Initial Mathematical Model Research Articles

Identification of Wind Load Exerted on the Jacket Wind Turbines from Optimally Placed Strain Gauges Using C-Optimal Design and Mathematical Model Reduction

Wind turbine towers experience complex dynamic loads during actual operation, and these loads are difficult to accurately predict in advance, which may lead to inaccurate structural fatigue and strength assessment during the structural design phase, thereby posing safety risks to the wind turbine tower. However, online monitoring of wind loads has become possible with the development of load identification technology. Therefore, an identification method for wind load exerted on wind turbine towers was developed in this study to estimate the wind loads using structural strain, which can be used for online monitoring of wind loads. The wind loads exerted on the wind turbine tower were simplified into six equivalent concentrated forces on the topside of the tower, and the initial mathematical model for wind load identification was established based on dynamic load identification theory in the frequency domain, in which many candidate sensor locations and directions were considered. Then, the initial mathematical model was expressed as a linear system of equations. A numerical example was used to verify the accuracy and stability of the initial mathematical model for the wind load identification, and the identification results indicate that the initial mathematical model combined with the Moore–Penrose inverse algorithm can provide stable and accurate reconstruction results. However, the initial mathematical model uses too many sensors, which is not conducive to engineering applications. Therefore, D-optimal and C-optimal design methods were used to reduce the dimension of the initial mathematical model and determine the location and direction of strain gauges. The C-optimal design method adopts a direct optimisation search strategy, while the D-optimal design method adopts an indirect optimisation search strategy. Then, four numerical examples of wind load identification show that dimensionality reduction of the mathematical model leads to high accuracy, in which the C-optimal design algorithm provides more robust identification results. Moreover, the fatigue damage calculated based on the load identification wind loads closely approximates that derived from finite element simulation wind load, with a relative error within 6%. Therefore, the load identification method developed in this study offers a pragmatic solution for the accurate acquisition of the actual wind load of a wind turbine tower.

A reconstruction method for structural stress distribution of wind turbine tower using optimised mathematical model

Wind turbine towers experience complex dynamic loads during actual operation, and these loads are difficult to accurately predict in advance, which may lead to inaccurate structural strength assessment during the structural design phase, thereby posing safety risks to the wind turbine tower. Therefore, a reconstruction method for structural stress distribution of wind turbine tower was developed based on modal expansion and linear superposition theory to estimate the full-field stress distribution of a tower, which can be used for online monitoring of structural strength. The dynamic stress distribution of the tower is assumed to be the superposition of several structural modal stress distributions, in the reconstruction method for structural stress distribution developed in this study. The modes with the greatest contribution to the wind turbine structural response were selected based on the modal effective mass, and used for the base functions of an initial mathematical model for the reconstruction of structural stress distribution of the tower, in which many candidate strain gauge locations and directions were considered. Then, the initial mathematical model was expressed as a linear system of equations. Two numerical examples were used to verify the accuracy and stability of the initial mathematical model for the reconstruction of structural stress distribution of the tower, and the reconstruction results indicate that the initial mathematical model combined with the Moore–Penrose inverse algorithm can provide stable and accurate reconstruction results. However, the initial mathematical model uses too many sensors, which is not conducive to engineering applications. Therefore, D-optimal and C-optimal design methods were used to reduce the dimensions of the initial mathematical model, optimise the system of equations, and determine the location, direction and number of strain gauges. Finally, the numerical examples of stress distribution reconstruction show that dimensionality reduction of the mathematical model leads to higher accuracy, in which the C-optimal design algorithm providing a more robust reconstruction outcome.

