УПРАВЛЕНЧЕСКИЕ МОДЕЛИ УГЛОВОГО ДВИЖЕНИЯ КОРОМЫСЛА С ВИНТОВЫМИ ЭЛЕКТРОПРИВОДАМИ

The subject of study in the article is the forming models' process for the angular motion of the rocker with screw electric actuators. The purpose is to develop the approach to the simplest models formation for the angular motion of the rocker with screw electric actuators as the automatic control object. Tasks: to form the physical model of rocker with screw electric actuators. Using the Lagrangian formalism develop the non-linear mathematical description of the angular motion process of a rocker with screw electric actuators. To obtain the linearized mathematical description of the automatic control object in form of state space in the cases when one sensor (angular position) and two sensors (angular position and angular velocity of the rocker) are used. To obtain the description of the automatic control object in the frequency domain using Laplace transforms. To form graphic models of the automatic control object using structural diagrams in the time and frequency domains. To analyze the functional properties of the automatic control object: stability, controllability, observability, structural and signal diagnosability in the cases when one sensor (angular position) and two sensors (angular position and angular velocity of the rocker) are used. To formulate the conditions for using mathematical descriptions as mathematical models of the automatic control object. The methods used are the Lagrange method, analytical linearization, state space, Laplace transform, Lypunov, Kalman criteria, diagnosability. The following results were obtained: the approach to the formation of the simplest models for the angular motion of a rocker with screw electric actuators as an object of automatic control for solving specific problems of analysis and synthesis was formed. Conclusions. The scientific novelty lies in the formation of the approach to the formation of the simplest control models for the angular motion of the rocker with screw electric actuators which differs from the known completeness of accounting for the acting forces and moments.

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АЛГОРИТМЫ УПРАВЛЕНИЯ УГЛОВЫМ ДВИЖЕНИЕМ КОРОМЫСЛА С ВИНТОВЫМИ ЭЛЕКТРОПРИВОДАМИ

Aerospace technic and technology ◽

10.32620/aktt.2020.4.06 ◽

2020 ◽

pp. 44-59

Author(s):

Анатолий Степанович Кулик ◽

Константин Юрьевич Дергачев ◽

Сергей Николаевич Пасичник ◽

Юрий Александрович Немшилов

Keyword(s):

Automatic Control ◽

State Space ◽

Mathematical Description ◽

Transfer Functions ◽

Control Object ◽

The State ◽

Angular Motion ◽

Synthesis Process ◽

Electric Actuator ◽

Functional Features

The subject of study in the article is the process of forming algorithms for controlling the angular motion of the rocker with a screw electric actuator. The purpose is to develop approaches to the formation of algorithms for controlling the angular motion of the rocker with a screw electric actuator as the automatic control object. Tasks: to specify the synthesis process of the state control algorithm for a linear mathematical description of the automatic control object in the state space according to the minimum criterion of the integral from the weighted error module. To form the block diagram of the automatic control system by the state. To improve the approach to the development of algorithms for controlling automatic control objects by output for mathematical description in the frequency domain. To illustrate the features of the approach on the specific example of automatic control object represented by transfer functions in terms of references and disturbances. To develop the simulation scheme in Simulink and study the reactions to stepwise references and disturbances. To develop the approach to the formation of control algorithms for the diagnosis of the rocker as the automatic control object. To describe the procedure and means of deep diagnosis of emergency situations of the automatic control object. To develop means of recovery the automatic control object. The methods used are the state space method, transfer function method, integral optimality criteria, methods of diagnosing, and recovering. The following results were obtained: approaches to the formation of algorithms for controlling the angular motion of the rocker with a screw electric actuator using linear mathematical descriptions in time and frequency domains were formed. Conclusions. The scientific novelty lies in the formation of approaches to the development of algorithms for controlling the angular position of the rocker with a screw electric actuator which differs from the known accounting the structural and functional features of the automatic control object.

