Model Predictive Controller Design for the Dynamic Positioning System of a Semi-submersible Platform

This paper researches how to apply the advanced control technology of model predictive control （MPC） to the design of the dynamic positioning system （DPS） of a semi-submersible platform. First, a linear low-frequency motion model with three degrees of freedom was established in the context of a semi-submersible platform. Second, a model predictive controller was designed based on a model which took the constraints of the system into account. Third, simulation was carried out to demonstrate the feasibility of the controller. The results show that the model predictive controller has good performance and good at dealing with the constraints or the system.

Mathematical Models of Tire-Longitudinal Road Adhesion and Their Use in the Study of Road Vehicle Dynamics

Mathematical models of tire-longitudinal road adhesion for use in the study of road vehicle dynamics are set up so as to express the relations of longitudinal adhesion coefficients with the slip ratio. They perfect the Pacejka's models in practical use by taking into account the influences of all essential parameters such as road surface condition. vehicle velocity. slip angle. vertical load and slip ratio on the longitudinal adhesion coefficients. The new models are more comprehensive more concise. simpler and more convenient in application in all kinds of simulations of car dynamics in various sorts of braking modes.

Mathematical Models of Tire-Lateral Road Adhesion for Use in Road Vehicle Dynamics Studies

Mathematical models of tire-lateral mad adhesion for use in mad vehicle dynamics studies are set up to express the relations of adhesion coefficients with slip ratio in lateral direction.The models of tire-lateral mad adhesion revolutionize the Pacejka's model in concept and therefore make it possible for applications in vehicle dynamics studies by the expression of lateral adhesion coefficient as a function of wheel slip ratio,instead of the wheel slip angle,taking into account in the mean time the influences of mad surface condition, vehicle velocity,vertical load,tire slip angle,and wheel camber angle.

Mathematical Model and Its Hybrid Dynamic Mechanism in Intelligent Control of Ironmaking

A hybrid dynamic model was proposed, which considered both the hydrokinetic and the chaotic properties of the blast furnace ironmaking process; and great emphasis was put on its mechanism. The new model took the high complexity of the blast furnace as well as the effects of main parameters of the model into account, and the predicted results were in very good agreement with actual data.

Mathematical modeling for dynamic stability of sandwich beam with variable mechanical properties of core

The paper is devoted to mathematical modelling of static and dynamic stability of a simply supported three-layered beam with a metal foam core. Mechanical properties of the core vary along the vertical direction. The field of displacements is for- mulated using the classical broken line hypothesis and the proposed nonlinear hypothesis that generalizes the classical one. Using both hypotheses, the strains are determined as well as the stresses of each layer. The kinetic energy, the elastic strain energy, and the work of load are also determined. The system of equations of motion is derived using Hamilton＇s principle. Finally, the system of three equations is reduced to one equation of motion, in particular, the Mathieu equation. The Bubnov-Galerkin method is used to solve the system of equations of motion, and the Runge-Kutta method is used to solve the second-order differential equation. Numerical calculations are done for the chosen family of beams. The critical loads, unstable regions, angular frequencies of the beam, and the static and dynamic equilibrium paths are calculated analytically and verified numerically. The results of this study are presented in the forms of figures and tables.

Dynamic Factor Method of Computing Dynamic Mathematical Model for System Simulation

The computational methods of a typical dynamic mathematical model that can describe the differential element and the inertial element for the system simulation are researched. The stability of numerical solutions of the dynamic mathematical model is researched. By means of theoretical analysis, the error formulas, the error sign criteria and the error relationship criterion of the implicit Euler method and the trapezoidal method are given, the dynamic factor affecting the computational accuracy has been found, the formula and the methods of computing the dynamic factor are given. The computational accuracy of the dynamic mathematical model like this can be improved by use of the dynamic factor.

Mathematical Model, Optimal Control and Transmission Dynamics of Avian Spirochaetosis

Avian Spirochaetosis is an acute endemic tick-borne disease of birds, caused by Borrelia anserins, a species of Borrelia bacteria. In this paper, we present a compartmental mathematical model of the disease for the bird population and Tick population. The disease steady-state and the conditions for reaching a stable disease-free steady state are determined. The analysis by Lyapunov method shows both local and global stability. Further investigation involves the introduction of controls to the model;the existence and uniqueness of optimal control are established. Finally, the effect of the controls is investigated using numerical solutions.