ВИЗНАЧЕННЯ ЕФЕКТИВНОЇ ПОРИСТОСТІ ПОРІД-КОЛЕКТОРІВ ЗА ДАНИМИ СТРУКТУРИ ЇХ ПУСТОТНОГО ПРОСТОРУ У ВІЗЕЙСЬКИХ І ТУРНЕЙСЬКИХ ВІДКЛАДАХ БЕРЕЗІВСЬКОГО РОДОВИЩА

Background. Currently, it is quite important to track the patterns of the internal structure of reservoirs with their physical properties. The analysis of well-logging data in the well 203 of the Berezivske field of the Dnipro-Donetsk depression is necessary to assess the prospectivity of complexly structured reservoirs. Methods. The methodology for studying the void space structure in complexly structured reservoirs involved several stages: interpretation of well logging data; determination of parameters for the initial mathematical model of the reservoir; inversion of data from acoustic surveys into a curve of the distribution of different void formats; evaluation of reservoir rock types with determination of their effective porosity. Results. Based on the data of compressional and shear wave velocities, as well as density, three distinct rock groups were identified: compacted sandstone, calcareous sandstone and limestone. The initial approximation was obtained for each rock sample, including the set of void formats and their concentration within the reservoir layers. Direct analysis of the resulting data by the authors revealed that the most optimal void formats for the investigated intervals are: for intergranular voids – 0.07 to 0.9; for transitional voids and microcracks – 0.05 to 0.077; for microcracks – 0.007 to 0.0019; for caverns – 4 to 8. Based on the research results, it has been established that granular-cavernous porosity (39,2 %) and fracturedcavernous-granular porosity (29,5 %) are prevailing types of reservoirs. Conclusions. The calculated values of the void formats were used for these formations to quantitatively assess effective porosity based on the obtained data and specific electrical resistivity values at different depths of investigation. The resulting approximation of α = 0.6996 was selected, which reduced the error in calculating the effective porosity of reservoir rocks. The obtained results have demonstrated that the proposed methodologies are essential for understanding and quantitatively assessing the void space structure and filtration-capacitive properties of reservoir rocks, particularly when we are facing with a limited well logging data and restrictive core sampling.

METHOD OF MINIMIZATION SIDELOBES LEVEL AUTOCORRELATION FUNCTIONS OF SIGNALS WITH NON-LINEAR FREQUENCY MODULATION

Context. At present, when creating new and upgrading existing radar systems, solid-state generator devices are widely used, which imposes certain restrictions on the peak power of probing signals. To overcome this limitation, longer duration signals with internal pulse modulation are used. The main efforts of the researchers are focused on reducing the maximum level of the side lobes of the autocorrelation function of such signals, which, without taking additional measures, has a significant level, which complicates the work of systems for detecting and stabilizing the level of false alarms. Attention is paid to signals with non-linear frequency modulation, which consist of two and three linearly frequency-modulated fragments. The maximum level of the side lobes of such signals depends significantly on the frequency-time parameters of the fragments, and therefore it is very difficult to obtain its stable value. Searching for signals with minimal side lobe level values by optimizing their time-frequency parameters is a difficult task, because changing the parameters of previous signal fragments leads to changes in the parameters of subsequent fragments
 Objective. The aim of the work is to develop a method for simplifying the search for local minima of the level of side lobes of two- and three-fragment signals with nonlinear frequency modulation by using a modified mathematical model with a whole number of periods of radio oscillations of linear-frequency modulated fragments.
 Method. The developed method is based on the proposed modification of the mathematical model, which corrects the frequencytime parameters of two- and three-fragment signals with non-linear frequency modulation by modifying the values of the frequency modulation speed while providing an integer number of complete periods of radio frequency oscillations for each of the fragments, which simplifies the process of finding local minima of the level of side lobes.
 Results. Modification of the initial mathematical model leads to the expansion of the possible range of values of frequency-time parameters, ratios of durations and frequency deviations of linearly-frequency modulated fragments and ensures stability of the mathematical model with a decrease in the maximum level of side lobes of the autocorrelation function.
 Conclusions. It has been experimentally confirmed that the use of the proposed method of modifying the input frequency-time parameters of signals with non-linear frequency modulation in the vast majority of cases reduces the maximum level of side lobes and simpli-fies the process of finding its local minima. The optimal ratios of durations and deviations of the frequency of the signal frag-ments are determined, subject to these, stable operation of the models is ensured and, in most cases, - less than the value of the maximum level of the side lobes.

