Mathematical Model For Control Research Articles

MATHEMATICAL MODEL OF REPELLENT EFFECT IN DENGUE TRANSMISSION

Dengue is a disease caused by the dengue virus, transmitted through the bite of an infected female Aedes aegypti. Dengue virus is a member of the genus Flavivirus, family Flaviviridae. Indonesia is one of the countries with the most dengue cases in Southeast Asia. Therefore, dengue transmission must be controlled to reduce the increase in dengue cases. One of the controls is by using repellents. Repellent is one of the human protection strategies to avoid mosquito bites used by spraying or smearing. This study models dengue transmission by reviewing the effect and control of repellent. A mathematical model of repellent effect and control in dengue transmission uses a SIR compartment model. The SIR model is modified by involving mosquitoes and the human population. Repellent is used in both susceptible humans, infected humans, and recovered humans. Numerical and analytical simulations are conducted to analyze the behavior of each compartment of the mosquito and human populations in dengue transmission. Analytical results show that the factors affecting the spread of infection are the transmission rate of the dengue virus and the loss of human-repellent protection. The transmission rate of dengue virus in the interval increases the infected human by 2.73%, while the rate of loss of human repellent protection in the interval increases the infected human by 0.03%. Optimal control is used to minimize the number of infected humans who do not use repellent. The results of numerical simulations on the optimal control problem show that an increase in the proportion of healthy humans who have campaign effect and use repellent regularly in the range of 14.67% can reduce infected individuals by 0.647%.

Comprehensive mathematical model for efficient and robust control of irrigation canals

Linear control-oriented models are important to represent canal dynamics for designing controllers. This study focuses on hydraulic control structure (gate) modelling to address the complex interdependent behavior inherent in irrigation canals. A comprehensive mathematical model that incorporates the water level with gate-opening to model discharge is introduced for single and multiple canal pool scenarios. The proposed model captures the hydraulic coupling within and among canal pools, a key finding. The model is evaluated extensively under uniform and non-uniform flows across three distinct canals, highlighting the model’s applicability to various systems. The uncertainty inherent within the nominal model is also assessed for varying operating conditions and hydraulic parameters. The proposed model is compared with the existing and the Saint-Venant (SV) model, showing improved accuracy in water-level predictions. This advancement in hydraulic modelling contributes to adaptable canal models essential in developing robust controllers to enhance water management in irrigation canals.

Mathematical model and electronic system for real-time O2 control in storage boxes: Development and validation under fluctuating temperatures

Modified atmosphere storage containers with gas-permeable membranes are effective in reducing post-harvest losses, mainly at low temperatures but become ineffective in controlling O2 and CO2 at temperatures above 3 °C. This study aimed to develop a method to control O2 in a storage box. This method uses a diffusion tube, that blocks air from entering the box but allows for air exchange when an air blower is activated. The blower ON frequency (BOF) was modelled as a function of temperature, considering the type and amount of produce, blower properties, tube dimension, and the O2 setpoint. The effects of temperature and gas composition on respiration rate kinetics were analysed with Michaelis-Menten and Arrhenius equations. The model was used to program the microcontroller to control the blower. Validation was performed using a 190 L box containing 25 kg of broccoli. The developed model maintained the desired O2 concentration under fluctuating temperatures. The BOF values ranged from 25.6 to 549.2 s h−1, for temperature fluctuations between 4 and 23 °C. The time required to reach the 3% O2 in the box differed depending on the blower's state. With the blower turned ON from the beginning, it took 24.9 h. However, when the blower was initially turned OFF, it took 11.1 h. Despite temperature changes, the system maintained O2 at 3.8 ± 0.29% and CO2 at 14.4 ± 0.66%. The system is promising for commercial use and best suited for CO2 tolerant produce because it requires a separate mathematical model and control mechanism.

