Synthesis of Programmed Motion Based on Special Optimal Control

2021 ◽  
Vol 22 (8) ◽  
pp. 395-403
Author(s):  
V. S. Khoroshavin ◽  
V. S. Grudinin
Keyword(s):  
Control Systems ◽  
Phase Trajectory ◽  
Sliding Mode ◽  
Synthesis Method ◽  
Coordinate Space ◽  
Initial State ◽  
Relay Control ◽  
Higher Derivatives ◽  
Linear And Nonlinear ◽  
Special Control

A method is proposed for the synthesis of a closed-loop system with controls that ensure the movement of an object with minimal deviations from a given trajectory of the output coordinate and its higher derivatives and a transition to this set. To solve the problem, the Pontryagin maximum principle is used to study special situations without analysis of auxiliary variables, supplemented by the apparatus of general position conditions for nonlinear systems in an extended coordinate space, taking into account the object, a functional that is nonlinear regarding deviations of the output coordinate and the explicit occurrence of time. The combined use of these methods allows us, firstly, to find special trajectories of coordinates that are higher derivatives of the output coordinate, and after excluding time, a special phase trajectory is found, which is a switching line for reaching the final state, a given programmed motion along which in a closed system is carried out by special control. Secondly, access to a special phase trajectory from the initial state is carried out for linear objects by relay control, and for nonlinear objects, under certain boundary conditions, relay control is supplemented by a special control of the speed problem. Examples of control of programmed motion with oscillatory and aperiodic processes of a given duration for linear and nonlinear objects are given. Taking into account the nature of equilibrium states, determined by the methods of the qualitative theory of differential equations, and restrictions on control and coordinates, topologies of trajectories are obtained for the implementation of a continuous special control or sliding mode. New algorithms and structures of control systems are obtained. The results are accompanied by modeling, illustrating the effectiveness of algorithms and structures of control systems according to the proposed synthesis method and confirming analytical materials. The results of the work can be used to control linear and nonlinear objects in mechatronics, robotics, thermal processes and other industries.

The synthesis method of regulators for multichannel systems using neural networks

2020 ◽  
pp. 111-118
Author(s):  
Александр Александрович Воевода ◽  
Дмитрий Олегович Романников
Keyword(s):  
Neural Networks ◽  
Reinforcement Learning ◽  
Automatic Control ◽  
Control Systems ◽  
Synthesis Method ◽  
Neural Net ◽  
Initial State ◽  
Set Point ◽  
Automatic Control Systems ◽  
Policy Gradient

Синтез регуляторов для многоканальных систем - актуальная и сложная задача. Одним из возможных способов синтеза является применение нейронных сетей. Нейронный регулятор либо обучают на предварительно рассчитанных данных, либо используют для настройки параметров ПИД-регулятора из начального устойчивого положения замкнутой системы. Предложено использовать нейронные сети для регулирования двухканального объекта, при этом обучение будет выполняться из неустойчивого (произвольного) начального положения с применением методов обучения нейронных сетей с подкреплением. Предложена структура нейронной сети и замкнутой системы, в которой уставка задается при помощи входного параметра нейронной сети регулятора The problem for synthesis of automatic control systems is hard, especially for multichannel objects. One of the approaches is the use of neural networks. For the approaches that are based on the use of reinforcement learning, there is an additional issue - supporting of range of values for the set points. The method of synthesis of automatic control systems using neural networks and the process of its learning with reinforcement learning that allows neural networks learning for supporting regulation is proposed in the predefined range of set points. The main steps of the method are 1) to form a neural net input as a state of the object and system set point; 2) to perform modelling of the system with a set of randomly generated set points from the desired range; 3) to perform a one-step of the learning using the Deterministic Policy Gradient method. The originality of the proposed method is that, in contrast to existing methods of using a neural network to synthesize a controller, the proposed method allows training a controller from an unstable initial state in a closed system and set of a range of set points. The method was applied to the problem of stabilizing the outputs of a two-channel object, for which stabilization both outputs and the first near the input set point is required