Mathematical modeling of robust automatic control system of magnetic levitation with uncertain parameters

The topic of the research is the development of automated control systems for real processes, which must satisfy various requirements, for example, resistance to unmodeled dynamics (robust stability), as well as meet the required quality of transient processes that arise in the case of external disturbances of various natures. In this regard, there is a need to create appropriate mathematical models for the control of non-stationary objects, the model of which includes uncertain parameters. The problem of developing and studying a mathematical model for controlling the process of electrodynamic magnetic levitation, the main problem of which is dynamic stability, is considered. It is noted that systems using the effect of magnetic levitation are widely used, for example, in shipbuilding, in elements of ship mechanisms, instrument making, as well as in the transportation of various cargoes. The relevance of the work related to the need to develop such automatic control systems that can suppress the emerging oscillatory motion of levitating bodies is substantiated. The initial mathematical model of the magnetic levitation control process, which has uncertain coefficients in differential equations and is nonlinear, is considered. To “hang” at a given (working) point of a levitating body, it is enough to create a mathematical control model in the vicinity of this point based on the linearization of the original mathematical model. A PID-based controller and feedback are added to the resulting model. The four controller coefficients are adjusted using special algorithms, taking into account the requirements for the robustness of the control system. Numerical experiments are carried out to analyze the behavior of the control system depending on the magnitude of the parameter uncertainty. Based on the analysis performed, a conclusion about the robustness of the developed control system for the object under consideration is made. The results of the study are presented in graphical form. The MATLAB system is used as a toolkit.

Расчет времени промерзания надземного водовода в условиях отрицательных температур

Purpose: When the water movement in the pipeline is stopped in conditions of negative temperatures, its freezing and destruction are possible, which leads to the failure of water supply systems for a long time. For accident-free operation of the water pipeline, it is important to know the time during which its complete or partial freezing occurs. The purpose of this work is to study the physical processes that occur during freezing, to formulate the basic mathematical model and its numerical solution, to build an analytical solution in a quasistationary approximation, to obtain formulas that are convenient for freezing time calculation and to determine the range of parameter values at which they are valid. Methods: The mathematical model of the freezing process relies on the use of energy conservation law. When constructing a difference scheme, the integrointerpolation method is used to numerically solve the nonlinear differential equations of the model. To obtain an approximate analytical solution, the method of separating equations describing processes that occur at different speeds, is used. Results: The mathematical model of pipeline freezing during water movement shutdown under conditions of constant negative temperature of the surrounding atmosphere has been formulated and substantiated. Within the framework of the quasi-stationary approximation, simple formulas for the freezing time of the water pipeline have been obtained. The criteria for the applicability of these formulas have been established. The numerical solution of equations of initial mathematical model is compared with the results obtained within quasi-stationary approximation. Practical significance: The ratios obtained in the work make it possible to estimate the time during which repair work should be carried out and the movement of water in the pipeline should be restored before its destruction due to freezing occurs.

Rostering of air traffic controllers – current practices in Europe, key performance trade-offs and future opportunities

The process of staff planning and rostering is one of the key factors affecting the performance of an Air Navigation Service Provider in terms of capacity and cost-efficiency delivered to airspace users. This paper gives a summary of previous works and current rostering practices applied at Area Control Centres (ACCs) in Europe. Furthermore, it identifies key trade-offs between rostering flexibility, capacity and productivity by establishing a relationship between ACC demand, rostering flexibility in place and the number of Air Traffic Control Officers (ATCOs) needed, as well as by exploring how varying rostering practices applied in ACCs affect spare capacity in the system. To that end, an initial mathematical model for optimizing ATCO staffing requirements has been proposed and tested on a case study involving three representative ACCs, reflecting different hourly variability in demand. The results suggest that - for different combinations of shift patterns and capacity profiles - substantial variation exists in both the minimum number of ATCOs and the associated spare ACC capacity. It has also been shown that a certain amount of spare capacity is inevitably present in the system due to inability to perfectly match ATCO hours with demand. Different options and enablers for exploiting such capacity are also discussed in the paper.

