure fluctuations by about 45% compared to basinI. Accordingly, in some points, the bottom of basinII did not collide directly with the jet due to the hydraulic jump. As a result, the values of pressure and pressure fluctuations decreased mainly therein. New original best-fit relationships were proposed for the mean pressure, the statistical coefficient of the probability distribution, and the standard deviation of pressure fluctuations to estimate the pressures with different probabilities of occurrence in basinI and basinII. The results could be useful for a more accurate, safe design of the slab thickness, and reduce the operation and maintenance costs of dissipation basins. Full article
(This article belongs to the Special Issue Applications of Mathematical Models in Engineering)
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Article
Experimental Validation of a Sliding Mode Control for a Stewart Platform Used in Aerospace Inspection Applications
Mathematics 2020, 8(11), 2051; https://doi.org/10.3390/math8112051 - 17 Nov 2020
Cited by 5 | Viewed by 633
Abstract
The authors introduce a new controller, aimed at industrial domains, that improves the performance and accuracy of positioning systems based on Stewart platforms. More specifically, this paper presents, and validates experimentally, a sliding mode control for precisely positioning a Stewart platform used as [...] Read more.
The authors introduce a new controller, aimed at industrial domains, that improves the performance and accuracy of positioning systems based on Stewart platforms. More specifically, this paper presents, and validates experimentally, a sliding mode control for precisely positioning a Stewart platform used as a mobile platform in non-destructive inspection (NDI) applications. The NDI application involves exploring the specimen surface of aeronautical coupons at different heights. In order to avoid defocusing and blurred images, the platform must be positioned accurately to keep a uniform distance between the camera and the surface of the specimen. This operation requires the coordinated control of the six electro mechanic actuators (EMAs). The platform trajectory and the EMA lengths can be calculated by means of the forward and inverse kinematics of the Stewart platform. Typically, a proportional integral (PI) control approach is used for this purpose but unfortunately this control scheme is unable to position the platform accurately enough. For this reason, a sliding mode control (SMC) strategy is proposed. The SMC requires: (1) a priori knowledge of the bounds on system uncertainties, and (2) the analysis of the system stability in order to ensure that the strategy executes adequately. The results of this work show a higher performance of the SMC when compared with the PI control strategy: the average absolute error is reduced from 3.45 mm in PI to 0.78 mm in the SMC. Additionally, the duty cycle analysis shows that although PI control demands a smoother actuator response, the power consumption is similar. Full article
(This article belongs to the Special Issue Applications of Mathematical Models in Engineering)
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Article
An Efficient Design and Implementation of a Quadrotor Unmanned Aerial Vehicle Using Quaternion-Based Estimator
Mathematics 2020, 8(10), 1829; https://doi.org/10.3390/math8101829 - 18 Oct 2020
Cited by 1 | Viewed by 711
Abstract
The main goal of the research is to design a low-cost, performing quadrotor unmaned aerial vehicle (UAV) system. Because of low cost limits, the performance must be ensured by other ways. The present proposal is a quaternion-based estimator used in the control loop. [...] Read more.
The main goal of the research is to design a low-cost, performing quadrotor unmaned aerial vehicle (UAV) system. Because of low cost limits, the performance must be ensured by other ways. The present proposal is a quaternion-based estimator used in the control loop. In order to make the proposed solution easy to be reproduced by the reader, step-by-step instructions are given, including component choices, design, and implementation. Throughout the article, detailed description of the system model is given. The efficacy of the suggested quaternion-based predictive control is evaluated by extended experimental results. Full article
(This article belongs to the Special Issue Applications of Mathematical Models in Engineering)
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Article
Solitary Wave Solutions of the Generalized Rosenau-KdV-RLW Equation
Mathematics 2020, 8(9), 1601; https://doi.org/10.3390/math8091601 - 17 Sep 2020
Cited by 6 | Viewed by 831
Abstract
This paper investigates the solitary wave solutions of the generalized Rosenau–Korteweg-de Vries-regularized-long wave equation. This model is obtained by coupling the Rosenau–Korteweg-de Vries and Rosenau-regularized-long wave equations. The solution of the equation is approximated by a local meshless technique called radial basis function [...] Read more.
This paper investigates the solitary wave solutions of the generalized Rosenau–Korteweg-de Vries-regularized-long wave equation. This model is obtained by coupling the Rosenau–Korteweg-de Vries and Rosenau-regularized-long wave equations. The solution of the equation is approximated by a local meshless technique called radial basis function (RBF) and the finite-difference (FD) method. The association of the two techniques leads to a meshless algorithm that does not requires the linearization of the nonlinear terms. First, the partial differential equation is transformed into a system of ordinary differential equations (ODEs) using radial kernels. Then, the ODE system is solved by means of an ODE solver of higher-order. It is shown that the proposed method is stable. In order to illustrate the validity and the efficiency of the technique, five problems are tested and the results compared with those provided by other schemes. Full article
(This article belongs to the Special Issue Applications of Mathematical Models in Engineering)
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Article
Event-Based Implementation of Fractional Order IMC Controllers for Simple FOPDT Processes
Mathematics 2020, 8(8), 1378; https://doi.org/10.3390/math8081378 - 17 Aug 2020
Cited by 7 | Viewed by 781
Abstract
Fractional order calculus has been used to generalize various types of controllers, including internal model controllers (IMC). The focus of this manuscript is towards fractional order IMCs for first order plus dead-time (FOPDT) processes, including delay and lag dominant ones. The design is [...] Read more.
Fractional order calculus has been used to generalize various types of controllers, including internal model controllers (IMC). The focus of this manuscript is towards fractional order IMCs for first order plus dead-time (FOPDT) processes, including delay and lag dominant ones. The design is novel at it is based on a new approximation approach, the non-rational transfer function method. This allows for a more accurate approximation of the process dead-time and ensures an improved closed loop response. The main problem with fractional order controllers is concerned with their implementation as higher order transfer functions. In cases where central processing unit CPU, bandwidth allocation, and energy usage are limited, resources need to be efficiently managed. This can be achieved using an event-based implementation. The novelty of this paper resides in such an event-based algorithm for fractional order IMC (FO-IMC) controllers. Numerical results are provided for lag and delay dominant FOPDT processes. For comparison purposes, an integer order PI controller, tuned according to the same performance specifications as the FO-IMC, is also implemented as an event-based control strategy. The numerical results show that the proposed event-based implementation for the FO-IMC controller is suitable and provides for a smaller computational effort, thus being more suitable in various industrial applications. Full article
(This article belongs to the Special Issue Applications of Mathematical Models in Engineering)
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