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Motions models of a two-wheeled experimental sample

RADIOELECTRONIC AND COMPUTER SYSTEMS ◽

10.32620/reks.2021.1.03 ◽

2021 ◽

pp. 40-49

Author(s):

Anatoliy Kulik ◽

Konstantin Dergachov ◽

Sergey Pasichnik ◽

Sergey Yashyn

Keyword(s):

Automatic Control ◽

State Space ◽

Experimental Model ◽

Functional Properties ◽

Angular Position ◽

The Body ◽

Angular Motion ◽

Physical Models ◽

Experimental Sample ◽

Electric Drives

The subject of study is the physical processes of translational and angular motion of a two-wheeled experimental sample. The goal is to develop physical, mathematical, and graphic models of the translational and angular motions of a two-wheeled experimental sample as an object of automatic control. The objectives: to form physical models of a two-wheeled experimental sample; to develop a nonlinear mathematical description of the processes of translational and angular sample`s motions using the Lagrange approach; to obtain a linearized mathematical sample`s description as an object of automatic control in the state space and frequency domain; to generate graphic models in the form of structural diagrams in the time and frequency domains; to analyze the functional properties of an object of automatic control: stability, controllability, observability, structural and signal diagnosability concerning violations of the functional properties of electric drives and sensors of the angular position of the body and wheels. The methods of the study: the Lagrange method, Taylor series, state-space method, Laplace transformations, Lyapunov, Kalman criteria, and diagnosability criterion. The results: physical models of a two-wheeled experimental sample have been obtained in the form of a kinematic diagram of the mechanical part and the electric circuit of an electric drive; mathematical descriptions of translational and angular motions have been developed in nonlinear and linearized forms; structural diagrams have been developed; functional characteristics of a two-wheeled experimental model as an object of automatic control have been analyzed to solve problems of control algorithms synthesis. Conclusions. The scientific novelty lies in obtaining new models that describe the translational and angular motion of a two-wheeled experimental model as an object of automatic control. The obtained models differ from the known ones by considering the dynamic properties of sensors and electric drives, as well as the relationship of movements.

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Algorithms for control of longitudinal motion of a two-wheel experimental sample

RADIOELECTRONIC AND COMPUTER SYSTEMS ◽

10.32620/reks.2021.2.02 ◽

2021 ◽

pp. 16-30

Author(s):

Anatoly Kulik ◽

Konstantin Dergachev ◽

Sergey Pasichnik ◽

Yuri Nemshilov ◽

Evgeny Filippovich

Keyword(s):

Control System ◽

Automatic Control ◽

State Space ◽

Mathematical Description ◽

Control Object ◽

The State ◽

Control Algorithms ◽

Longitudinal Motion ◽

Experimental Sample ◽

Short Period

The subject of study is the process of forming algorithms for controlling the angular and translational movements of a two-wheeled experimental sample (TWES). The aim is to develop approaches to the formation of control algorithms for the translational and angular movements of a non-stationary automatic control object. Tasks: to concretize the process of synthesis of a control algorithm by state according to the criterion of the minimum integral of the weighted error modulus for a linear mathematical description of an automatic control object in the state space. Form a block diagram of an automatic control system by the state. Improve the approach to the synthesis of output control algorithms for mathematical description in the frequency domain of short-period and long-period motions of TWES. Illustrate the peculiarity of the approach using a specific example of a TWES under control and disturbing influences. Develop a simulation scheme in the Simulink environment and investigate responses to external step influences. Develop an approach to the formation of control algorithms by the diagnosis of TWES as an object of automatic control. Describe the procedure and means of deep diagnostics of emergencies of TWES. Develop algorithms for restoring the operability of the automatic rational control system. Used methods are a method of state space, the method of relative functions, the method of transfer functions, the method of optimization by integral criterion, the method of synthesis by logarithmic asymptotic frequency characteristics, methods of diagnosing and restoring operability. The following Results: three approaches were formed to the formation of control algorithms of the angular and translational movements of the TWES using linear mathematical descriptions in the time and frequency domains. Conclusions. The scientific novelty lies in the formation of approaches to the combined control of angular and translational movements, considering the structural and parametric features of the mathematical descriptions of TWES.

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Measurement of the angular motion parameters of the mirror of the scanning device

Izmeritel`naya Tekhnika ◽

10.32446/0368-1025it.2021-6-3-7 ◽

2021 ◽

pp. 3-7

Author(s):

Petr A. Pavlov ◽

Elena M. Ivashchenko

Keyword(s):

Angular Velocity ◽

Angular Position ◽

Low Frequency ◽

Frequency Region ◽

Angular Motion ◽

Main Attention ◽

Scanning Angle ◽

Scanning Device ◽

Environmental Monitoring System

A scanning device for a space-based environmental monitoring system has been investigated. The main attention is paid to the study of the parameters of the angular motion of the mirror of the scanning device, the uniformity of rotation of which largely determines the quality of the image of the Earth's surface. The principle and results of measuring the parameters of the mirror rotation carried out in a wide angular range are considered. The measurements were performed using a dynamic goniometer-autocollimator, which has been calibrated at the State Standard of Plane Angle Unit GET 22-2014. The repeatability of the average angular velocity of the scanning device mirror and the repeatability of the initial scanning angle are calculated. Nonstationarity in mathematical expectation and variance in random deviations of the angular motion of the mirror from the linear law of scanning is noted. The use of wavelet analysis revealed the frequency of excitation of oscillations in the low-frequency region of the spectrum. The possibility of using the a dynamic goniometer-autocollimator for measuring not only the angular position of the scanning device mirror, but also the angular velocity is shown.

