Control Analysis with Modified LQR Method of Anti-Tank Missile with Vectorization of the Rocket Engine Thrust

This article approaches the issue of the optimal control of a hypothetical anti-tank guided missile (ATGM) with an innovative rocket engine thrust vectorization system. This is a highly non-linear dynamic system; therefore, the linearization of such a mathematical model requires numerous simplifications. For this reason, the application of a classic linear-quadratic regulator (LQR) for controlling such a flying object introduces significant errors, and such a model would diverge significantly from the actual object. This research paper proposes a modified linear-quadratic regulator, which analyzes state and control matrices in flight. The state matrix is replaced by a Jacobian determinant. The ATGM autopilot, through the LQR method, determines the signals that control the control surface deflection angles and the thrust vector via calculated Jacobians. This article supplements and develops the topics addressed in the authors’ previous work. Its added value includes the introduction of control in the flight direction channel and the decimation of the integration step, aimed at speeding up the computational processes of the second control loop, which is the LQR based on a linearized model.

MATHEMATICAL MODELING OF THE HYDRAULIC DRIVE OF THE SECTIONS OF A WIDE-COLLECTING CULTIVATOR WITH SEQUENTIAL ACTIVATION OF HYDRAULIC CYLINDERS

The publication discusses the issues of mathematical modeling of dynamic processes occurring in a complex hydromechanical system of the hydraulic drive of the wide-cut cultivator sections with consistent wear of the hydraulic cylinders. The analysis of known designs of wide-cutting tools and agricultural units is carried out. It is noted that one of the tendencies in the development of domestic agricultural engineering is an increase in the width of coverage of tillage machines. In this regard, hydraulic drives for decomposition and assembly of sections of these machines are widely used. The use of this type of drive is due to its compactness, speed and power. The basic schematic diagrams of hydraulic drives for decomposition of wide-cut tillage machines are considered. On the basis of the analysis, a schematic diagram of the hydraulic drive for assembling (decomposing) sections of a wide-grip cultivator with sequential actuation of hydraulic cylinders is proposed and the principle of its operation is described. A mathematical model has been developed for the hydraulic drive of the wide-grip cultivator sections in the working and transport position. The mathematical model consists of the equations of the continuity of the flows of the working fluid, which describe the processes occurring in the hydraulic drive, and the equations of moments and forces, from which it is possible to determine the force factors acting on the elements of the system. It is difficult to obtain an analytical solution to the resulting system of equations, therefore, to find solutions, numerous methods were applied, namely the Runge-Kutta-Feldberg method with an automatic change in the integration step. On the basis of the obtained dependencies, an analysis of the operation of the hydraulic drive with sequential wear of the hydraulic cylinders was carried out and recommendations were proposed on the design device and directions for improving the hydraulic drive of the tillage unit sections.

Modeling the Influence of Engine Dynamics on Its Indicator Diagram

This article presents a proposal to describe the pressure changes in the combustion chamber of an engine as a function of the angle of rotation of the crankshaft, taking into account changes in rotational speed resulting from acceleration. The aim of the proposed model is to determine variable piston forces in simulation studies of torsional vibrations of a crankshaft with a vibration damper during the acceleration process. Its essence is the use of a Fourier series as a continuous function to describe pressure changes in one cycle of work. Such a solution is required due to the variable integration step during the simulation. It was proposed to determine the series coefficients on the basis of a Fourier transform of the averaged waveform of a discreet open indicator diagram, calculated for the registration of successive cycles. Recording of the indicative pressure waveforms and shaft angle sensor signals was carried out during tests on the chassis dynamometer. An analysis of the influence of the adopted number of series coefficients on the representation of signal energy was carried out. The model can also take into account the phenomenon of work cycle uniqueness by introducing random changes in the coefficients with magnitudes set on the basis of determined standard deviations for each coefficient of the series. An indispensable supplement to the model is a description of changes in the engine rotational speed, used as a control signal for the PID controller in the simulation of the load performed by the dynamometer. The accuracy of determining the instantaneous rotational speed was analyzed on the basis of signals from the crankshaft position angle sensor and the piston top dead center (TDC) sensor. Limitations resulting from the parameters of digital signal recording were defined.