A Mathematical Model of Lassa Fever Transmission and Control in Ebonyi State, Nigeria

Lassa virus is transmitted from rodents to humans, but it is not known whether humans can transmit Lassa fever to rats. The virus is thought to spread to humans through contact with contaminated food or surfaces. Other forms of infection include handling rodents for food (people often get rodent blood and urine on their hands) and bites. It can also spread through the use of contaminated medical equipment, such as reusing needles. The state variables of the Lassa Fever model equation is expressed as nonlinear ordinary differential equations in the technique of an initial value problem (IVP) having 10 parameters. As a result of measuring the spread of Lassa fever and determining the stability equilibrium, Lassa fever was found to be stable at an equilibrium point <i>ε</i><sub>0</sub> for which the basic reproduction number <I>R</I><sub>0</sub>< 1. This paper optimized three control measures as a means to limit the spread of Lassa fever. The first two measures - regular hand washing and keeping homes and environment clean reduced the rate and impact of transmission between rodents and humans and the treatment of Lassa fever patients reduce transmission to human hosts, which were achieved by the operation of Pontryagin’s Maximum Principle. Therefore, the results of this study demonstrate that the joint control measures adopted in this paper are effective strategies to combat the spread of disease.

Research on force/position switching control of servo actuator for hydraulically driven joint robot

According to the robot’s walking motion characteristics, the position/force switching control is studied to realize the segmental control of the robot stroke. This stroke is controlled by position when the foot end of the robot descends from the suspension to the ground. To avoid excessive contact force when the robot touches the ground, force control is carried out when the foot touches the ground. Due to the force and position control methods and control parameters of the hydraulic quadruped robots are different, the precise mathematical model for the joint position control and joint force control of the leg joints of the hydraulic quadruped robot is established using the system identification method. A fuzzy multi-model switching algorithm is proposed to solve the problem of jumping and jitter of system parameters in the process of force/position switching. Through simulation and prototype experiments, fuzzy multi-model switching is compared with direct switching and multi-model switching, and the switching effect of the algorithm is verified.

A Model of an Automated Electronic Document Management System Operating under Conditions of Probable Compromise of Signature Keys, Based on a Hierarchical Decomposition of Trusted Storage Environments

The results of an analysis of the functioning of the electronic document management system in the context of the development of methods and means of cryptanalysis and an avalanche increase in the number of processed documents are presented. A conceptual model and method for decomposing the storage subsystem into contours of operational and long-term storage of electronic documents are proposed. A mathematical model of hierarchical control of the integrity of electronic documents is presented, which takes into account the integrative properties of electronic documents, as well as requirements for storage periods and information security. The methodology and results of assessing the advantages of the developed technical solution based on the logical-probabilistic method are presented.

Security-aware analytical framework : A mathematical model and machine learning for dynamical system control in secure environments

This study presents a Security-Aware Analytical Framework (SAAF) that is meant to make dynamic system control better in safe places. The framework uses a new mathematical model and advanced machine learning methods to make vital systems more resistant to possible security threats. The mathematical model gives a defined picture of how the system works and where its security holes are. This makes it possible to measure risks and come up with proactive control strategies. Using machine learning techniques, the system changes with changing danger scenarios, allowing for identification and reaction to threats in real time. A risk evaluation tool, a dynamic danger prediction model, and an adaptable control system are some of the most important parts of the SAAF. The risk assessment tool checks for weaknesses in the system, and the dynamic threat prediction model uses machine learning to guess when security might be broken. These guesses are used by the adaptive control method to change system settings on the fly, which improves security without lowering working efficiency. The suggested framework works well by being simulated in a number of safe settings. These settings show how it can reduce security risks and make sure that dynamic systems are strong even as threats change. This study helps to improve methods that focus on security for protecting key assets.