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IMPLEMENTATION OF THE METHODS OF IDENTIFICATION OF STATIC CONTROL OBJECTS

Science Evolution ◽

10.21603/2500-1418-2017-2-2-72-78 ◽

2017 ◽

pp. 72-78

Author(s):

Sergey Pachkin ◽

Roman Kotlyarov ◽

Roman Kotlyarov

Keyword(s):

Mathematical Model ◽

Control System ◽

Automatic Control ◽

Automatic Control System ◽

Mathematical Description ◽

Control Object ◽

Parametric Identification ◽

Identification Problem ◽

Temperature Control System ◽

The Mathematical Model

One of the main tasks solved in the development of automatic control systems is the identification of the control object, which consists in obtaining its mathematical description. The nature and type of the mathematical model is determined by the goals and tasks for which it will be used. In the present case, the aim of obtaining the model is the synthesis of an automatic control system. Proceeding from the requirements of control problems, the identification problem consists in determining the structure and parameters of the mathematical model that ensure the best similarity of the model and object responses to the same input action. The article considers the experimental method of obtaining a mathematical description of the control object based on the results of measuring its input and output parameters and then processing the obtained results. The control object is the EP10 emulator made by the Oven Company, which is a miniature furnace. The emulator is used in experimental research in the process of commissioning using thermostat controls, and also applicable for educational purposes as part of training and research stands. As a result of structural identification with subsequent adjustment of the coefficients with the help of parametric identification, a model of the control object in the form of a second order aperiodic link is obtained. Parameters and type of the mathematical model allowed to make calculations and determine the parameters of adjustment of the TRM251 PID-controller. The software implementation of the automatic control system in the MatLAB environment made it possible to evaluate transient processes in a closed system. Thus, the calculation and analysis of the automatic control system in the first approximation were made. The final result can be obtained at the stage of commissioning the automatic temperature control system in the EP10 emulator using adaptation algorithms.

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Synthesis of a Scalar Automatic Control System of a Valve Engine with Field Control for a Rowing Electric Installation with an Azipod Propulsion and Steering System

Известия высших учебных заведений Электромеханика ◽

10.17213/0136-3360-2021-6-29-35 ◽

2021 ◽

Vol 64 (6) ◽

pp. 29-35

Author(s):

Vitaly Vysotsky ◽

◽

Igor Markov ◽

Yuri Matveev ◽

◽

...

Keyword(s):

Control System ◽

Automatic Control ◽

Automatic Control System ◽

Electric Drive ◽

Structural Complexity ◽

Control Object ◽

Steering System ◽

Synchronous Machine ◽

Object A ◽

Valve Engine

The article deals with the main trends in the development of marine automatic AC electric drive systems. A variant of the implementation of an electric drive using an electromechanical converter of a synchronous machine with electromagnetic field excitation is presented. A promising electric drive system with a valve engine for the icebreaker's with the Azipod propulsion and steering system is proposed. The aim of the work is to eliminate the structural complexity and expand the functional capabilities of the electric drive by using a scalar automatic control system of the frequency of rotation in the two-zone control of the valve motor of the EPS. The novelty lies in the use of the approach and representation of the control object-a valve motor as an analog of a DC collector motor controlled by an armature and by a field. The analysis of control processes is directly related to the processes of electromechanical energy conversion occurring in a synchronous machine.