Raytracing Simulated GPS Radio Wave Propagation Paths Experiencing Large Disturbances When Going through the Top of the Sub-Cloud Layer

Global positioning satellite system (GPS) radio waves that reach the tropical lower troposphere are strongly affected by small-scale water vapor fluctuations. We examine along-the-ray simulations of the impact parameter at every ray integration step using the high-resolution European Centre for Medium-Range Weather Forecasts ERA5 reanalysis as the input model states. We find that disturbances to the impact parameter arise when ray paths go through the top of the sub-cloud layer, where there is a pronounced reduction with increasing height in the humidity, and wet refractivity has a strong local vertical gradient, creating multipath. Additionally, the horizontal gradients of refractivity cause the impact parameter to vary along the ray. The disturbances to the impact parameter are confined to an area about 250 km horizontally and 4 km vertically from the perigee point. Beyond 250 km from the perigee, the impact parameter remains constant. The vertical gradient of refractivity is largest at the top of the sub-cloud layer, usually between 1.5 and 3.0 km, and becomes negligibly small above 4 km.

Build-a-Cell: Engineering a Synthetic Cell Community

Build-a-Cell is a global network of researchers that aims to develop synthetic living cells within the next decade. These cells will revolutionize the biotechnology industry by providing scientists and engineers with a more complete understanding of biology. Researchers can already replicate many cellular functions individually, but combining them into a single cell remains a significant challenge. This integration step will require the type of large-scale collaboration made possible by Build-a-Cell’s open, collective structure. Beyond the lab, Build-a-Cell addresses policy issues and biosecurity concerns associated with synthetic cells. The following review discusses Build-a-Cell’s history, function, and goals.

Diagnosis of the Static Excitation Systems of Synchronous Generators with the Use of Hardware-in-the-Loop Technologies

In this paper, testing and diagnosis methods for the static excitation systems of power plant synchronous generators using Hardware-In-the-Loop technology are described. These methods allow a physical excitation system to be connected to a real-time model of a power plant unit. A feature of a static excitation system is the presence of generator self-excitation—that is, when the input voltages of the excitation system are defined by a synchronous generator. These voltages are determining by the digital model, which creates additional difficulties with combining a digital model with a real excitation system. Various ways to solve this problem are described in this article; in particular, we focus on the option in which the gate-impulses of a thyristor converter are applied to the digital model by a real static excitation system. The real-time models are based on the method of average voltages in the integration step. This method is effective for providing numerical stability for the models of power schemes and their functioning in real time mode over a long period. A synchronization method for the calculation time of the model with real time is described. The adequacy of the described method is proved by the results of the static excitation system of synchronous generators testing in operating and fault modes.

Automated constitutive modeling of isotropic hyperelasticity based on artificial neural networks

Herein, an artificial neural network (ANN)-based approach for the efficient automated modeling and simulation of isotropic hyperelastic solids is presented. Starting from a large data set comprising deformations and corresponding stresses, a simple, physically based reduction of the problem’s dimensionality is performed in a data processing step. More specifically, three deformation type invariants serve as the input instead of the deformation tensor itself. In the same way, three corresponding stress coefficients replace the stress tensor in the output layer. These initially unknown values are calculated from a linear least square optimization problem for each data tuple. Using the reduced data set, an ANN-based constitutive model is trained by using standard machine learning methods. Furthermore, in order to ensure thermodynamic consistency, the previously trained network is modified by constructing a pseudo-potential within an integration step and a subsequent derivation which leads to a further ANN-based model. In the second part of this work, the proposed method is exemplarily used for the description of a highly nonlinear Ogden type material. Thereby, the necessary data set is collected from virtual experiments of discs with holes in pure plane stress modes, where influences of different loading types and specimen geometries on the resulting data sets are investigated. Afterwards, the collected data are used for the ANN training within the reduced data space, whereby an excellent approximation quality could be achieved with only one hidden layer comprising a low number of neurons. Finally, the application of the trained constitutive ANN for the simulation of two three-dimensional samples is shown. Thereby, a rather high accuracy could be achieved, although the occurring stresses are fully three-dimensional whereas the training data are taken from pure two-dimensional plane stress states.