Software Control of the Movement of a Differential Drive Robot for Different Friction Models

Introduction. Designing motion control systems for mobile robots requires the construction of mathematical models. Researchers have repeatedly addressed this topic. In particular, works have been published on the calculations of multiphysical processes, modeling the movement of various types of wheels under certain conditions. In addition, the dynamics of deformable contacting bodies during sliding, rolling and rotation, issues of autonomy and controllability of mobile robots were considered. Note, however, that the dynamics and positioning accuracy of wheeled robots is largely determined by friction. The literature does not present studies on the dynamics of a robot with a differential drive taking into account the interrelationships of sliding, spinning and rolling friction effects based on the theory of multicomponent friction. Research in this area can reveal new dynamic effects. Based on the data obtained in this way, it is possible to improve the accuracy of positioning in building mathematical control models. The presented work aims at investigating the movement of an automatic device with a differential drive taking into account three contact models: nonholonomic, Coulomb friction, and multicomponent models.Materials and Methods. The scheme of a two-wheeled robot with differential drive and continuous movement on the support surface was adopted as the basic one. The movement of the device was provided through software control. The dynamics was described in the form of Appel equations. Mathematical models were used for calculations, taking into account friction in different ways. Coordination of the actions of the mechanism was formed at a dynamic level. The control actions were the moments of the wheel motors. When visualizing the models under study, the built-in numerical methods of the Wolfram Mathematica system were used with a minimum accuracy of 10-6.Results. When building a mathematical model, the equations for the angular velocities of the wheels were determined. The authors took into account the presence of a contact site and derived the equations of dynamics of a differential drive robot. The elements of the system were force and moment projections, indicators of platform spin, masses, angular accelerations, and inertia of the wheels. It was shown how control actions were formed within the framework of nonholonomic mechanics. The model of engines that created a moment of control on the driving wheels was described. The solution was derived as the relationship between the inductance of the conductors of electric motors and the operation of the power supply. Three models describing the dynamics of a differential drive robot were examined in detail. The first model was nonholonomic. The second and third included a system of equations for the dynamics of a differential drive robot for a general case with a contact platform. At the same time, in the second model, the switching time in the engine was ignored and the Coulomb friction was involved. In the third model, a parameter to determine the speed of transients in the engine was introduced, and Pade decomposition was involved. This was a model with multicomponent friction. The calculation results were shown in the form of graphs. On them, the studied models were visualized in the form of curves of different colors. Comparison of the graphs showed in which cases, after the completion of transients, the control provided the required accuracy. These were models 1 and 2. In model 3, the software control generated an error in the angular velocity of rotation of the platform. This error could not be predicted within the framework of the 1st and 2nd models. In all the systems considered, the sliding speed of the wheels in the transverse direction dropped to zero. The condition of continuous motion of the support wheel was obtained and validated.Discussion and Conclusion. Software control is acceptable in models that do not take into account wheel friction during simultaneous sliding, spinning and rolling (general case of spatial motion). However, it is important to consider the relationship between these processes and multicomponent friction. This is required for the robot to perform program movements more accurately. It was established that software control in a model that takes into account the friction of spinning and rolling caused deviations from the program values of the angular velocity of the platform. The results obtained can be used in the building of a control system with predictive models.

A deterministic mathematical model for optimal control of diphtheria disease with booster vaccination

Diphtheria is an infectious disease caused by a strain of Corynebacterium diphtheria and forms part of the childhood vaccine-preventable diseases. The Diphtheria vaccine is a component of one of the routine vaccines given to children thrice before their first birthday. The protection against diphtheria derived from the diphtheria vaccine in infancy wanes in later childhood, necessitating a booster dose to protect the child as they grow older. To determine the impact of a booster dose of the diphtheria vaccine amidst a contaminated environment, a diphtheria model that incorporates a vaccine booster and a contaminated environment is formulated. The reproduction number R0 is computed and used to prove the local and global stability of the disease-free equilibrium. Global sensitivity analysis is conducted via the application of Latin Hypercube Sampling (LHS) with a Partial Rank Correlation coefficient on the infected humans and the contaminated environment to deduce the most sensitive parameters of the dynamics of diphtheria disease. Then, the model is further extended based on the result of the global sensitivity analysis by introducing four time-dependent controls, disinfection, screening/treatment, booster vaccination, and hygiene practice, to form an optimal control model. The control model is analyzed using Pontryagin’s maximum principle. The numerical simulation shows that diphtheria disease will reduce drastically in the community if any control combination involves booster vaccination since the diphtheria vaccine in infancy wanes after ten years. In a situation where there are limited resources to implement all the controls simultaneously, it is recommended to implement any two of the combined controls: disinfection of the environment and administration of booster vaccination or screening/treatment of the asymptomatic infected and administration of booster vaccination. The study shows that the best combination is to disinfect the environment, screen/treat the asymptomatic infected humans, and administer booster vaccination to the community.