Mathematical Model of Pantograph Arc Based on Probability Distribution of Arc Parameters

Pantograph arc has become a potential hazard for the safe running of electric locomotive. It is essential to build an accurate mathematical model of pantograph arc for arc simulation. Pantograph arc experiments were carried out. And the probability distribution characteristics of arc parameters such as arc ignition moment, arc extinction moment and arc duration were analyzed. A mathematical model of pantograph arc was established. Firstly, Habedank model was selected as an initial mathematical model. The model parameters were optimized by using particle swarm optimization algorithm. Secondly, the initial mathematical model was preliminarily improved by using time-varying model parameters. Thirdly, taking into account the randomness of arc phenomenon, the model was further improved by adding a pulse function, and then the final mathematical model of pantograph arc was obtained. The pulse generation time and pulse width of the pulse function vary along with uniform distribution function and truncated normal distribution function, respectively. Finally, a simulation module of pantograph arc was designed with MATLAB software, and the effectiveness of the mathematical model was proved. The proposed model can describe the electrical characteristics of pantograph arc more accurately, and it can be used to further analyze the evolution of pantograph arc.

OBSERVER OF SPEED AND FLUX LINKAGE IN THE SYSTEM OF VECTOR CONTROL OF ASYNCHRONOUS ELECTRIC DRIVE

The use of physical sensors in electric drive control systems requires taking into account their additional dynamics in the model of the control object, which can cause problems with the synthesis of regulators due to an excessive increase in the order of the control object model. The use of observers makes it possible to recover state variables that are not available for direct measurement and to exclude additional sensors, which contributes to the improvement of operational and cost indicators of control systems. The structure of the observer in asynchronous electric drives must contain such an adaptation function that ensures the asymptotic convergence of the observer to the reference model, which is a real object of control.
 The article presents a synthesis of the speed observer and flux linkage of the rotor of an asynchronous machine in a sensorless field-oriented control system. Equations of electromagnetic processes in an asynchronous machine, formulas of coordinate converters and equations of a PI controller are used as the initial mathematical model. By transforming the differential equations of the asynchronous machine, the structure of the adaptation function is determined, which adjusts the observer model in such a way that the deviations of the stator currents from their calculated values ​​go to zero. In this way, the adaptation function, which uses the vector product of the rotor flux linkage vectors and the stator current, ensures the stability of the movement of the speed identifier.
 In the proposed observer of the speed of an asynchronous machine, which uses stator currents to ensure the asymptotic stability of the observer, in the process of research on mathematical models, self-oscillations of the speed estimate were not found, in contrast to the well-known observer, which uses deviations of the flux links. It is possible to avoid self-oscillations not only by selecting the gain factors of the PI controller, but also due to the fact that there are no integrators not covered by negative feedback in the structure of the observer's electromagnetic circuits.

Design, failure analysis, and optimization of a high-flow water valve: A case study

An 800-L/min high-flow water cartridge poppet valve with the commonly used single feed channel was designed to meet the moving speed of the hydraulic powered roof support in the coal mine. Mathematical model was used to explore the dynamic displacement of the valve, and the experimental displacement was measured to verify the accuracy of the simulation value. However, an interesting phenomenon occurred that the experimental opening and closing time of the valve becomes longer and longer with the increase of flow, even vibration appears when the flow is up to 800 L/min, and the simulation error is also getting bigger. To find the reason and solutions, the computational fluid dynamics technology is used. It is discovered that the valve is subjected to radial imbalanced force that is not considered in the initial mathematical model, which leads to big simulation error at high flow condition. Then, the new mathematical model is proposed. The relative simulation error of the response time decreases to 11.7% from 33.3% in the opening process and decreases to 4.6% from 76.9% in the closing process at 800 L/min. A symmetrical dual channel is designed to improve the performance of the valve. The imbalanced force on the dual-channel valve is 63.9% lower than that of the original valve, and the corresponding opening and closing time decreases by 37.5% and 69%, respectively. Furthermore, a double channel valve with auxiliary passage is proposed for super high flow valves. The innovation of this study is correcting the mathematical model by considering the additional radial imbalanced force induced by the asymmetrical flow channel of the valve. It is of great help to successful design of the 800-L/min water directional valve. The case study systematically provides reference for design, failure analysis, and optimization of new products in fluid engineering.

