Mathematical Model For Control Research Articles

Mathematical model for prevention and control of cholera transmission in a variable population

Mathematical model for prevention and control of cholera transmission in a variable population

Ant Colony Optimization based Optimal Tuning of Fractional Order (FO) PID Controller for controlling the Speed of a DC Motor

This paper deals with the use of a FOPID Controller for the direct current motor speed controlling process. FOPID Controller consists of fractional integral-derivative terms along with the integer order proportional terms. It is a specific controller in which orders of derivative and integral lie in between fractions of 0 and 1. Mathematical model of DC motor and controller is presented whose field has been excited by an external source. In this paper, the simulation part of a DC motor for controlling its speed using a FOPID Controller has been performed. There are five degrees of freedom in FOPID controller contrary to traditional PID controller which have only three. The values of the five parameters (Kp, Ki, Kd, λ, μ) of a FOPID Controller have been improved by reducing the ITAE (Integral Time Absolute Error) cost to best possible value using the ACO i.e. Ant Colony Optimization Technique. The closed loop ZNT (Ziegler-Nichols Tuning) method used for the tuning of DC motor. Simulink model of proposed system has been developed and simulated to find out the minimum cost. The intensification in the steady and transient behaviors of the system. The results also exhibit significant improvement in the rise time, settling time and peak overshoot as compared to the other optimization methods.

Application of Artificial Intelligence and Computer Vision Technologies in Solving Problems of Automation of Processing and Recognition of Biological Objects

The article considers the application of artificial intelligence and computer vision technologies to solve the automation of processing and analysis of botanical micro and macro objects (images of fern spores). Also, there is a problem of developing software for a digital twin of an agrobot. The first problem is an interdisciplinary research aimed at solving applied and fundamental problems in botanical objects' biosystematics and studying microevolutionary processes using computer vision technologies, methods of intelligent image analysis, machine learning, and artificial intelligence. The article presents the developed software module FAST (Functional Automated System Tool) for solving the direct problem — performing measurements from images obtained by scanning electron microscopy, virtual herbaria image library, entomological collections, or images taken in a natural environment.
 The second problem is software development for the digital twin of the agrorobot, designed for precise mechanical processing of plants and soil. The proposed solution includes several components: the control unit — NVIDIA Jetson NANO computing module; the actuator — 6-axis robotic arm; the machine vision unit based on an Intel RealSense camera; the chassis unit — tracked tracks and software drivers and components for their control. The digital twin of the robot considers the environmental conditions and the landscape of the operation area.
 The use of ROS (Robot Operating System) allows minimal effort to transfer a digital model to a physical one (prototype and serial robot) without changing the source code. Furthermore, consideration of the environmental conditions during the programming stage provides opportunities for further development and testing of real-life mathematical models for device control.

Indirect field-oriented control of twin-screw electromechanical hydrolyzer

Goal. Development of a mathematical model of indirect field-oriented control of a twin-screw electromechanical hydrolyzer. Methodology. The paper presents a mathematical model of Indirect field-oriented control of twin-screw electromechanical hydrolyzer. The mathematical model was developed in the MATLAB / Simulink software environment. The determination of the main parameters of a twin-screw electromechanical hydrolyzer was carried out by developing a finite element model in the Comsol Multiphysics software environment. Results. Based on the results of a mathematical study, graphical dependences of the distribution of magnetic induction in the air gap of a ferromagnetic rotor, a spatial representation of the distribution of magnetic induction on a 3D model of a ferromagnetic rotor of a twin-screw electromechanical hydrolyzer were obtained. The results of finite element modeling were confirmed by a practical study of a mock-up of a ferromagnetic rotor of a twin-screw electromechanical hydrolyzer. By implementing the MATLAB / Simulink model, graphical dependences of the parameters of the ferromagnetic rotor of a twin-screw electromechanical hydrolyzer are obtained under the condition of a stepwise change in the torque and a cyclic change in the angular velocity. Originality. The paper presents an implementation of the method of indirect field-oriented control for controlling the ferromagnetic rotor of a twin-screw electromechanical hydrolyzer. The work takes into account the complex design of the ferromagnetic rotor of a twin-screw electromechanical hydrolyzer. Practical significance. The practical implementation of the results of mathematical modeling makes it possible to achieve effective control of a complex electromechanical system, allows further research to maintain the necessary parameters of the technological process and to develop more complex intelligent control systems in the future.