Dynamic mathematical model and numerical calculation method on spontaneous combustion of loose coal

Through the experiment of coal spontaneous combustion and relationship particle size with oxidation character of loose coal, some calculation formula of characteristic parameters is got in the process of coal spontaneous combustion. According to these theories of porous medium hydrodynamics, mass transfer and heat transfer, mathematical models of air leak field, oxygen concentration field and temperature field are set up. Through experimental and theoretical analysis, 3 D dynamic mathematical model of coal spontaneous combustion is set up. The method of ascertaining boundary condition of model is analyzed, and finite difference method is adopted to solve 2 D mathematical model.

New approach to assess sperm DNA fragmentation dynamics： Fine-tuning mathematical models

Background： Sperm DNA fragmentation（sDF） has been proved to be an important parameter in order to predict in vitro the potential fertility of a semen sample. Colloid centrifugation could be a suitable technique to select those donkey sperm more resistant to DNA fragmentation after thawing. Previous studies have shown that to elucidate the latent damage of the DNA molecule, sDF should be assessed dynamically, where the rate of fragmentation between treatments indicates how resistant the DNA is to iatrogenic damage. The rate of fragmentation is calculated using the slope of a linear regression equation. However, it has not been studied if s DF dynamics fit this model. The objectives of this study were to evaluate the effect of different after-thawing centrifugation protocols on sperm DNA fragmentation and elucidate the most accurate mathematical model（linear regression, exponential or polynomial） for DNA fragmentation over time in frozen-thawed donkey semen.Results： After submitting post-thaw semen samples to no centrifugation（UDC）, sperm washing（SW） or single layer centrifugation（SLC） protocols, sD F values after 6 h of incubation were significantly lower in SLC samples than in SW or UDC.Coefficient of determination（R-2） values were significantly higher for a second order polynomial model than for linear or exponential. The highest values for acceleration of fragmentation（aSDF） were obtained for SW, fol owed by SLC and UDC.Conclusion： SLC after thawing seems to preserve longer DNA longevity in comparison to UDC and SW. Moreover,the fine-tuning of models has shown that sDF dynamics in frozen-thawed donkey semen fit a second order polynomial model, which implies that fragmentation rate is not constant and fragmentation acceleration must be taken into account to elucidate hidden damage in the DNA molecule.

Mathematical Modelling of Work of Modern Friction-Polymer Shock Absorbers and Determining the Dynamical Force during the Impact

Shock absorbers are main elements into construction of train wagons that secure protection from longitudinal forces which appear during transitional regimes of movement. Besides, development of new constructive solutions for shock absorbers is quite popular development of their working mathematical models. This paper presents modem shock absorber with elastic block made from polymer elements that increase quantity of absorbed energy. This is achieved by increasing the stiffness characteristic of polymer elastic block. The construction is relatively simple and technology used to create the construction is with more or less low price. If there is not enough elastic stiffness of the polymer block, there is a possibility for not meeting the UIC （International Union of Railways） norms for absorbed energy. Therefore, according to the mentioned characteristic, shock absorbers are divided into three groups. The mathematical model presented in this paper allows calculating the necessary elastic characteristic of the polymer block for a short time. Differential equation of movement of the shock absorber elements is presented in this paper. Force change of polymer block for various impact velocities participates in the differential equation of movement where initial velocity V0 and the current meaning of the velocity x are taken into consideration. The presented equation is solved by using program language MATLAB/Simulink by developing a simulation model.

Mathematical Model of Dynamics of Micropolar Orthotropic Elastic Thin Bars with Free Fields of Displacements and Rotations

In the present paper, initial-boundary value problem of plane stress state of micropolar theory of elasticity is considered for orthotropic material in the domain of thin rectangle. General hypotheses are formulated, which are the qualitative results of the asymptotic method of integration of the stated initial-boundary value problem. On the basis of the accepted hypotheses general applied one-dimensional models of dynamics of bending deformation of micropolar orthotropic elastic thin bars with free fields of displacements and rotations are constructed with and without consideration of shear deformations. With the help of the constructed models different dynamic problems of micropolar bars can be studied. Here concrete problems of free and forced vibrations of hinged supported micropolar orthotropic elastic thin bar are studied. Numerical analysis is done and specific features of dynamic characteristics of micropolar material are revealed. Particularly, it is shown that there is a frequency of vibrations of the micropolar bar that does not depend on bar sizes.