Fuzzy-interpolative control of temperatures for the intelligent rooftop greenhouse

This paper is focusing on intelligent rooftop greenhouses. An initial mathematical model implying recirculation factors for greenhouse and underneath building ventilation systems was upgraded in the sense of reducing interactions among parameters, by discarding the recirculation factors. The initial approach relied on basic fuzzy-interpolative temperature controllers working with a network of ventilation fans, adapted to the changes of the weather conditions and of the building configuration by means of a central expert adaptive rule base. This paper proposes a flexible distributed fans network, locally adapted, working under the control of temperature self-adaptive interpolative controllers. This approach enables us to adapt such buildings, that are now confined to warm temperatures, to a wide range of climates, to value a great part of renewable resources of our cities and to initiate a process of increasing the carbon offset at large scale. The new configuration is tested by simulations.

Generation of address sequences with specified switching activity and address repeatability

Objectives. The problem of developing a methodology for generating address sequences with a given switching activity and repeatability of addresses widely used in testing modern computing systems is being solved. The relevance of this problem lies in the fact that the main characteristic of the difference and their effectiveness for address sequences is the switching activity of both individual address bits and their sequences.Methods. Presented results are based on a universal method for generating quasi-random Sobol sequences, which are effectively used to generate targeted test sequences. As an initial mathematical model, a modification of the indicated generation method proposed by Antonov and Saleev is used. The main idea of proposed approach is based on the use of rectangular (m + k) × m generating matrices V of arbitrary rank r to generate address sequences.Results. The main properties of sequences generated in accordance with the new mathematical model are determined. A number of statements are given that substantiate the requirements for generator matrices to ensure the maximum period of generated sequences and the multiplicity of repetition of used addresses. The problem of synthesizing the sequences with given values of switching activity F(A) and F(ai) is solved. It is shown that in order to find a generating matrix for generating such sequences, it is necessary to solve the problem of decomposing an integer into terms. This decomposition represents the value of switching activity in the (m + k)-ary mixed number system, in which the weights of the digits are represented as powers of two from 20 to 2m+k-1, and the values of the digits w(vi) lie in the range from 0 to m+k-1. On the basis of proposed restrictions, the notion of an integer decomposition diagram similar to the Young diagram is introduced, and the operation of its modification is defined.Conclusion. The proposed mathematical model expands the possibilities of generating test address sequences with the required values of switching activity of both test sets and their individual bits. The use of generating matrices of non-maximal rank makes it possible to formalize the method of generating address sequences with even repetition of addresses.

The inverse problem of external ballistics for identifi cation of aerodynamic coeffi cients of a spin-stabilized projectile within the modifi ed point-mass trajectory model

The aim of this paper is to develop a technique for the identifi cation of the projectile aerodynamic coefficients using the free-fl ight-test measurements. An algebraic method for solving the inverse problem of external ballistics is proposed. As the initial mathematical model of the projectile fl ight, a simplifi ed version of the modifi ed point-mass trajectory model in explicit form is used. For all aerodynamic coefficients of the model, exact explicit analytic expressions for their dependence on the experimentally measurable trajectory parameters are derived. Importantly, within the proposed approach, the solution to the inverse problem is unique.

