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The compatible work is considered and the obtained results of the known algorithms generating unobstructed trajectories of different length and smoothness are investigated. Their operation is performed within the framework of the developed software product LSTr. The use of the analyzed set of these algorithms on the set of considered sections of the generated trajectories according to the obtained results allows a differentiated approach to the use of different algorithms on different sections of trajectories, determined by the accepted criteria of length and / or smoothness. The scientific novelty of the work and its practical significance in this area of research are determined.

The effect of Zn/Al ratio and addition of silica to Al–Znx oxides on the structure and catalytic properties of supported NiMo catalysts in hydrodesulfurization reaction of thiophene was studied. NiMo catalysts were synthesized by simultaneous impregnation of Ni acetate and 12-molybdophosphoric acid on Al–Znx and Al–Zn0.16–Si mixed oxide (with x = Zn/Al ratio of 0.05–0.57) prepared by hydrothermal synthesis at 180 °C. Colloidal SiO2 was added to the Al–Znx oxides (Si/Al = 0.3 ratio) to modify textural and structural properties of NiMo catalysts. These materials were characterized by N2 physisorption,SEM, XRD, FTIR, UV–Vis DRS, TPR–H2, TPD–NH3, XPS, HRTEM and tested in thiophene conversion at 280–400 °C and 1.0 MPa. It was found out that the surface area of the supports calcined at 500 °C, decreases with the increasing Zn/Al ratio, which could be due to the interaction of the Zn with the alumina, leading to formation of Zn-spinel. After impregnation of the supports with NiMo active components, the presence of Zn increases the amount of surface Mo in octahedral sites at Zn/Al = 0.21 ratio. At this ratio maximum in HDS activity of NiMo/Al–Znx samples was observed. Addition of silica to Al-Zn mixed oxide (Zn/Al = 0.16) leads to more active NiMo catalyst due to formation of more Ni(Zn)–Mo–S active species as revealed by XRD and HRTEM.

A new method for the automated selection of robotic mechanic-assembly technologies according to technical and economic criteria was proposed. The choice is made on the known set of robotized mechanic assembly technologies, components of the system of technical and economic criteria, analyzed methods for depreciation expense of residual value of industrial robots and other organizational and technological input data. The content of the latter is: the period of operation of industrial robots in flexible production cells, period and volume of production, quantity and volume of product batches for launch in manufacturing. The process of selecting robotic mechanic-assembly technologies is performed at the minimum value of one of the user-selected technical and economic criteria from their pre-developed system. Each of the criteria with different degree of detailing reproduces the content of the «robotic» component of the cost of production of a product unit and is determined by using only industrial robots. The performed formalization of the selection process made it possible to develop algorithmic support, which underlies functioning of the developed computer program in the software environment MS Excel. The performance of a computer program was tested on the examples that on the set of the synthesized robotic mechanic-assembly selection technologies differ only by varying data on the organizational and technological features of using industrial robots in mechanic-assembly flexible production cells. The analysis of the obtained results showed that the selection criterion, determined by the use of the straight-line method of depreciation expense of industrial robots, regardless of the number of their useful years, is the smallest criterion for the examined examples under equal conditions. The mathematical generalizations were formed and the recommendations on using the methods of depreciation expense of the cost of industrial robot, which determine their residual cost when calculating selection criteria, were given. The method for the selection of robotic mechanic-assembly technologies is invariant in the context of the possibility of its use in different countries with different regulatory base concerning the existing methods of depreciation expense for determining residual value of industrial robots

Control problems for objects prone to oscillations in automatic control systems often arise in practice. In some confirmed cases, for almost linear systems it is useful to use linear regulators, otherwise, control objects are nonlinear. Moreover, its nonlinearity cannot be fully compensated by inverse nonlinearity at the object input. In a low-signal mode, transient processes in nonlinear systems can be ideal, but with small changes in the input amplitude, the transient processes can become unstable without a qualitative change in the state. The methodology for ensuring parametric invariance is actively developing. In particular, numerical methods are designing to ensure parametric invariance for systems with indefinitely mathematical descriptions. This paper offers two options for solving the problem of ensuring parametric invariance, which makes it possible to find a parametric synthesis of the system and find some compromise version of the regulation for extended input amplitude ranges. The proposed method is investigated by numerical simulation, and its effectiveness has been demonstrated.