A mathematical model for cell cycle control: graded response or quantized response

ABSTRACT Cell cycle is an important and complex biological system. A lot of efforts have been put in understanding cell cycle arrest for its vital role in clinical therapies. The cell-cycle-arrest outcomes upon stimulation are complicated. The response could be stringent or relaxed, and graded or quantized. A model fully addressing various cell-cycle-arrest outcomes is to be developed. Here, we developed a mathematical model of cell cycle control incorporating distinct characteristics of various cell-cycle-arrest outcomes. The model can simulate two typical properties of cell cycle arrest, quantized and graded. We also characterized the inheritable quiescence and refractory state, which were crucial in long-term response of the population. Then, we monitored cells respond to multiple stimulations, and the results indicated that cells responded to stimulations with small interval did not induce significantly sustained cell cycle arrest as the existence of refractory state. Our work will benefit fundamental research and make efforts to predicting outcomes of clinical therapeutics.

Theory of centrosome size control via localized assembly and distributed disassembly of pericentriolic matter

How centrosomes control their size and growth, despite continuous turnover in their component parts, is a longstanding question. Recent studies suggest that size control of centrosomes is achieved through the depletion of a limiting subunit pool in the cytoplasm. While the limiting pool model ensures centrosome size scaling with cell size, it does not ensure robust size control of a pair of centrosomes in the presence of stochasticity. Here we present a mathematical model for centrosome size control via localized assembly and distributed disassembly of the pericentriolic matter (PCM) in a limiting cytoplasmic pool.

Dynamic Discrete Inventory Control Model with Deterministic and Stochastic Demand in Pharmaceutical Distribution

This paper presents an inventory control problem in a private pharmaceutical distribution company from the Republic of Serbia. The company realizes that distribution within nine neighbouring countries and inventory control in the pharmaceutical supply chain is centralized. In order to constitute a conceptual model of the problem, we propose the modern control theory concept. The conceptual model is based on the specific practical assumptions and constraints of the supply chain. Thereafter, a dynamic discrete mathematical model of inventory control is formulated to reflect elements of the system and their relations. The model considers multiple pharmaceutical products, variable lead time, realized stochastics and deterministic demand, and different ordering policies (Lot for Lot and Fixed Order Quantity). Deterministic demand is represented as a sales forecast for each product per month, while stochastic demand is generated as a random variation of sales forecast in a range of ±20%. Two objective functions are defined as the maximization of the difference between planned average inventory level and realized average inventory level, and the minimization of stock-out situations. We develop a procedure for the determination of reorder points and the number of deliveries to achieve proposed objective functions. The model overcomes shortages of theoretically-based distribution requirements planning models and offers solutions to the limitations in inventory control practice. Real-life data, collected over two years, are used for the validation of the proposed model and the solution procedure. Numerical examples illustrate the model application and behaviour.

Multiparameter Identification of Permanent Magnet Synchronous Motor Based on Model Reference Adaptive System—Simulated Annealing Particle Swarm Optimization Algorithm

The accurate identification of permanent magnet synchronous motor (PMSM) parameters is the basis for high-performance drive control. The traditional PMSM multiparameter identification method experiences problems with the uncertainty of the identification results and low identification accuracy due to the under-ranking of the mathematical model of motor control. A multiparameter identification of PMSM based on a model reference adaptive system and simulated annealing particle swarm optimization (MRAS-SAPSO) is proposed here. The algorithm first identifies the electrical parameters of the PMSM (stator winding resistance R, cross-axis inductance L, and magnetic linkage ψf) by means of the model reference adaptive system method. Second, the result is used as the initial population in particle swarm optimization identification to further optimize and identify the electrical and mechanical parameters (moment of inertia J and damping coefficient B) in the motor control system. Additionally, in order to avoid problems such as premature convergence of the particle swarm in the optimization search process, the results of the adaptive simulated annealing algorithm to optimize multiparameter identification are introduced. The simulation experiment results show that the five identification parameters obtained by the MRAS-SAPSO algorithm are highly accurate and stable, and the errors between them and the real values are below 2%. This also verifies the effectiveness and reliability of this identification method.

Research on the decision support system for optimal operation of large reservoir power generation

In order to give full play to the efficiency of power generation and improve the utilization rate of water resources, the optimal operation of reservoir power generation has become one of the hot researches by the experts and scholars. Luntan Key Water-Control Project is taken as an example, which gives consideration to the comprehensive benefits of flood control and power generation. Based on building both the mathematical models of flood pre-release control and the medium-long term power generation, a decision support system with fast online optimization is developed by using SOA architecture and J2EE technology. The results show the system can improve the operation level of the reservoir power generation, reduce effectively the water abandoning rate, realize the scientific optimal operation, provide scientific basis for the management decision, and create more comprehensive benefits.