Predictive Mathematical and Statistical Modeling of the Dynamic Poverty Problem in Burundi: Case of an Innovative Economic Optimization System

The mathematical and statistical modeling of the problem of poverty is a major challenge given Burundi’s economic development. Innovative economic optimization systems are widely needed to face the problem of the dynamic of the poverty in Burundi. The Burundian economy shows an inflation rate of -1.5% in 2018 for the Gross Domestic Product growth real rate of 2.8% in 2016. In this research, the aim is to find a model that contributes to solving the problem of poverty in Burundi. The results of this research fill the knowledge gap in the modeling and optimization of the Burundian economic system. The aim of this model is to solve an optimization problem combining the variables of production, consumption, budget, human resources and available raw materials. Scientific modeling and optimal solving of the poverty problem show the tools for measuring poverty rate and determining various countries’ poverty levels when considering advanced knowledge. In addition, investigating the aspects of poverty will properly orient development aid to developing countries and thus, achieve their objectives of growth and the fight against poverty. This paper provides a new and innovative framework for global scientific research regarding the multiple facets of this problem. An estimate of the poverty rate allows good progress with the theory and optimization methods in measuring the poverty rate and achieving sustainable development goals. By comparing the annual food production and the required annual consumption, there is an imbalance between different types of food. Proteins, minerals and vitamins produced in Burundi are sufficient when considering their consumption as required by the entire Burundian population. This positive contribution for the latter comes from the fact that some cows, goats, fishes, ···, slaughtered in Burundi come from neighboring countries. Real production remains in deficit. The lipids, acids, calcium, fibers and carbohydrates produced in Burundi are insufficient for consumption. This negative contribution proves a Burundian food deficit. It is a decision-making indicator for the design and updating of agricultural policy and implementation programs as well as projects. Investment and economic growth are only possible when food security is mastered. The capital allocated to food investment must be revised upwards. Demographic control is also a relevant indicator to push forward Burundi among the emerging countries in 2040. Meanwhile, better understanding of the determinants of poverty by taking cultural and organizational aspects into account guides managers for poverty reduction projects and programs.

Robust Fuzzy Sampled-Data Control for Dynamic Positioning Ships

A robust H∞sampled-data stabilization problem for nonlinear dynamic positioning(DP) ships with Takagi-Sugeno(T-S) fuzzy models is discussed in this paper. Input delay approach is used to convert the sampleddata DP ship system to a fuzzy system with time-varying delay. Adequate conditions are derived to determine the system's asymptotical stability and achieve H∞performance via Lyapunov stability theorems. Then, the fuzzy sampled-data controller is obtained by analyzing the stabilization condition. Simulation result shows that the proposed method and the designed controller for a DP ship are effective so that the DP ship can maintain the desired position, heading and velocities in the existence of varying environment disturbances.

Hybrid Dynamic Variables-Dependent Event-Triggered Fuzzy Model Predictive Control

This article focuses on dynamic event-triggered mechanism(DETM)-based model predictive control(MPC) for T-S fuzzy systems.A hybrid dynamic variables-dependent DETM is carefully devised,which includes a multiplicative dynamic variable and an additive dynamic variable.The addressed DETM-based fuzzy MPC issue is described as a “min-max” optimization problem(OP).To facilitate the co-design of the MPC controller and the weighting matrix of the DETM,an auxiliary OP is proposed based on a new Lyapunov function and a new robust positive invariant(RPI) set that contain the membership functions and the hybrid dynamic variables.A dynamic event-triggered fuzzy MPC algorithm is developed accordingly,whose recursive feasibility is analysed by employing the RPI set.With the designed controller,the involved fuzzy system is ensured to be asymptotically stable.Two examples show that the new DETM and DETM-based MPC algorithm have the advantages of reducing resource consumption while yielding the anticipated performance.

