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 Âûïóñê 101
- Krasnov D. Construction of reduced state observers for systems with affine disturbances
The object of study is linear single-channel systems with affine parametric and external disturbances, presented in the so-called triangular form "input-output". The relative degree in control is equal to the dimension of the state vector and does not change upon transition to the canonical form "input-output" under the assumption of smoothness of external disturbances. It is known that for such systems, only by measuring the output variable, it is possible to construct an observer of mixed variables and restore linear combinations of state variables and external influences with a given accuracy. The estimates obtained are sufficient for the synthesis of dynamic feedback, which provides tracking of the output variable of a given signal. The paper considers an important practical case when, for a certain set of sensors, the output (adjustable) variable is not measured. It is necessary to design a reduced state observer for its evaluation in order to proceed to the construction of a mixed variables observer. First, motivating examples of second-order systems with different dimensions and different channels of action of external disturbances are considered. It is shown that when measuring both state variables with the help of piecewise linear corrective actions of the state observer, it is possible to restore external disturbances by their influence on the system (i.e., without using a dynamic disturbance generator). Conditions are formulated under which this principle can also be used in a system with external disturbances and incomplete measurements to restore an unmeasured state variable. The results obtained are extended to finite-dimensional single-channel systems of arbitrary order with affine disturbances, in which the output variable is not measured. The conditions of existence and the method of synthesis of a reduced observer with a piecewise-linear corrective action, which gives an estimate of the output variable, are formalized. The developed approach does not require the identification of external disturbances and solves the problem of observing the output variable with any given accuracy.
- Berlin L., Galyaev A., Kravtsova S. About two-switching control class in the time-optimal control problem of two non-synchronous oscillators
The time-optimal control problem in a system consisting of two non-synchronous oscillators is considered. The studied formulation has a number of distinctive features, such as, for example, that each of the oscillators is controlled by a common bounded scalar control and the goal is to accelerate the first oscillator from rest to a given position in the shortest time. At the terminal moment the phase coordinates of the second oscillator become zero again. The optimal control is a relay mode, so solutions with different numbers of control switchings are the key. The basic one is the three-switching control class and for a larger number of unknown switching moments the necessary optimality conditions are known. The two-switching control class obtained by degeneracies is of interest, where functional dependences are written out for the values of interval durations. Mathematical modeling was carried out to illustrate the obtained analytical results.
- Zhukov P., Fomin A., Glushchenko A. Algorithmic stability and complexity of implicit adaptation of nonstationary thermal conductivity mesh model to heated substance
This paper deals with the process of adaptation of a numerical model of nonstationary thermal conductivity implemented with the help of finite difference methods. The algorithmic stability has already been proved for the classical representation of these models in most applications and problems, but in this case we consider a problem related to the parametric adaptation of the equation of nonstationary heat conduction to the heated substance implemented by solving of the related variational problem. The basis of this approach implies replacement of thermophysical parameters of the equation in question by freely adjustable parameters and their adaptation ("model training") by a stochastic gradient method. Optimization of algorithmic equations that do not have an analytical form is associated with unstable initial conditions and "training" trajectories. To avoid falling into these regions we need to impose restrictions on the adjustable parameters. In this paper, such constraints are derived on the basis of proven stability conditions for the classical finite-difference model of non-stationary thermal conductivity. As a result of the numerical experiments, it is shown that the proposed constraints allow one to increase, on average, the number of stable initial conditions by 13%, as well as the number of experiments when stable trajectories are achieved - by 61%. In addition to this result, an analytical comparison of the growth orders of algorithmic complexity of the classical model and the modified one is also made. As a result of the calculations, it is found that both models have a growth order of O(n4), which is confirmed by numerical experiments.