A Mathematical Model for Effective Control and Possible Eradication of Malaria

In this paper, a deterministic mathematical model for the transmission and control of malaria is formulated. The main innovation in the model is that, in addition to the natural death rate of the vector (mosquito), a proportion of the prevention efforts also contributes to a reduction of the mosquito population. The motivation for the model is that in a closed environment, an optimal combination of the percentage of susceptible people needed to implement the preventative strategies (α) and the percentage of infected people needed to seek treatment can reduce both the number of infected humans and infected mosquito populations and eventually eliminate the disease from the community. Prevention effort α was found to be the most sensitive parameter in the reduction of ℛ0. Hence, numerical simulations were performed using different values of α to determine an optimal value of α that reduces the incidence rate fastest. It was discovered that an optimal combination that reduces the incidence rate fastest comes from about 40% of adherence to the preventive strategies coupled with about 40% of infected humans seeking clinical treatment, as this will reduce the infected human and vector populations considerably.

Improvement of a Mathematical Model and Model Predictive Control for Strip Steering Control in Hot Strip Finishing Mill

Improvement of a Mathematical Model and Model Predictive Control for Strip Steering Control in Hot Strip Finishing Mill

Neuroscience Perspectives on Adaptive Manual Control with Pursuit Displays

Cyberneticists develop mathematical human control models which are used to tune manual control systems and understand human performance limits. Neuroscientists explore the physiology and circuitry of the central nervous system to understand how the brain works. Both research human visuomotor control tasks, such as the pursuit tracking task. In this paper we discuss some commonalities and differences in both approaches to better understand the adapting human controller. Special attention is given to Adaptive Model Theory, which studied adaptive human control using several linear and nonlinear control engineering techniques. The insights gained yield schemes and concepts which pave the way for key future work on this topic.

Probabilistic Perspective on Compensatory, Pursuit and Preview Manual Control

Mathematical human control models are widely used in tuning manual control systems and understanding human performance. Human behavior is commonly described using linear time-invariant models, averaging-out all non-linear and time-varying effects, which are gathered into the remnant. These models are limited in their capability to capture particular tracking strategies that an experienced subject may learn to use. In this paper, we consider manual control from a different perspective, namely through investigating the probability densities of the tracking error for different regions of the target signal amplitude. Results show that distinct strategies become apparent for compensatory, pursuit and preview tracking tasks. Effects of these strategies are often averaged-out by current models and can only be captured in situation-dependent models. Modeling this systematic human adaptation not captured in linear models could potentially lead to better model fits and explain/reduce part of the remnant.

Mathematical Model for False Codling Moth Control Using Pheromone Traps

False codling moth (FCM) is regarded as the most significant indigenous pest. Over 70 host plants are attacked by larval, many of which are horticultural crops with fruit, pods, and berries, such as beans, grapes, citrus, capsicum, avocado, guava, pomegranate, and ornamental plants. They eat macadamia nuts, cotton, tea, and a variety of other wild plants as well. Female moths are drawn to the flower heads as well as other parts of the plant, making this pest especially problematic on roses grown for cut flowers. Therefore, controlling this pest is of importance. For more effective control, pheromone traps are used to capture males attracted to the artificial pheromone. In this study, mathematical model of FCM control using pheromone trap is developed. The model, is based on biological and ecological assumptions, and is governed by an ODE system. The coexistence and pest free equilibria is determined through a theoretical analysis. The theoretical analysis of the model allows for the identification of pheromone threshold values that are practical for field applications. We show that there is a threshold above which the global asymptotic stability of the trivial equilibrium is guaranteed. Finally, we demonstrate the theoretical results through numerical experiments.

Control System of a Robotic Irrigation Machine Based on the Mamdani Fuzzy Algorithm

The article analyzes the tasks that can be solved by agricultural robots. The purpose of the study was the robotization of the "Fregat" type crop irrigation machine by the fuzzy control of irrigation technological processes, which allows to control the irrigation rate. It is proposed to use in a robotic irrigation machine the analog valve-setter of the speed of the last cart, powered by electricity. It is recommended to include a diagnostic subsystem in the fuzzy control system of the flow control valve, which includes sensors for measuring the soil moisture and the slope of the irrigation machine in various areas of the field. The mathematical model of fuzzy control of the irrigation machine is developed based on the software control of the water supply depending on the terrain of the field, the speed of irrigation machine and soil moisture to reduce water consumption and improve the efficiency and quality of irrigation. The Mamdani algorithm, which is implemented in the MATLAB package, is proposed as a fuzzy inference system. The formalization of the description of the indicators of the irrigation machine is carried out by specifying linguistic variables. The proposed mathematical model can be used in the design of control systems for other robotic agricultural machines.

