ALGORITHM OF CONTROLLING AN ADAPTIVE HYDRAULIC CIRCUIT FOR MOBILE MACHINES

Hydraulic systems based on adjustable pumps, proportional electrohydraulic equipment and controllers are used in mobile machines. The authors propose a new scheme of the hydraulic system for mobile machines, which provides the auger drilling operation. A number of studies have shown that a certain ratio should be maintained between the frequency of auger rotation and its feed during operation, where the productivity of soil disruption should not exceed the productivity of transporting loose soil from the drilling zone. Ensuring the required ratio between the speed of the auger rotation and its feed is implemented by a controller that works according to a certain algorithm. A nonlinear mathematical model of the hydraulic system was developed to create the algorithm for controller operation and setting. The equations of the mathematical model are solved in the MATLAB-Simulink environment by the Rosenbrock method. As a result of solving the equations for the mathematical model, the dependences of variables describing the state of the hydraulic system on time are obtained. The values of the controller settings are determined at which the hydraulic system works steadily, the error of flow rate stabilization, the time for pressure adjustment and readjustment does not exceed the allowable values. The algorithm for controlling the auger feed value is formed. This algorithm provides the necessary ratio between the auger feed and speed, as well as reducing the feed rate in the case of soil hardness increases. This creates the conditions for uninterrupted pit drilling at full depth and protection of the hydraulic system from overload.

CHEMICAL CONVERSIONS OF REDUCED CARBON COMPOUNDS AND NITROGEN OXIDES IN THE CRAMPED AERODYNAMIC CONDITIONS OF THE URBAN ATMOSPHERE

The kinetics of chemical transformations of the most significant pollutants in the cramped aerodynamic conditions of the urban atmosphere is considered, i.e. in the gaps between rows of wide buildings with significant height. High concentrations created in those areas lead to sufficiently high values of reaction rates. The process is described by a stiff system of differential equations, the solution of which is performed by Rosenbrock method. The effect of reduced carbon compounds and nitrogen oxides in a wide range of their concentrations on the rate of formation of a highly toxic secondary pollutant is investigated. In the course of numerical experiments, conditions are determined that correspond to its maximum value. In that case, the transfer of substances from the reaction zone does not have time to occur.

On a method of nonlinear optimization for the comparison of spatial structure of molecules

To compare the geometry of two or more geometric structures consisting of N ordered points, and which can be considered as solids in three-dimensional space, we developed a method based on the minimization of a certain comparison function. This function is the sum of squared distances between pairs of elements of the two structures under comparison with the same indices. Distances change when changing the mutual orientation of the structures with all possible shifts and rotations of the structures as rigid bodies. The comparison function is minimized with respect to Euler angles, provided that centers of mass of two compared structures are superposed. The minimization of the comparison function with respect to Euler angles is carried out numerically by the Rosenbrock method. The developed method for comparison of geometric structures is used to solve problems in structural chemistry, that is to compare molecules with the same structural formula in one crystal.

COMPARATING ANALYSIS OF COORDINATE SEARCH METHODS EFFICIENCY FOR THE OPTIMAL SOLAR PANEL POSITION FINDING

The work is devoted to the investigation of the effectiveness of the coordinate search methods for solving the problem of finding the position of the solar panels, in which the greatest power of the produced current is achieved. The existing solutions in the market of sun surveillance systems (solar trackers) are analyzed. The advantages and disadvantages of such systems are presented in comparison with fixed panels. It is proposed to improve the hardware and software for research of the solar panels efficiency, developed by the authors and highlighted in the previous works, by integrating the program realization of the algorithm of coordinate search of the maximum power of solar panels into the existing. For this purpose, the efficiency of three algorithms for coordinate search of the maximum, namely, the method of coordinate ascending, the Huck-Jeeves method and the Rosenbrock method, was studied in three parameters. Experiments were carried out on data obtained both experimentally using the lab stand for solar panel efficiency research, and by generation using mathematical model of the solar panel efficiency dependance on the angle of radiation, described in previous works. TThe results of experiments are analyzed, which showed a fundamental difference between the work of coordinatewise search algorithms on a mathematical model and experimental data. The main indicators of the efficiency of algorithms are substantiated on the basis of the meteorological conditions in which the measurement was carried out for the formation of experimental data. Conclusions are drawn regarding the efficiency of using these coordinate-based search methods for solving the problem of finding the optimal position of solar panels. Further prospects for research on this topic and the possibility of using coordinate-wise search methods in software of solar panels with a biaxial orientation on the position of the Sun are given.

Mathematical modelling of platelet rich plasma clotting. Pointwise unified model

The mechanistic modelling of blood clotting and fibrin-polymer mesh formation is of significant value for medical and biophysics applications. This paper presents a combination of two pointwise kinetic models represented by system of ODEs. One of them represents the reaction dynamics of clotting factors including the role of the platelet membranes. The second one describes the fibrin-polymer formation as a multistage polymerization process with a sol-gel transition at the final stage. Complex-value second order Rosenbrock method (CROS) is employed for the computational experiments. A sensitivity analysis method built into the computational scheme helps clarify non-evident dependencies in the exhaustive system of ODEs. The unified model was primarily verified using conditions of factor VII deficiency. The model, however requires a significant effort to be tested against experimental data available.

Evaluating Rosenbrock Methods for Usage in Real-Time Simulation of Multibody Models

The upward trend in the usage of sensors and intelligent systems in mechanical systems is requiring the continuing growth in hardware-in-the-loop (HIL) testing in theautomotive industry. This trend in turn is requiring that more sophisticated multibody system models (MBS) be incorporated into hardware-in-the-loop design and testing phases. Running sophisticated multibody models consisting of a large number of bodies and a variety of compliant elements is a challenging on a HIL system. The models must be detailed enough to give realistic results yet run fast enough to meet strict turnaround times of the HIL system. This paper will explore the use of a Rosenbrock method in a real-time environment and compare its performance and accuracy to other integrators in particular to a Backward Difference Formula (BDF) that is restricted in order and number of iterations.

A Strongly A-Stable Time Integration Method for Solving the Nonlinear Reaction-Diffusion Equation

The semidiscrete ordinary differential equation (ODE) system resulting from compact higher-order finite difference spatial discretization of a nonlinear parabolic partial differential equation, for instance, the reaction-diffusion equation, is highly stiff. Therefore numerical time integration methods with stiff stability such as implicit Runge-Kutta methods and implicit multistep methods are required to solve the large-scale stiff ODE system. However those methods are computationally expensive, especially for nonlinear cases. Rosenbrock method is efficient since it is iteration-free; however it suffers from order reduction when it is used for nonlinear parabolic partial differential equation. In this work we construct a new fourth-order Rosenbrock method to solve the nonlinear parabolic partial differential equation supplemented with Dirichlet or Neumann boundary condition. We successfully resolved the phenomena of order reduction, so the new method is fourth-order in time when it is used for nonlinear parabolic partial differential equations. Moreover, it has been shown that the Rosenbrock method is strongly A-stable hence suitable for the stiff ODE system obtained from compact finite difference discretization of the nonlinear parabolic partial differential equation. Several numerical experiments have been conducted to demonstrate the efficiency, stability, and accuracy of the new method.