The features of using Role-playing games in educating students - prospective teachers are considered. In practical classes on teaching methods of various disciplines, Role-playing games are often used, associated with conducting a fragment of a lesson or a full lesson. Typically, these practical classes are organized on an empirical level. The version of the Role-playing game "Observing Mathematics Lessons", developed on the basis of the theory of contextual learning, is presented. Psychological and pedagogical principles: simulation of specific conditions, game modelling of the content and forms of professional activity, collaborative activities are used in the design of the game. These principles are the basis for creating a game model, which consists of: game goals, a set of roles that indicate the functions of the player, the scenario and the rules of the game. The simulation model contains: didactic goals, the subject of the game and the evaluation system. An important difference developed by the Role-playing game is to take into account the personality types of students - participants in the game. Students with personality types typical for STEM students were selected for the role of "good pupil”. The roles of the "bad pupils" were played by students with personality types typical for students who usually do not have academic success in mathematics. A survey has been conducted, which showed that the proposed Role-playing game enable the simulation of the real situation of an observing mathematics lesson.

Various methodologies and tools applied to identification of vehicle and collision impact seek to present more and more accurate solutions to reproduce, restore, recreate and investigate the casualty. Modern computer technology and software provide the tools to solve specific problems developing mathematical modelling of complex mechanical systems involving vehicles and other objects in a road accident. Scientists generally utilize the Standard Test Method for Impact Testing calculating the energy of deformation of both vehicles, however, one of its limitations is the evaluation of the kinetic energy of the vehicles in post-collision taking into consideration vehicle rotation and linear displacement. To improve the analysis, dynamic traffic simulation is used, taking into account the variations in the coefficient of friction, suspension elasticity and damping. The proposed method is based on a system of two equations derived from two principles: the Principle of Conservation of Mechanical Energy and the Principle of Conservation of Momentum in the impact phase. The new approach is conducted on mathematical modelling and computer simulation of vehicle motion after the impact, wherefrom the linear and angular velocities are analysed. This is achieved by the numerical solution of the differential equations of motion of the cars after the impact, and the given initial conditions that satisfy the solution are used to solve the system of equations. The main findings of the study can be grouped as follows: 1) The positions of the vehicles prior to the moment of first impact and the post-impact orientation of velocity vectors are more precise. 2) The variability of the tire-road friction coefficient is taken into consideration. 3) The value of coefficient of restitution according to Newton’s theory of impact is unnecessarily determined.

The present study investigates the coefficient of friction of new composites based on UHMWPE with the addition of different percentages of carbon nanotubes (CNTs) - 0.5%, 0.75%, 1.0% and 1.5%. UHMWPE samples with carbon nanotubes, samples of 0.5%, 0.75%, 1.0% and 1.5% carbon nanotubes (UHMWPE-CNTs) and samples with the same carbon nanotube content were made, but with carbon nanotubes subjected to Electroless Nickel Composite Coating with nanoparticles of SiC (UHMWPE-NiCNTs). The coefficient of friction is investigated with a tribometer in a kinematic scheme "Thumb-Disc" without lubricant in a high-alloy steel frame with hardness HRC=56.9 and roughness Ra=2.35 μm. All samples were tested under the same friction conditions - friction path, sliding speed, roughness of the counterpart and samples, ambient temperature. Results and regularities of the effect of carbon nanotubes UHMWPE-CNTs and UHMWPE-NiCNTs on the coefficient of friction at different normal loads are obtained. The microhardness of the materials under investigation was measured and its relationship to the percentage of CNTs and NiCNTs and to the coefficient of friction was analyzed. It was found that the highest micro-hardness belongs to the materials with 1.5% carbon nanotubes having a composite nickel plating (UHMWPE- 1.5NiCNT). This study and the results are related to the implementation on contract: ДН 07/28-15.12.2016 "Research and creation of new wear-resistant coatings using composites and nanomaterials", funded by the National Science Fund at the Ministry of Education and Science, Bulgaria.

The analysis of the concepts used for engineering analysis of existing product samples is given: Remanufacturing, Repair, Reverse engineering, Redesign, Repurposing. In all cases, there is a decryption phase consisting analysis of technical state and identification. The identification involves the analysis of a design, the identification of units that make it up, the definition of technical specifications and the complete reproduction a technical documentation of existing product. The analysis of the technical condition and identification are presented using the approaches of the pattern recognition process. The problem of further use of the product after identifying the causes of destruction and studying the design and functionality is presented as the process of recognizing the project type: Repair, Redesign, Repurposing, etc. The developed approach was used to analyze the technical state and identification the transmission parameters. The design structure matrix and the morphological map of damage were used to determine the root causes of the transmission failure and the damage scenario.