THEORETICAL AND METHODOLOGICAL STUDY OF THE METROLOGICAL SUPPORT SYSTEM

The system of metrological support is the basis of product quality management at a machine-building enterprise. The most important element of metrological support is the real quality parameters. It was studied that the administrative management system does not create conditions for the implementation of objective technical management and, as a result, for the optimization of the management structure, reduction of production costs and quality assurance. This problem can be solved only through the development of appropriate mathematical models of metrological support systems and production process control. However, in order to build mathematical models of metrological support and production process control systems, it is necessary to establish functional and structural diagrams of the technological process and form a process for obtaining graphic models using product reliability parameters. A model is a simplified system that reflects individual elements and more important aspects of the process under study. The same process can be described by different models, and one model can describe different processes. One of the most important and difficult issues in modeling is the definition of key indicators of the system, which should more fully reflect the quality of the product. These parameters include failure, durability, time spent on product development and commissioning, etc. Thus, the problem of modeling a metrological assurance system can be formulated as follows: it is necessary to find a system that meets the aggregate requirements of the initial data, and in this case the quality indicators should have the best values in accordance with a previously selected higher criterion.

Labor flexibility integration in workload control in Industry 4.0 era

The paradigm shift toward Industry 4.0 is facilitating human capability, and at the center of the research are the workers—Operator 4.0—and their knowledge. For example, new advances in augmented reality and human–machine interfaces have facilitated the transfer of knowledge, creating an increasing need for labor flexibility. Such flexibility represents a managerial tool for achieving volume and mix flexibility and a strategic means of facing the uncertainty of markets and growing global competition. To cope with these phenomena, which are even more challenging in high-variety, low-volume contexts, production planning and control help companies set reliable due dates and shorten lead times. However, integrating labor flexibility into the most consolidated production planning and control mechanism for a high-variety, low-volume context—workload control—has been quite overlooked, even though the benefits have been largely demonstrated. This paper presents a mathematical model of workload control that integrates labor flexibility into the order review and release phase and simulates the impact on performance. The main results show that worker transfers occur when they are most needed and are minimized compared to when labor flexibility is at a lower level of control—shop-floor level—thus reducing lead time.

Model experiments with different cycloidal propeller algorithms using same electric controller

This article presents a methodology of controlling the cycloidal propeller electronically in model scale by an experimental approach. It establishes the function of single-unit controlled multiple propeller models such as Kirsten-Boeing and Voith-Schneider propeller. It also deals with the execution of different maneuvering cases like straight acceleration, autopilot, zigzag, crash stop. Blade motors independently control the pitching of the propeller-blades unlike the mechanism of the conventional cycloidal propeller. PID control and heuristic control are investigated for this purpose. Mathematical models for system identification, pulse generation, position, and speed control of propeller blades, and disc and synchronizations are demonstrated. Based on model experimental results, advantages/disadvantages of PID and heuristic control are discussed.

Model Predictive Control for Automatic Carrier Landing with Time Delay

This paper focuses on the problem of automatic carrier landing control with time delay, and an antidelay model predictive control (AD-MPC) scheme for carrier landing based on the symplectic pseudospectral (SP) method and a prediction error method with particle swarm optimization (PE-PSO) is designed. Firstly, the mathematical model for carrier landing control with time delay is given, and based on the Padé approximation (PA) principle, the model with time delay is transformed into an equivalent nondelay one. Furthermore, a guidance trajectory based on the predicted trajectory shape and position deviation is designed in the MPC framework to eliminate the influence of carrier deck motion and real-time error. At the same time, a rolling optimal control block is designed based on the SP algorithm, in which the steady-state carrier air wake compensation is introduced to suppress the interference of the air wake. On this basis, the PE-PSO delay estimation algorithm is proposed to estimate the unknown delay parameter in the equivalent control model. The simulation results show that the delay estimation error of the PE-PSO algorithm is smaller than 2 ms, and the AD-MPC algorithm proposed in this paper can limit the landing height error within ±0.14 m under the condition of multiple disturbances and system input delay. The control accuracy of AD-MPC is much higher than that of the traditional pole assignment algorithm, and its computational efficiency meets the requirement of real-time online tracking.

Mathematical model of mobile network reliability control based on nonlinear proportional differential

Mathematical model of mobile network reliability control based on nonlinear proportional differential