Numerical investigation of flows with condensation in micronozzles

The paper considers the numerical simulation of the flow of argon with account for the condensation process in the micronozzle and behind it. To describe phase transitions, the initial mathematical model of viscous heat-conducting gas flow is supplemented with the equation of formation and growth of condensation nuclei in the flow. The developed mathematical model allows for simulating the process of gas condensation at low pressures and temperatures. It is shown that the condensate mass fraction in the flow is not less than 1% at the pressure and temperature of 5 bar and 200 K, respectively, when argon flows out of a micronozzle to the environment with the pressure of 0.01 Pa. At the nozzle exit, the size of condensed particles reaches 80 angstroms. The obtained results confirm the necessity to take into account the condensation phenomenon in micronozzle flows of inert gases.

Development of simplified mathematical model of P-88 recovery boiler for operating modes at loads near the nominal

To improve the design of the elements of combined-cycle plants, and their structural and mode optimization, mathematical models are required. These models show energy efficiency indicators of the equipment under changing operating conditions. Modeling of recovery boilers is traditionally carried out with the application of specialized software systems that implement submodels of thermal-hydraulic calculations of the elements of the boiler water-steam and gas paths. This approach makes it difficult to solve practical tasks, since it requires licensed software and appropriate qualifications of an engineer. The current direction of solving this problem is statistical processing of the results of calculation data obtained with the application of specialized software systems, and development of a simplified mathematical model in the form of regression dependencies of boiler performance on variable parameters. In this study, the problem is solved in relation to the P-88 boiler of the combined-cycle plant-325 power unit in the load range near the nominal one. The initial mathematical model is developed with the application of the software package “TRAKT” designed for verification and engineering design of boilers. The simplified mathematical model is based on the methods of regression analysis of statistical data. The accuracy of the model is estimated based on the operational data of the combined-cycle plant -325 power unit. The authors have developed the mathematical model of the P-88 recovery boiler, which allows to determine the main performance indicators of the boiler when the electric power of the gas turbine and the outdoor air temperature are changing at the loads near the nominal value. The performance indicators are determined without application of specialized software for design calculation of the boiler. The accuracy of the initial mathematical model implemented in the software package “TRACT” is characterized by deviation of the calculation results data from the operational data in the corresponding modes of no more than 2 %. The additional uncertainty value introduced into the calculation results data does not exceed 1,5 % when we transfer from the initial mathematical model to the simplified one. The resulting mathematical description will allow solving the problems of mode optimization and evaluating the efficiency of the recovery boiler and the power unit under changing operating conditions.

Information dualism of the problem of optimum terminal control of dynamic object

The article deals with the problem of synthesis of terminal control. A functional, a nonlinear mathematical model of a dynamic object, restrictions on the maximum permissible values of control are given. The control law is synthesized. The following statement is proved: the synthesis of the optimal control is carried out using the entire initial mathematical model of the dynamical object, but to calculate the control at any particular moment of time, it is possible to use a reduced (truncated) model, which simplifies the computational algorithms. Thus, there is an informational dualism of the manage- ment task. The approach is an extension of the principle of information redefinition of Yu.B. Germeier to the area of optimal terminal control.

The Use of Core Warming as a Treatment for Coronavirus Disease 2019 (COVID-19): an Initial Mathematical Model