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.

Study on dynamic control system of tunnel variable air volume ventilation based on first-order delay and predictive compensation control model

Using a variable air volume ventilation system is an efficient way to save energy in the tunnel. To address the issues of low control parameter accuracy and high operating energy consumption, the transient flow field and ventilation resistance characteristics were analyzed using conservation equations, and the first-order delay mathematical model of tunnel ventilation control was established by taking tunnel and jet fan parameters into account. The airflow dynamic control model's related parameters and transfer function were also solved. The overshoot, steady value, and adjustment time of the control system were evaluated using simulation and experiment. In full-scale experiments, the required wind speed was converted into the frequency of the jet fans to achieve variable air volume ventilation control. The results show that the variable air volume ventilation control system has the characteristics of nonlinear, and the first-order delay time transfer function is related to the 1/2-th power of ventilation resistance and pressure. The control system performs well, and the response parameters are all within the error range. Moreover, the discussion results of the comparative tests also illustrated that the purpose of dynamic wind speed adjustment could be achieved through frequency conversion control.

Active Vibration Control Using Loudspeaker-Based Inertial Actuator with Integrated Piezoelectric Sensor

With the evolution of the aerospace industry, structures have become larger and more complex. These structures exhibit significant characteristics such as extensive flexibility, low natural frequencies, numerous modes, and minimal structural damping. Without implementing vibration control measures, the risk of premature structural fatigue failure becomes imminent. In present times, the installation of inertial actuators and control signal acquisition units typically requires independent setups, which can be cumbersome for practical engineering purposes. To address this issue, this study introduces a novel approach: an independent control unit combining a loudspeaker-based inertial actuator (LBIA) with an integrated piezoelectric ceramic sensor. This unit enables autonomous vibration control, offering the advantages of ease of use, low cost, and lightweight construction. Experimental verification was performed to assess the mechanical properties of the LBIA. Additionally, a mathematical model for the LBIA with an integrated piezoelectric ceramic sensor was developed, and its efficacy as a control unit for thin plate structure vibration control was experimentally validated, showing close agreement with numerical results. Furthermore, the LBIA’s benefits as an actuator for low-frequency mode control were verified through experiments using external sensors. To further enhance control effectiveness, a mathematical model of the strain differential feedback controller based on multi-bandpass filtering velocity improvement was established and validated through experiments on the clamp–clamp thin plate structure. The experimental results demonstrate that the designed LBIA effectively reduces vibration in low-frequency bands, achieving vibration energy suppression of up to 12.3 dB and 23.6 dB for the first and second modes, respectively. Moreover, the LBIA completely suppresses the vibration of the fourth mode. Additionally, the improved control algorithm, employing bandpass filtering, enhances the effectiveness of the LBIA-integrated sensor, enabling accurate multimodal damping control of the structure’s vibrations for specified modes.

APPLICATION OF THE SCENARIO APPROACH TO THE ANALYSIS AND CONTROL OF RISKS IN THE OPERATION OF COMPLEX DYNAMIC SYSTEMS UNDER CONDITIONS OF INTERVAL UNCERTAINTY