Electrical research in geology is used quite widely and with great efficiency. The use of ready-made signal recorders for these purposes is possible, but not effective enough, since in any case, they need to be modified to provide additional functions. Such functions include the synchronization of measurements with signals from positioning systems GPS or GLONASS. This synchronization is necessary in order for the measurement results to be linked to actual space and time coordinates as accurately as possible. The same measurements taken at different times may give different results due to changes in the orientation of the Earth relative to the Sun and Moon, as well as for other uncontrollable reasons. The need to accurately determine the coordinates of the measurement is obvious. The creative team of the commonwealth of organizations, the key of which is the Siberian Branch of the Federal State Budgetary Institution of Science of the Federal Research Center “Unified Geophysical Service of the Russian Academy of Sciences”, carried out the development and initial testing of a specialized signal recorder for electrical research. The additional modification was required to eliminate the identified deficiencies. This paper reports the main technical solutions when creating this recorder, describes the modification ,and gives an example of using this recorder for field measurements.

Many robotic systems, as well as industrial installations, transport facilities, research benches, require simultaneous control of two or more parameters. In this case, it is necessary to design multi-channel control systems called MIMO systems, which means many inputs and many outputs. In the literature, there are very few publications on methods for designing such systems in the case when the object model is described by a matrix transfer function containing elements in each position in the form of a second or higher order filter and a delay link. There are no analytical methods for solving such a problem; therefore, such problems are solved by methods of numerical optimization. An additional complication of the problem arises when it is required to provide a high order of astatism, for example, the second order. This paper solves such a problem, describes special methods and techniques to obtain an effective result.

The article describes practical experience of implementing several versions of the AndroBoard walking robot control device. Successful testing of a board based on a proprietary Andromeda hexapod robot was carried out. Performance was tested on the algorithms of angular orientation of the body and linear movement.

Designing of regulators (controllers) is relevant in many areas of technology. The analytical calculation of the regulators does not justify itself, since it is possible only for objects that have the simplest models; there are relatively few such objects. For objects with a complex model, the method of numerical optimization is most effective. These methods can be used not only when the mathematical model of the object is known, but also in that case, the mathematical model of the object is not known. For this, a series of tests is performed with a real object, a given indicator of the quality of its work is evaluated, and the optimal regulator is calculated by the search procedure. Known search procedures are characterized by an extremely large required number of tests, some of which may prove fatal for the control object, so this method has not yet found wide application. This makes it extremely urgent to develop fast search algorithms that can soften the test mode and reduce their number. The paper offers several effective solutions to speed up the search algorithms, which gives new algorithms that are more effective than all known ones, including those that are embedded in specialized software for these purposes.

Automatic feedback control systems provide the highest control accuracy in all engineering and technology fields. It applies both to static and dynamic accuracy. If the object is prone to oscillations and also contains a significant delay, then it may be an initial movement in the opposite direction in the transition process. Here the output changes in the opposite direction to the required. Such behavior of the transition process may be unacceptable in many tasks, although the final movement can be achieved in the right direction and by the desired increment. It means the static error can be made negligible. There are many objects prone to oscillations in nature and technology. These are actuators on string suspensions, an inverted pendulum, especially with many plants, the robotic vehicles, etc. Among the many practical problems in the paper we consider the class of Managed Pressure Drilling Control System and logging during drilling, where is a strong tendency to fluctuations. But this is also a characteristic feature of many technological processes. Unfortunately, attention is rarely paid to eliminate a reverse overshoot among indicators of dynamic accuracy in these systems. Many textbooks for a regulator design even do not mention this characteristic due to rare appearances. However, reverse overshoot is one of the most critical indicators of dynamic accuracy. This paper solves the problem of the reverse overshoot suppressing for control of the most complex dynamic objects based on analysis of the various methods of controller design and method of numerical optimization. Additional techniques have been found that allow the most effective solution. It has been tested by simulation modeling corresponding to the tasks of managed well drilling.