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Analysis and Synthesis of a Fuzzy Controller by the Phase Plane Method

Mekhatronika Avtomatizatsiya Upravlenie ◽

10.17587/mau.22.507-517 ◽

2021 ◽

Vol 22 (10) ◽

pp. 507-517

Author(s):

Y. A. Bykovtsev

Keyword(s):

Control System ◽

Automatic Control ◽

Automatic Control System ◽

Phase Plane ◽

Fuzzy Controller ◽

Piecewise Linear ◽

Plane Method ◽

Phase Trajectories ◽

Analysis And Synthesis ◽

Phase Plane Method

The article is devoted to solving the problem of analysis and synthesis of a control system with a fuzzy controller by the phase plane method. The nonlinear transformation, built according to the Sugeno fuzzy model, is approximated by a piecewise linear characteristic consisting of three sections: two piecewise linear and one piecewise constant. This approach allows us to restrict ourselves to three sheets of phase trajectories, each of which is constructed on the basis of a second-order differential equation. Taking this feature into account, the technique of "stitching" of three sheets of phase trajectories is considered and an analytical base is obtained that allows one to determine the conditions for "stitching" of phase trajectories for various variants of piecewise-linear approximation of the characteristics of a fuzzy controller. In view of the specificity of the approximated model of the fuzzy controller used, useful analytical relations are given, with the help of which it is possible to calculate the time of motion of the representing point for each section with the involvement of the numerical optimization apparatus. For a variant of the approximation of three sections, a technique for synthesizing a fuzzy controller is proposed, according to which the range of parameters and the range of input signals are determined, at which an aperiodic process and a given control time are provided. On the model of the automatic control system of the drive level of the mechatronic module, it is shown that the study of a fuzzy system by such an approximated characteristic of a fuzzy controller gives quite reliable results. The conducted studies of the influence of the degree of approximation on the quality of control show that the approximated characteristic of a fuzzy controller gives a slight deterioration in quality in comparison with the smooth characteristic of a fuzzy controller. Since the capabilities of the phase plane method are limited to the 2nd order of the linear part of the automatic control system, the influence of the third order on the dynamics of the system is considered using the example of a mechatronic module drive. It is shown that taking into account the electric time constant leads to overshoot within 5-10 %. Such overshoot can be eliminated due to the proposed recommendations for correcting the static characteristic of the fuzzy controller.

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Design and Experimental Validation of a LQG Control System for the Stabilization of a 2DOF Commercial Gimbal Using Physical Modelling Techniques

Volume 7A: Dynamics, Vibration, and Control ◽

10.1115/imece2020-24137 ◽

2020 ◽

Author(s):

Julián Andres Gómez Gómez ◽

Camilo E. Moncada Guayazán ◽

Sebastián Roa Prada ◽

Hernando Gonzalez Acevedo

Keyword(s):

Mathematical Model ◽

Control System ◽

State Space ◽

Transient Response ◽

Space Form ◽

Angular Position ◽

Physical Modelling ◽

Motor Shaft ◽

Brushless Dc ◽

The Mathematical Model

Abstract Gimbals are mechatronic systems well known for their use in the stabilization of cameras which are under the effect of sudden movements. Gimbals help keeping cameras at previously defined fixed orientations, so that the captured images have the highest quality. This paper focuses on the design of a Linear Quadratic Gaussian, LQG, controller, based on the physical modeling of a commercial Gimbal with two degrees of freedom (2DOF), which is used for first-person applications in unmanned aerial vehicle (UAV). This approach is proposed to make a more realistic representation of the system under study, since it guarantees high accuracy in the simulation of the dynamic response, as compared to the prediction of the mathematical model of the same system. The development of the model starts by sectioning the Gimbal into a series of interconnected links. Subsequently, a fixed reference system is assigned to each link body and the corresponding homogeneous transformation matrices are established, which will allow the calculation of the orientation of each link and the displacement of their centers of mass. Once the total kinetic and potential energy of the mechanical components are obtained, Lagrange’s method is utilized to establish the mathematical model of the mechanical structure of the Gimbal. The equations of motion of the system are then expressed in state space form, with two inputs, two outputs and four states, where the inputs are the torques produced by each one of the motors, the outputs are the orientation of the first two links, and the states are the aforementioned orientations along with their time derivatives. The state space model was implemented in MATLAB’s Simulink environment to compare its prediction of the transient response with the prediction obtained with the representation of the same system using MATLAB’s SimMechanics physical modelling interface. The mathematical model of each one of the three-phase Brushless DC motors is also expressed in state space form, where the three inputs of each motor model are the voltages of the corresponding motor phases, its two outputs are the angular position and angular velocity, and its four states are the currents in two of the phases, the orientation of the motor shaft and its rate of change. This model is experimentally validated by performing a switching sequence in both the simulation model and the physical system and observing that the transient response of the angular position of the motor shaft is in accordance with the theoretical model. The control system design process starts with the interconnection of the models of the mechanical components and the models of the Brushless DC Motor, using their corresponding state space representations. The resulting model features six inputs, two outputs and eight states. The inputs are the voltages in each phase of the two motors in the Gimbal, the outputs are the angular positions of the first two links, and the states are the currents in two of the phases for each motor and the orientations of the first two links, along with their corresponding time derivatives. An optimal LQG control system is designed using MATLAB’s dlqr and Kalman functions, which calculate the gains for the control system and the gains for the states estimated by the observer. The external excitation in each of the phases is carried out by pulse width modulation. Finally, the transient response of the overall system is evaluated for different reference points. The simulation results show very good agreement with the experimental measurements.