Introduction. The paper provides a description of the scenario approach to risk control in the operation of complex technical systems under conditions of uncertainty. The scenario is understood as the optimal control action on the system parameters, which allows minimizing the possible costs associated with the implementation of the corresponding risk event.
 The aim of the study is to develop effective risk management methods for the operation of a complex dynamic system under conditions of uncertainty based on a scenario approach that makes it possible to implement the optimal control action on the parameters of an object in the event of a threat of an emergency.
 Materials and methods. The article describes the application of the scenario method to the management of risks that arise during the operation of a complex dynamic system under conditions of interval uncertainty. This approach is based on the application of methods of interval analysis and the theory of situational management.
 The scientific novelty of the implemented approach lies in the use of the interval analysis apparatus, which makes it possible to most correctly take into account the possible errors associated with measuring the values of the system parameters and apply the optimal control actions necessary for correction in the event that the permissible indicators go beyond the operability area.
 Discussion and conclusion. The mathematical model of risk control developed in the course of the study carried out during the process of functioning of a complex technical system under conditions of interval uncertainty based on the scenario approach allows the selection of optimal control actions (scenarios) that allow minimizing possible errors and inaccuracies that arise due to deviation from the calculated nominal values.

A Dynamic Control Model of the Blades Position for the Vertical-Axis Wind Generator by a Program Method

This article discusses the construction of a dynamic model for controlling the position of the blades of a vertical-axis wind generator using an automatic approach; a method is presented that relates the rotation of the motor to the position of the blades, which allows the optimization of the operation of the control system. In the research process, an automatic approach is used, which makes it possible to carry out numerical calculations that predict the behavior of the system at various values of motor rotation. The model allows us to analyze the dependence of the position of the blades on the rotation of the motor and determine the optimal parameters of the mathematical control model. The main goal of our study is to develop a mathematical model of the mechanism for further adjustment of the wind turbine blade position control system depending on the wind speed.

An optimal control model for Covid-19 spread with impacts of vaccination and facemask

A non-linear system of differential equations was used to explain the spread of the COVID-19 virus and a SEIQR model was developed and tested to provide insights into the spread of the pandemic. This article, which is related to the aforementioned work as well as other work covering variations of SIR models, Hermite Wavelets Transform, and also the Generalized Compartmental COVID-19 model, we develop a mathematical control model and apply it to represent optimal vaccination strategy against COVID-19 using Pontryagin's Maximum Principle and also factoring in the effect of facemasks on the spread of the virus. As background work, we analyze the mathematical epidemiology model with the facemask effect on both reproduction number and stability, we also analyze the difference between confirmed COVID-19 cases of the Quarantine class and anonymous cases of the Infectious class that is expected to recover. We also apply control theory to mine insights for effective virus spread prevention strategies. Our models are validated using Matlab mathematical model validation tools. Statistical tests against data from Jordan are used to validate our work including the modeling of the relation between the facemask effect and COVID-19 spread. Furthermore, the relation between control measure ξ, cost, and Infected cases is also studied.

Development of a mathematical model for assessing the quality of service on a packet switching subnet

Currently, data traffic is growing rapidly, and ensuring optimal network performance and effective data flow management have become the most important tasks. In this context, the quality of network service plays a crucial role in achieving these goals. This article suggests an approach to solving the problem of efficient service in ISDN. Namely, optimization of resource distribution between channel switching and packet switching subnets in ISDN to calculate optimal quality of service characteristics. In the process of ISDN design analysis, an optimization problem is compiled, where the evaluation of the packet-switched subnet service is used as an objective function, and the evaluation of the circuit-switched subnet service is used as one of the constraints for this task. To calculate the main characteristics of a packet-switched subnet, the subnet is considered as a service system with a delay. During the study, the methods of optimal movement of the generalized channel boundary between the subnets of channel switching and packet switching were identified, depending on the data parameters and the state of the integrated network, which made it possible to develop an optimal mathematical model of optimal control of the generalized boundary. To calculate the bandwidth for channel switching and packet switching subnets, an algorithm has been compiled to implement the resulting model and a program in C++ has been compiled. The study of the generalized boundary and the dynamic redistribution of bandwidth between subnets represents a new approach to network optimization. The results are based on the use of the classical Erlang formula for systems with service failures and on load distribution plans, which makes it possible to effectively manage the maintenance process in the network