The permanent consumption increasing of energy, foods, techniques and other goods and serviced worldwide leads to the intensifier of their production and to the constant market expansion. In turn, the processes taking place in some of these productions are responsible for the deterioration of the quality of the environment. Over the last decade, science and industry have followed the environmental policies and one of the developing approaches is being the use of by-products as raw materials for new production. The waste to energy technologies meets the requirements both of sustainable managing of wastes and energy production by sources with zero carbon footprint. Typical for this technological approach is its local application and in this study is performed an overview analysis of the possibilities for utilization of livestock manures in systems for production of biogas in Bulgaria. Based on the statistical data for number, and type of farm animals in the country for 2020, their localization, and the potential for gas production of their manure, the calculations were made. The obtained results are presented by regional division and it was estimated that total 1142 installation with 500 kWh capacity could be realized in the investigated farms plants. The obtained results are promising and they are prerequisite for further technological and economic investigations of this waste to energy technology

In the paper presented the method of brainstorming with some examples is presented and the main requirements to the moderator, discussion participants and critics have been analyzed. The correspondence between the performing roles of the participants in the brainstorming session and the team roles of Belbin was determined. The procedure of brainstorming session with participants who are ideally suited for Belbin's team roles is described. An experiment was carried out with students performing a course project on machine elements using the developed method. The experiment showed the greater efficiency of the project teams, formed in accordance with the Belbin methodology and performing brainstorming in accordance with the developed recommendations.

Automatic control systems are used in all areas of technology, their accuracy determines the accuracy of the work of robots, manipulators on conveyors, transport systems and high-precision measuring systems. Static error is always minimized through the use of integrating link in regulator. High dynamic accuracy can be ensured by the correct calculation of the proportional and derivative links. If the coefficients are not calculated correctly, the system may lose stability. The minimum dynamic error is ensured only with the most correctly designed regulator. The best design method in the case of a relatively complex mathematical model of the object is a method of numerical optimization. There are software tools for modeling such systems and optimizing regulator, such as VisSim, SimInTech, Simulink + MATLAB, Mathcad, and others. These systems do not use the best algorithms for the specific purpose of the synthesis of PID-regulator, but simply the most well-known numerical optimization algorithms, such as Powell, Polak-Ribiere, Fletcher-Reeves, Monte-Carlo. As a result, in some cases, the coefficients calculated by the regulator are not efficient enough. The paper proposes an improvement in the numerical optimization algorithm. The proposed algorithm was studied by numerical simulation using an example of an object taken from an article by other authors, which allowed us to compare the results obtained by these authors with the results of using this algorithm. Comparison showed that the proposed method is more effective than all the previously described methods. The choice of the best cost (goal) function for these purposes and optimization of the task and simulation time are also necessary. All recommendations are combined into a formal description of the proposed methodology for solving the problem

One of the biggest problems in deep boring (which is very important in some processes in military production) is the displacement of the cutting tool. This problem could be solved in modern machine centers with numerical control which allow controlling the boring process parameters in real time and with very high precision. This paper is devoted to the development of a mathematical model for controlling the displacements of the cutting tools at boring of deep holes on machining centers. To achieve the goal, a full three-factor experiment was carried out. A graphical representation of the created model is proposed. The areas of its application are indicated. The developed model can be used in the synthesis of automatic control systems for metal cutting machines electric drives, which ensures high accuracy of technological operations.

The paper solves the problem of developing a two-wheeled balancing robot. The technology for solving this problem can be extended to any close problem, commonly it can be called stabilization of an inverted pendulum. The relevance of the development is justified by the need to solve control problems in many important technical systems, such as small-sized autonomous two-wheeled robots, stabilization of the antenna of a space device, stabilization of rocket motion on a jet stream, and so on. The practical solution to this problem using the simplest possible actuators, mainly due to correctly designed controllers implemented on digital microcontrollers, makes this development a useful training stand for training highly qualified specialists in the field of robotics, mechatronics and automation.

The controller design for a high-order object prone to oscillations under sufficient of interest in automation and robotics is being solved. For the first time, the square root in the error growth detector used as a component for the cost function calculating unit is proposed. Justification for this proposal is given, and the effectiveness of such modification of the cost function is demonstrated on example of object. Software SimInTech was used for some calculations. It was shown that strong procedures of optimization are wide necessary for controller design.