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Algebraic methods in analysis and synthesis of stabilizing feedback compensators in linear multivariable automatic control systems

10.12681/eadd/30518 ◽

2012 ◽

Author(s):

Χριστίνα Καζαντζίδου

Keyword(s):

Automatic Control ◽

Control Systems ◽

Algebraic Methods ◽

Automatic Control Systems ◽

Analysis And Synthesis

Το αντικείμενο της παρούσας ιδακτορικής ιατριβής είναι η ανάπτυξη καιεξέλιξη μαθηματικών τεχνικών ανάλυσης και σύνθεσης σταθεροποιητικώνελεγκτών ή αντισταθμιστών για γραμμικά και χρονικά αναλλοίωτα πολυμετα-βλητά συστήματα Αυτομάτου Ελέγχου με αλγεβρο-πολυωνυμικές μεθόδους.Τέτοιες μέθοδοι είναι μοντέρνες τεχνικές ανάλυσης και σύνθεσης συστημάτων,σημάτων και βιομηχανικών διαδικασιών που βασίζονται σε μαθηματικά μοντέλαφυσικών συστημάτων και διαδικασιών, τα οποία συνίστανται από συστήματαγραμμικών διαφορικών και αλγεβρικών εξισώσεων ή εξισώσεων διαφορών μεσταθερούς συντελεστές. Οι μαθηματικές τεχνικές ανάλυσης και σύνθεσηςσταθεροποιητικών ελεγκτών τέτοιων συστημάτων προκύπτουν ως συνέπειεςαλγεβρικών ιδιοτήτων μαθηματικών μοντέλων πολυμεταβλητών συστημάτων, ταοποία περιγράφονται με πίνακες ρητών συναρτήσεων, και κάτω απόμετασχηματισμούς που περιγράφουν με αλγεβρικό τρόπο τη διασύνδεσημαθηματικών μοντέλων πολυμεταβλητών συστημάτων μέσω ανάδρασης. Σκοπόςτους είναι ο έλεγχος και η αλλαγή (όποτε αυτή είναι δυνατή) των δομικώνιδιοτήτων συστημάτων, όπως για παράδειγμα της ευστάθειας, της χρονικήςαπόκρισης ή της απόκρισης στο πεδίο των συχνοτήτων, σε αντίστοιχεςεπιθυμητές ιδιότητες για το προκύπτον κλειστό σύστημα.

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The motion of a geosynchronous satellite

Symposium - International Astronomical Union ◽

10.1017/s0074180900148326 ◽

1986 ◽

Vol 114 ◽

pp. 293-295

Author(s):

K. B. Bhatnagar

Keyword(s):

Angular Velocity ◽

Solar Radiation ◽

Radiation Pressure ◽

Angular Position ◽

Orbital Plane ◽

Solar Radiation Pressure ◽

Orbital Inclination ◽

Geosynchronous Satellite ◽

The Earth ◽

Earth’S Equatorial Ellipticity

The motion of a geosynchronous satellite has been studied under the combined gravitational effects of the oblate Earth (including its equatorial ellipticity), the Sun, the Moon and the solar-radiation pressure. It is observed that the orbital plane rotates with an angular velocity the maximum value of which is 0.058°/yr. and regresses with a period which increases both as the orbital inclination and the altitude increase. The effect of earth's equatorial ellipticity on the regression period is oscillatory whereas that of Solar-radiation pressure is to decrease it.The synchronism is achieved when the angular velocity of the satellite is equal to the difference between the spin-rate of the Earth and the regression rate of the orbital plane. With this angular velocity of the satellite, the ground trace is in the shape of figure eight, though its size and position relative to the Earth change as the time elapses. The major effect of earth's equatorial ellipticity is to produce a change in the relative angular position of the satellite as seen from the Earth. If the satellite is allowed to execute large angle oscillations the mid-point of oscillation would be at the position of the minor axis of the earth's equatorial section. The oscillatory period T has been determined in terms of the amplitude Γ and the tesseral harmonic J2(2). From this result we can determine the value of J2(2) as T and Γ can be observed accurately.

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