- Geraskin M., Ivanova M. Modeling interactions of institutions of housing markets based on power, exponential and log cost functions
The article presents a system of optimality conditions for housing market agents (realtor, bank and insurer) with power, exponential and logarithmic cost functions corresponding to different types of economies of scale. The results of numerical experiments are presented, demonstrating the nature of price interdependencies in these markets for various types of functions. In contrast to the study of the "realtor – bank – insurer" system based on linear cost functions, this work presents the following conclusions: firstly, in the case when all agents have concave cost functions, then the real estate price, mortgage interest rate and insurance tariff lower than in the case when agents have convex cost functions; secondly, an increase in the intrasystem commission rate leads to an increase in the price of the agent who pays the commission, and a decrease in the price of the agent who receives it; thirdly, an increase in the commission rate leads to a sharper decrease in the price of an agent, in the case when he has a convex cost function, while the counterparty has a concave one, than otherwise. When comparing the effectiveness of using different types of cost functions, it was found that logarithmic and exponential functions provide greater accuracy than power functions.
- Tretyakova E. Simulation of a water hammer in an axial piston pump
The paper presents an approach to modeling an axial piston pump compact series with an inclined block and performed a hydrodynamic calculation. Existing models of the axial piston pump were studied, during which a jump in flow was found at the time of water hammer, but the "shock magnitude" was unknown. During modeling, assumptions related to the properties of the working fluid and the geometry of the plunger were introduced, and temperature changes were also not taken into account. Four stages were identified in the modeling process. The first stage involves the creation of a fluid volume - a fluid model from a solid model of the pump. In the second step, a mesh was created. The third stage is devoted to creating macros for the movement of the previously selected pump components. At the fourth stage, all prepared parts of the model are uploaded to Fluent 18.1 and the calculation parameters are set. The adequacy of the resulting model was assessed by comparing the simulated total pump flow with the theoretical flow calculated analytically. Upon the simulation, the amplitude of the pressure jump was calculated during the water hammer in the operating mode of the pump at the maximum discharge pressure. A method was proposed to reduce it. Changes have been made to the design of the plunger. The strength of the modified structure was calculated.
- Yakovlev I., Elizarova A., Saitova G. Determining the architecture of a neural network in the problem of estimating the state of the battery charge
The problem of estimating the state of charge of the battery, based on neural networks, is considered. Two types of recurrent nonlinear autoregressive neural networks were investigated in the problem of estimating the state of charge of a battery during its use. The main criterion for the quality of forecasting was the mean square error. According to the results of the study, the optimal structure of the neural network was chosen.
- Kokunko J. Design of a reference actions generator for a mobile robot control system
Planning the path of an autonomous wheeled robot can pose problems such as ensuring motion safety, smoothness and bounded curvature of the path and its rate of change, considering the design constraints of the robot as a mechanical control object. The joint solution of these problems can lead to cumbersome analytical calculations that are not realizable in real-time. In this paper, we propose to simplify and automate the generation of planar paths for a wheeled robot, which will solve both of these problems. At the first stage, a primitive path is constructed in the form of a flat polyline. The second stage solves the problem of smoothing the articulation of the polyline. Instead of geometric calculations, a dynamic generator is designed as a copy of the equations of motion of the robot. The synthesis of the generator's correcting actions, which simulate the robot's control actions, is based on the decomposition method and S-shaped smooth and constrained nonlinear feedbacks. This ensures that the design constraints of the robot on velocity, acceleration and control torques are met, and the output variables of the generator will generate a naturally smoothed path with acceptable curvature when tracking the coordinates of the reference nonsmooth trajectory.
- Tuturov A. Development of a project of a graphic interface as an element of a decision support system for the duty shift of space vehicle control
The specifics of the work of duty shift specialists and the role of means of displaying information about the processes occurring in the space complex on decision-making on the control of spacecraft as part of the Earth's remote sensing orbital constellation are described. The task was set to develop a graphical interface project as an element of a decision support system for the on-duty shift of spacecraft control, consisting of specialists from space complex enterprises. The principles of separating service information, which are operated by shift shift specialists, into categories based on the nature of its sources, as well as a mechanism for displaying this information in real time using a graphical interface, in order to reduce the time spent on identifying the situation of abnormal operation of the ground and/or on-board software and hardware in the conditions of a limited time of a communication session with the spacecraft. The key feature of the proposed graphical interface is the "spacecraft state vector" - a method for displaying telemetry data of the elements of the spacecraft subsystems necessary to register an emergency situation on board the spacecraft and search for a strategy to stop / eliminate its consequences by ensuring functional stability - the ability of the system to save and / or restore the functions assigned to it.
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