Development of the theoretical and numerical methods in the theory of automatic control expands the class of control objects for which effective regulators have been found. Every time researchers find a solution to class of problems, the area of problems that have solutions is expanded. In contrast, the area of problems without solution is reduced. Unfortunately, nobody save a careful record of solved problems sometimes leads to duplication of research. It is wasting time and money. Therefore, before solving of a certain class problem every researcher must carefully study all the methods for solving problems for this class. There is not scientific result if the proposed solution is less effective than the existing one. Even if the proposed solution effectiveness is equal to existing well-known methods, the new solution is not essential for the development of science, unless a class of problems is found for which the proposed solution is more effective than others. This paper discusses solution of design a discrete controller for a discrete object. The object model is taken from paper where calculations were carried out according to the Ziegler-Nichols method. The insufficient efficiency of this method is shown, and the exceptional efficiency of the numerical optimization method with modified target functions is demonstrated. Also we consider a complicated example of the object for which the effective regulator has been found. Some recommendations for the proposed method using to the such objects are given.

The balancing two-wheeled robots are clear proof of the triumph of technology and programming, as well as the theory of automatic control. Developments in this area are carried out in all leading laboratories of robotics. Achievement of high speed and high precision always demonstrate the best professionalism of developers. These developments are relevant due to the applicability of the results in many areas of technology. To measure the angle of deviation from the equilibrium axis, sensors of different nature are used. The most promising for these purposes is MEMS-gyroscopes characterized by small dimensions, high reliability and speed. These sensors are successfully used for these purposes, but it have a characteristic nonlinearity leads to self-oscillations in an equilibrium state. This oscillatory mode cannot be eliminated by any optimization of the PID controller. This paper proposes a method for eliminating these auto-oscillations by applying oscillations from this sensor relative to the frame of the balancing robot. This feature provides the dynamic linearization of the sensor transfer characteristic due to the high-frequency component at the sensor output, which is generated by the mechanical deviation of this sensor, while the averaged signal has the required smooth dependence of the output varieties on the input value changes. We propose to introduce the deviation by a MEMS-actuator based on then electromagnetic hanging, a piezoelectric drive, or a different nature drive. The possible simplified structure of one device for introducing a deviation to the equilibrium sensor for the balancing robot is carried out. The method is investigated by mathematical modeling. We show its high effectiveness in design the practice technical solution.

Currently, there is an intensive development of various variants of balancing robots, one-wheeled and two-wheeled ones. Two classes of two-wheeled robots can be distinguished: a) as on a Segway; b) as on a bicycle and a motorcycle. Both of these options are structurally unstable systems. Such structures without the use of an effective system of maintaining balance are fundamentally unstable, in the de-energized state they overturn. The equilibrium can be provided by a system with negative feedback. The development of a one-wheeled balancing robot in the version with an existing pilot has already been decided in practice, but driving such a vehicle requires a pilot with certain skills to ride it. In the unmanned version, all actions performed by the pilot must be replaced by an electromechanical system, which, firstly, provides an imbalance in order to set the direction and speed of movement through the system, which maintains this balance due to the rotation of the wheel, secondly, ensures the maintenance of equilibrium in the direction of the axis of this single wheel; thirdly, it forms the necessary effects for turning. Electromechanical propulsion can be a flywheel, a pendulum; one can also use a fan. At high speeds, it is also possible to use aerodynamic forces, for example, wings, but such a solution at the present stage of the development of technology should rather be considered exotic. However, a robot that is almost an aircraft due to lift from fans, wings or an air cushion may be the ideal solution for high-speed movements on a relatively flat surface. In this case, a purely symbolic touch of the ground, perhaps even interrupted when overcoming too deep and (or) short recesses, allows the robot to be classified as a ground-based (or jumping) device, which frees it from the formalities necessary for the legal use of flying unmanned aerial vehicles, formally such device is not flying mean. Accordingly, the movement of such a robot should be tied to the landmarks and possibilities of the route, its functions are also associated with ground objects, and the possibility of a short-term flight is only an additional bonus. These considerations make it relevant to consider such a way to resolve the issue of stabilizing the equilibrium of a one-wheeled robot, such as the use of lifting force of fans. However, the presence of the wheel creates other possibilities for the load-carrying capacity of the device, and so on; short-term hover by inertia requires completely different energy costs than continuous flight. The purpose of this study is to develop a set of technical proposals for the implementation of high-speed unmanned robot for informational purposes: information gathering (video, audio, electrometer, etc.), as well as for the removal and delivery of small loads. The objectives of the study are to analyze the existing technical solutions and a motivated proposal for the basic principles of the design of the specified balancing robot. A key feature of such robots should be steady motion in an unmanned version along a predetermined trajectory over rough terrain, including the slope of the terrain both in the direction of motion and in the direction orthogonal to the direction of motion.