Mathematical Simulation of Dynamic Heat Transfer in a Human-Clothing-Environment System

A mathematical model has been developed to describe the dynamic heat transfer in the clothing microclimate under transient wear conditions. This model is solved numerically by the implicit finite difference method. If the physical activity and ambient conditions are specified, the model can predict the thermoregulatory response of the body. Experimental measurements with garments made of fibers with different levels of hygroscopicity are compared with predictions by the model. There is good agreement between prediction and experiment for the temperature of the clothing microclimate.

A Dynamic Modeling Analysis of Loom Dobbies and a Converted Positive Dobby Introduced

There are two different types of dobbies used for weavingmachines,i.e.the negative and the positive ones.In or-der to compare them,a dynamic modeling analysis ishere dealt with.Since the dynamic behavior of the posi-tive dobby is better,an electronic positive dobby conve-rted from the negative one(Staubli 2500 series)is prop-osed at the end of the paper.

A new model for evaluating the dynamic shear strength of rocks based on laboratory test data for earthquake-resistant design

The dynamic shear strength of rocks is required for the earthquake-resistant design of nuclear power plants in Japan.This research aims to propose a mathematical model for estimating the dynamic strength and to validate the model.Two different types of specimens were prepared for the model validation,and the monotonic and cyclic loading tests were conducted to obtain the mathematical model parameters.Subsequently,multistep cyclic loading tests were performed,followed by simulations using the mathematical model.The test results demonstrated that the dynamic shear strength exceeded the static shear strength,which agreed with previous researches.Furthermore,the dynamic shear strength calculated using the mathematical model was generally consistent with that obtained from the experimental data.

Mathematical modelling of translational motion of rail-guided cart with suspended payload

In this paper modelling of the translational motion of transportation rail-guided cart with rope suspended payload is considered. The linearly moving cart,driven by a travel mechanism,is modelled as a discrete six degrees of freedom (DOF) dynamic system. The hoisting mechanism for lowering and lifting the payload is considered and is included in the dynamic model as one DOF system. Differential equations of motion of the cart elements are derived using Lagrangian dynamics and are solved for a set of real-life constant parameters of the cart. A two-sided interaction was observed between the swinging payload and the travel mechanism. Results for kinematical and force parameters of the system are obtained. A verification of the proposed model was conducted.

Mathematical Model and Advanced Control for Gas-phase Olefin Polymerization in Fluidized-bed Catalytic Reactors

In this study, the developments in modeling gas-phase catalyzed olefin polymerization fluidized-bed reactors （FBR） using Ziegler-Natta catalyst is presented. The modified mathematical model to account for mass and heat transfer between the solid particles and the surrounding gas in the emulsion phase is developed in this work to include site activation reaction. This model developed in the present study is subsequently compared with well-known models, namely, the bubble-growth, well-mixed and the constant bubble size models for porous and non porous catalyst. The results we obtained from the model was very close to the constant bubble size model, well-mixed model and bubble growth model at the beginning of the reaction but its overall behavior changed and is closer to the well-mixed model compared with the bubble growth model and constant bubble size model after half an hour of operation. Neural-network based predictive controller are implemented to control the system and compared with the conventional PID controller, giving acceptable results.

MODELING OF OCCUPANT DYNAMIC RESPONSE TO CAR-BARRIERS CRASH ON HIGHWAY

The dynamic response involved in car-roadside barrier impacts is studied. Therisk of occupant injures in such accidents is investigated. An approach based on accident analysisand mathematical modeling is developed and described in three steps. Firstly a study of car-roadsidebarrier impact accidents is carried out with available data to define a system including car, road,roadside barrier, and occupant. Secondly a mathematical model to simulate car-to-barrier impact isdeveloped by using multi-body program MADYMO. Finally, dynamic responses of the occupant duringimpact are simulated using a car compartment model with a HYBRID III occupant model and an inputload pulse calculated in the second step. The dynamic responses of the car are analyzed by changingimpact conditions such as impact angle and impact velocity. The injury risks of the occupants arediscussed in terms of the occupant kinematics and calculated parameters: accelerations of the head,chest, and pelvis, as well as HIC value. Verification of model with experimental data is performed.Possible counter-measures for highway vehicle traffic safety and improvement of roadside barrierdesign are presented. Research prospects in this field are also proposed.