Stability Analysis and Optimization of Semi-Explicit Predictor–Corrector Methods

The increasing complexity of advanced devices and systems increases the scale of mathematical models used in computer simulations. Multiparametric analysis and study on long-term time intervals of large-scale systems are computationally expensive. Therefore, efficient numerical methods are required to reduce time costs. Recently, semi-explicit and semi-implicit Adams–Bashforth–Moulton methods have been proposed, showing great computational efficiency in low-dimensional systems simulation. In this study, we examine the numerical stability of these methods by plotting stability regions. We explicitly show that semi-explicit methods possess higher numerical stability than the conventional predictor–corrector algorithms. The second contribution of the reported research is a novel algorithm to generate an optimized finite-difference scheme of semi-explicit and semi-implicit Adams–Bashforth–Moulton methods without redundant computation of predicted values that are not used for correction. The experimental part of the study includes the numerical simulation of the three-body problem and a network of coupled oscillators with a fixed and variable integration step and finely confirms the theoretical findings.

RESEARCH OF TRANSIENT PROCESSES OF PRESSURE CHANGE WHEN OPERATING A HYDRAULIC SYSTEM WITH FOUR CONNECTED HYDRAULIC MOTORS

The publication is devoted to the study of the quality of the hydraulic system with four series-connected hydraulic motors. These hydraulic systems can be used to drive the working bodies of agricultural machines, have significant advantages in their layout, but at the same time and disadvantages, the elimination of which requires a detailed study of the processes occurring during the operation of this type of system. The analysis of the previous works of scientists in this area allows us to conclude that it is possible to conduct theoretical research in this direction. A mathematical model of the proposed hydraulic system has been developed, which takes into account the effect of external load on the shafts of hydraulic motors, the inertia of the system, the effect of leaks from the connections of the elements of the hydraulic system and possible overflows of the working fluid from the high-pressure zone to the low-pressure zone. At this stage, wave processes occurring in the cavities of the hydraulic system were not taken into account. The solution of the resulting system of differential equations was carried out using the Runge-Kutta-Feldberg method with automatic change of the integration step in the mathematical package MathCad. The resulting transient processes were analyzed for the amplitude of pressure surges and the frequency of its change. Carrying out this analysis allows you to obtain comprehensive information about the nature of transient processes in the hydraulic system in order to find such a ratio of design and technological parameters, in which the system under study met the requirements regarding the quality of work as part of a technological machine. During the research, special attention was paid to the processes occurring at the moment of starting the hydraulic system, and the moment of application of the technological load.

Fast Corotated Elastic SPH Solids with Implicit Zero-Energy Mode Control

We develop a new operator splitting formulation for the simulation of corotated linearly elastic solids with Smoothed Particle Hydrodynamics (SPH). Based on the technique of Kugelstadt et al. [2018] originally developed for the Finite Element Method (FEM), we split the elastic energy into two separate terms corresponding to stretching and volume conservation, and based on this principle, we design a splitting scheme compatible with SPH. The operator splitting scheme enables us to treat the two terms separately, and because the stretching forces lead to a stiffness matrix that is constant in time, we are able to prefactor the system matrix for the implicit integration step. Solid-solid contact and fluid-solid interaction is achieved through a unified pressure solve. We demonstrate more than an order of magnitude improvement in computation time compared to a state-of-the-art SPH simulator for elastic solids. We further improve the stability and reliability of the simulation through several additional contributions. We introduce a new implicit penalty mechanism that suppresses zero-energy modes inherent in the SPH formulation for elastic solids, and present a new, physics-inspired sampling algorithm for generating high-quality particle distributions for the rest shape of an elastic solid. We finally also devise an efficient method for interpolating vertex positions of a high-resolution surface mesh based on the SPH particle positions for use in high-fidelity visualization.