Mathematical Model for Spread and Control of Cocoa Black Pod Disease

Black pod disease is a major threat to cocoa production worldwide. A mathematical model for the spread of cacao black pod disease is presented in this article. The model takes into account several variables that influence the spread of the disease. A set of differential equations that are numerically solved using Runge-Kutta method embedded in MATLAB software are used to simulate the dynamics of disease transmission which form the basis of the model. Utilizing information from the literature and ecological observations from cocoa fields in West Africa, where black pod disease poses a serious threat to the production of cocoa, the model was verified. The model's outcomes highlight the significance of early detection and rapid intervention in mitigating the severity of cocoa black pod disease outbreaks. Moreover, it emphasizes the importance of adopting integrated disease management approaches that consider fungicide administration and removal of infected pods. The usefulness of mathematical modeling as a tool for understanding and managing cocoa black pod disease is illustrated by this study.

Current challenges and recent advances on the path towards continuous biomanufacturing.

Continuous biopharmaceutical manufacturing is currently a field of intense research due to its potential to make the entire production process more optimal for the modern, ever-evolving biopharmaceutical market. Compared to traditional batch manufacturing, continuous bioprocessing is more efficient, adjustable, and sustainable and has reduced capital costs. However, despite its clear advantages, continuous bioprocessing is yet to be widely adopted in commercial manufacturing. This article provides an overview of the technological roadblocks for extensive adoptions and points out the recent advances that could help overcome them. In total, three key areas for improvement are identified: Quality by Design (QbD) implementation, integration of upstream and downstream technologies, and data and knowledge management. First, the challenges to QbD implementation are explored. Specifically, process control, process analytical technology (PAT), critical process parameter (CPP) identification, and mathematical models for bioprocess control and design are recognized as crucial for successful QbD realizations. Next, the difficulties of end-to-end process integration are examined, with a particular emphasis on downstream processing. Finally, the problem of data and knowledge management and its potential solutions are outlined where ontologies and data standards are pointed out as key drivers of progress.

Design of tilted and decentered anamorphic optical system based on nodal aberration control

This paper proposes a design method for tilted and decentered anamorphic projection optics. In this method, the structure is designed in groups according to the magnification requirements; the anamorphic system section’s primary aberration is analyzed based on vector aberration theory, the tilted and decentered system section’s node behavior is analyzed based on node aberration theory, and spatial ray tracing is used to control the anamorphic optical system’s pupil to be elliptical to realize pupil matching between groups. A mathematical aberration balance and constraint control model is established. The node position is used as an evaluation function such that the node is close to or within the full field, thus controlling the primary aberration for the initial system over the full field. The initial system is constructed with increased optimization potential to satisfy the aberration and structural constraints. The initial structure for the tilted and decentered anamorphic projection optics (βx=1/4,βy=1/8) is constructed with the coma and astigmatism nodes close to or within the full field. The structure is then optimized to achieve a wavefront root-mean-square error for the EUV tilted and decentered anamorphic objective with NA= 0.55 of better than 0.025λ (λ = 13.5 nm).

Multi-Objective Optimization for Controlling the Dynamics of the Diabetic Population

To limit the adverse effects of diabetes, a personalized and long-term management strategy that includes appropriate medication, exercise and diet has become of paramount importance and necessity. Compartment-based mathematical control models for diabetes usually result in objective functions whose terms are conflicting, preventing the use of single-objective-based models for obtaining appropriate personalized strategies. Taking into account the conflicting aspects when controlling the diabetic population dynamics, this paper introduces a multi-objective approach consisting of four steps: (a) modeling the problem of controlling the diabetic population dynamics using a multi-objective mathematical model, (b) discretizing the model using the trapezoidal rule and the Euler–Cauchy method, (c) using swarm-intelligence-based optimizers to solve the model and (d) structuring the set of controls using soft clustering methods, known for their flexibility. In contrast to single-objective approaches, experimental results show that the multi-objective approach obtains appropriate personalized controls, where the control associated with the compartment of diabetics without complications is totally different from that associated with the compartment of diabetics with complications. Moreover, these controls enable a significant reduction in the number of diabetics with and without complications, and the multi-objective strategy saves up to 4% of the resources needed for the control of diabetes without complications and up to 18% of resources for the control of diabetes with complications.