scholarly journals ALGORITHM FOR SYNTHESIS OF QUASI-OPTIMAL IN SPEED THIRD-ORDER SYSTEMS WITH APERIODIC SLIDING MODE

2021 ◽  
Vol 1 (38) ◽  
pp. 48-56
Author(s):  
O. Derets ◽  
O. Sadovoi ◽  
H. Derets
Keyword(s):  
Control System ◽  
Control Systems ◽  
Electric Drive ◽  
Sliding Mode ◽  
Block Diagram ◽  
Order System ◽  
Practical Implementation ◽  
Third Order ◽  
Relay Control ◽  
Electric Drives

The relevance of the work is due to the growing requirements for the dynamic characteristics of electric drives. In particular, together with the requirements of ensuring high accuracy and maximum at given speed limits, a typical task of designing such systems is the mandatory formation of transition diagrams in the form of monotonic time functions. The purpose of this study is to develop an adaptive algorithm for the synthesis of the third-order sliding mode control systems based on the method of N-i switching. Changing the shape of transient trajectory depends on the magnitude of the movement, which requires adaptation of the settings of the control system of the electric drive to the features of the current positioning mode. On the basis of the N-i switching method, an algorithm for synthesizing the parameters of a re-lay control system with cascade-subordinated structure, ensures non-oscillatory initiation of a sliding mode at various positioning modes, has been created. It is constructed by integrating the results of a number of previous works, in which the synthesis of relay control systems based on the analysis of the roots of the sliding equation of the position regulator is performed. This algorithm cannot be formally considered as an optimization tool due to the incompatibility of this problem with the aperiodization taken as the purpose, which comes about for certain forms of transient trajectories. But for such cases, the loss of performance relatively optimal one is negligible. Thus, the result of the application of the proposed algorithm in most practically significant cases is an optimal third-order system with aperiodic entry into the sliding mode. When controlling the electric drive, such a system will ensure the monotonous nature of the movement of the working body of the electromechanical system. The developed block diagram is focused on the practical implementation of the algorithm by the software of controllers of precision electric drives.

Relay Control Systems with Discrete Time Equalizer

2020 ◽  
Author(s):  
Oleksii Sheremet ◽  
Oleksandr Sadovoi ◽  
Kateryna Sheremet ◽  
Yuliia Sokhina
Keyword(s):  
Control Systems ◽  
Discrete Time ◽  
Relay Control

Leistungsverzweigter Servopressenantrieb*/Power-split servo press drive - Control of a new servo press drive with mechanical power split

2015 ◽  
Vol 105 (05) ◽  
pp. 291-296
Author(s):  
B.-A. Behrens ◽  
R. Krimm ◽  
J. Jocker ◽  
T. Nitschke
Keyword(s):  
Control Systems ◽  
Operating Costs ◽  
Mechanical Power ◽  
Forming Technology ◽  
Servo Press ◽  
Drive Control ◽  
Power Split ◽  
Control Concept ◽  
High Dynamic ◽  
Special Control

Am Institut für Umformtechnik und Umformmaschinen der Leibniz Universität Hannover wird zurzeit an einer neuartigen Antriebslösung für Servopressen gearbeitet, welche die Vorteile von Servopressen und Exzenterpressen mit Schwungradantrieb vereint. Ziel ist, sowohl bei der Anschaffung als auch im Betrieb Kosten einzusparen. Für die Ansteuerung der Antriebsmotoren wurde ein spezielles Regelkonzept erarbeitet, das sich deutlich von bestehenden Regelungssystemen heutiger Servopressen abgrenzt.   At the Institute of Forming Technology and Machines (Leibniz Universität Hannover), a new drive concept for servo presses is being developed which combines the advantages of servo presses with a high dynamic powertrain and flywheel based eccentric presses. This is intended to save acquisition and operating costs. To control the drive engines, a special control concept has been developed which is completely different from control systems of modern servo presses.

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