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.

Numerical and Statistical Analysis of Dissipative and Heat Absorbing Graphene Maxwell Nanofluid Flow Over a Stretching Sheet

This paper is basically devoted to carry out an investigation regarding the unsteady flow of dissipative and heat absorbing hydromagnetic graphene Maxwell nanofluid over a linearly stretched sheet taking momentum and thermal slip conditions into account. Ethylene glycol is selected as a base fluid while graphene particles are considered as nanoparticles. The highly nonlinear mathematical model of the problem is converted into a set of nonlinear coupled differential equations by means of fitting similarity variables. Further, Runge-Kutta Fehlberg algorithms along with the shooting scheme are instigated to analyse the numerical solution. The variations in graphene Maxwell nanofluid velocity and temperature owing to different physical parameters have been demonstrated via numerous graphs whereas Nusselt number and skin friction coefficients are illustrated in numeric data form and are reported in different tables. In addition, a statistical method is implemented for multiple quadratic regression estimation analysis on the numerical figures of wall velocity gradient and local Nusselt number to establish the connection among heat transfer rate and physical parameters. Our numerical findings reveal that the magnetic field, unsteadiness, inclination angle of magnetic field and porosity parameters boost the graphene Maxwell nanofluid velocity while Maxwell parameter has a reversal impact on it. The regression analysis confers that Nusselt number is more prone to heat absorption parameter as compared to Eckert number. Finally, the numerical findings are compared with those of earlier published articles under restricted conditions to validate the numerical solution. The comparison of numerical findings shows an excellent conformity among the results.

Payload oscillation control of tower crane using smooth command input

This paper presents a smooth command (SC) input shaper for suppressing payload oscillations in rest-to-rest simultaneous radial and tangential motions of a tower crane. The radial and tangential acceleration profiles of the compound motions are represented by multi-sine wave functions with independent and variable maneuvering time. The proposed SC is designed using a nonlinear mathematical model of the tower crane while the parameters of the acceleration profiles and maneuvering times were optimized using a particle swarm algorithm (PSO). The simulated results were verified experimentally on a laboratory scale tower crane. The results confirm that the proposed SC input effectively canceled residual vibrations of the payload compound motions with a time length comparable to zero vibrations (ZV) shaper. Moreover, sensitivity analysis to variations in cable length reveals that the proposed command input is robust over a wide range of cable lengths.

Asymptotic Properties of One Mathematical Model in Food Engineering under Stochastic Perturbations

For the example of one nonlinear mathematical model in food engineering with several equilibria and stochastic perturbations, a simple criterion for determining a stable or unstable equilibrium is reported. The obtained analytical results are illustrated by detailed numerical simulations of solutions of the considered Ito stochastic differential equations. The proposed criterion can be used for a wide class of nonlinear mathematical models in different applications.

Children’s cognitive function and mental health based on finite element nonlinear mathematical model

This article uses a finite element nonlinear mathematical model to analyse the psychological conditions of children with certain physical defects. The thesis uses exercise and psychological intervention to intervene in children with material defects and scores the children’s mental state and cognitive status after the intervention. After our training and psychological intervention, the study found that the psychological evaluation scores of children with physical defects increased significantly. Before and after the intervention, there are apparent differences in children’s cognition in vocabulary and arithmetic. There is a nonlinear negative correlation between children’s cognitive abilities with physical defects and the scores of mental health status and neuropsychological evaluation. For this reason, the study concluded that movement and psychological intervention play a significant role in improving the cognitive function of children with physical defects.

Modeling the effects of insecticides and external efforts on crop production

In this paper a nonlinear mathematical model is proposed and analyzed to understand the effects of insects, insecticides and external efforts on the agricultural crop productions. In the modeling process, we have assumed that crops grow logistically and decrease due to insects, which are wholly dependent on crops. Insecticides and external efforts are applied to control the insect population and enhance the crop production, respectively. The external efforts affect the intrinsic growth rate and carrying capacity of crop production. The feasibility of equilibria and their stability properties are discussed. We have identified the key parameters for the formulation of effective control strategies necessary to combat the insect population and increase the crop production using the approach of global sensitivity analysis. Numerical simulation is performed, which supports the analytical findings. It is shown that periodic oscillations arise through Hopf bifurcation as spraying rate of insecticides decreases. Our findings suggest that to gain the desired crop production, the rate of spraying and the quality of insecticides with proper use of external efforts are much important.

A Model-Based Predictive Controller of the Level of Steel in the Mold with Disturbances Using a Repetitive Structure

Keeping the level of steel in the mold of the continuous casting process constant is fundamental for the quality of the steel produced and, consequently, its commercial value. It is challenging, considering the several disturbances that cause undesired variations in the mold level. The aim of this paper is to apply a repetitive structure composed of two controllers, a generalized predictive controller (GPC) and a repetitive GPC (R-GPC) with constraints to mitigate the bulging and clogging/unclogging disturbances and the casting speed variation in the mold level of the process. The R-GPC controller has the same characteristics as the GPC, such as performance, robustness to disturbances, and insertion of constraints, and its advantage is the elimination of periodic disturbances. The repetitive structure will be implemented with a robustness filter and tuned by a genetic algorithm (GA). The controller tests are performed by simulations of a nonlinear mathematical model of the mold level, validated using real data from the steel industry. The proposed controller reduces the bulging disturbance amplitude by 98.5% and at 25% of the frequency of reversions in the valve. Consequently, the proposed controller allows an increase in the valve life span, a reduction in maintenance costs, and quality improvement in the steel slab.

Mathematical insights into neuroendocrine transdifferentiation of human prostate cancer cells

Prostate cancer represents the second most common cancer diagnosed in men and the fifth most common cause of death from cancer worldwide. In this paper, we consider a nonlinear mathematical model exploring the role of neuroendocrine transdifferentiation in human prostate cancer cell dynamics. Sufficient conditions are given for both the biological relevance of the model’s solutions and for the existence of its equilibria. By means of a suitable Liapunov functional the global asymptotic stability of the tumour-free equilibrium is proven, and through the use of sensitivity and bifurcation analyses we identify the parameters responsible for the occurrence of Hopf and saddle-node bifurcations. Numerical simulations are provided highlighting the behaviour discovered, and the results are discussed together with possible improvements to the model.