Background: Increasing data suggest that elevated body temperature may be helpful in resolving a variety of diseases, including sepsis, acute respiratory distress syndrome (ARDS), and viral illnesses. SARS-CoV-2, which causes coronavirus disease 2019 (COVID-19), may be more temperature sensitive than other coronaviruses, particularly with respect to the binding affinity of its viral entry via the ACE2 receptor. A mechanical provision of elevated temperature focused in a body region of high viral activity in patients undergoing mechanical ventilation may offer a therapeutic option that avoids arrhythmias seen with some pharmaceutical treatments. We investigated the potential to actively provide core warming to the lungs of patients with a commercially available heat transfer device via mathematical modeling, and examine the influence of blood perfusion on temperature using this approach. Methods: Using the software Comsol Multiphysics, we modeled and simulated heat transfer in the body from an intraesophageal warming device, taking into account the airflow from patient ventilation. The simulation was focused on heat transfer and warming of the lungs and performed on a simplified geometry of an adult human body and airway from the pharynx to the lungs. Results: The simulations were run over a range of values for blood perfusion rate, which was a parameter expected to have high influence in overall heat transfer, since the heat capacity and density remain almost constant. The simulation results show a temperature distribution which agrees with the expected clinical experience, with the skin surface at a lower temperature than the rest of the body due to convective cooling in a typical hospital environment. The highest temperature in this case is the device warming water temperature, and that heat diffuses by conduction to the nearby tissues, including the air flowing in the airways. At the range of blood perfusion investigated, maximum lung temperature ranged from 37.6°C to 38.6°C. Conclusions: The provision of core warming via commercially available technology currently utilized in the intensive care unit, emergency department, and operating room can increase regional temperature of lung tissue and airway passages. This warming may offer an innovative approach to treating infectious diseases from viral illnesses such as COVID-19, while avoiding the arrhythmogenic complications of currently used pharmaceutical treatments.

Asymptotic Estimate of Stability of a Supersonic Boundary Layer in a Vibrationally Excited Gas on a Plate

An asymptotic theory of the neutral stability curve of a supersonic boundary layer in a vibrationally excited molecular gas on a flat plate is constructed. The equations of the two-temperature viscous heat-conducting gas dynamics are considered as the initial mathematical model of the flow. On the basis of their linearization about the self-similar boundary layer solution for a perfect gas, a spectral problem is derived for the eighth-order system of linear ordinary differential equations. An algebraic secular equation with a typical decoupling into inviscid and viscous parts is derived from the linear combination of the boundary values of its solutions decreasing outside the boundary layer which solved numerically. It is shown that the neutral stability curves calculated in this way confirm the effect of increasing flow stability against the background of the relaxation process and within 12–15% agree with the previously obtained results of the direct numerical solution of the full spectral problem. The solution of the simplified system of equations for calculating the critical Reynolds number gives a similar result.

The sensorless control system for controlling the speed of direct current motor

<p>This research aims to propose an algorithm for controlling the speed of the Direct Current (DC) motor in the absence of the sensor of speed. Based on the initial mathematical model of DC motor, the authors build the dynamic state equation of DC motor, and then build an estimation model to determine the speed of the DC motor without a sensor. The advantages of the proposed method are demonstrated through the closed-loop control model using the PID controller. In order for the results to be objective, we assume that the parameters of the DC motor in the estimation model are not known correctly. The results show that the quality of control in the absence of a sensor is equivalent to the case with the sensor.</p>

AggreRATE-Pred: a mathematical model for the prediction of change in aggregation rate upon point mutation.

Protein aggregation is a major unsolved problem in biochemistry with implications for several human diseases, biotechnology and biomaterial sciences. A majority of sequence-structural properties known for their mechanistic roles in protein aggregation do not correlate well with the aggregation kinetics. This limits the practical utility of predictive algorithms. We analyzed experimental data on 183 unique single point mutations that lead to change in aggregation rates for 23 polypeptides and proteins. Our initial mathematical model obtained a correlation coefficient of 0.43 between predicted and experimental change in aggregation rate upon mutation (P-value <0.0001). However, when the dataset was classified based on protein length and conformation at the mutation sites, the average correlation coefficient almost doubled to 0.82 (range: 0.74-0.87; P-value <0.0001). We observed that distinct sequence and structure-based properties determine protein aggregation kinetics in each class. In conclusion, the protein aggregation kinetics are impacted by local factors and not by global ones, such as overall three-dimensional protein fold, or mechanistic factors such as the presence of aggregation-prone regions. The web server is available at http://www.iitm.ac.in/bioinfo/aggrerate-pred/. Supplementary data are available at Bioinformatics online.