METHODS OF SYNTHESIS OF REGULATORS FOR HYDRODYNAMIC CONTROL SYSTEMS WITH DISTRIBUTED PARAMETERS

2021 ◽  
Vol 55 (3) ◽  
pp. 82-89
Author(s):  
KALIBERDA IGOR V. ◽  
Keyword(s):  
Mathematical Model ◽  
Control Systems ◽  
System Analysis ◽  
Structural Method ◽  
Frequency Method ◽  
Discrete Function ◽  
Distributed Parameters ◽  
Dimensional Approximation ◽  
The Mathematical Model ◽  
Systems With Distributed Parameters

An important problem of choosing a method for synthesizing regulators for constructing a system for controlling the parameters of hydrolithospheric processes is considered. The article deals with the issues of system analysis and synthesis of control systems with distributed parameters. The existing ways of solving mathematical equations describing models with spatial coordinates are shown. The main methods when there are solutions to the mathematical model are identified: analytical construction of optimal regulators and the structural method of analysis. Methods of approximation in cases where there is no solution to the mathematical model are described: methods of finite-dimensional approximation; decomposition of bilinear control systems; frequency method. The main provisions of the methods for solving the problem of discretization in partial derivatives are given. The preference of the frequency method of regulator synthesis in the creation of control systems for hydrolithospheric processes is shown. A hodograph is obtained in the form of logarithmic amplitude and phase frequency surfaces, which can be used to interpret the Nyquist stability criterion from graphs. A frequency method for the synthesis of multidimensional systems is considered, when the input effects to a distributed controller are implemented as a discrete function in space. The condition under which the object belongs to the class of spatially invariant objects is shown. It is concluded that the frequency method of regulator synthesis is the most convenient tool for creating systems with distributed parameters.

Optimal Model Selection Using MP Criterion for Uncertain Multivariable 2×2 Systems Based on IMC

2008 ◽  
Author(s):  
Inbal Shani ◽  
Neima Brauner ◽  
Coleman B. Brosilow
Keyword(s):  
Mathematical Model ◽  
Control Systems ◽  
Controller Design ◽  
Optimal Model ◽  
Time Constants ◽  
The Real ◽  
Real Process ◽  
Decoupled Control ◽  
The Mathematical Model ◽  
Performance Variations

IMC controller design for a process is based on choosing a mathematical model that describes the real process. The mathematical model describing such process is often not unique because the real variables of the process can vary within an interval. In such cases the performance of the control system varies, possibly substantially, as process parameters change. To limit such performance variations, we have developed an algorithm for choosing the model gains and the filter time constants of the IMC controller, to minimize the amount of interaction between outputs due to set point changes and disturbances for multivariable decoupled control systems. Some examples illustrate the algorithm.

Symmetric Control Systems

2021 ◽  
pp. 37-51
Author(s):  
A.I. Diveev ◽  
E.A. Sofronova
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Control Systems ◽  
Control Object ◽  
Terminal State ◽  
Initial State ◽  
Phase Constraints ◽  
The Mathematical Model

The paper focuses on the properties of symmetric control systems, whose distinctive feature is that the solution of the optimal control problem for an object, the mathematical model of which belongs to the class of symmetric control systems, leads to the solution of two problems. The first optimal control problem is the initial one; the result of its solution is a function that ensures the optimal movement of the object from the initial state to the terminal one. In the second problem, the terminal state is the initial state, and the initial state is the terminal state. The complexity of the problem being solved is due to the increase in dimension when the models of all objects of the group are included in the mathematical model of the object, as well as the emerging dynamic phase constraints. The presence of phase constraints in some cases leads to the target functional having several local extrema. A theorem is proved that under certain conditions the functional is not unimodal when controlling a group of objects belonging to the class of symmetric systems. A numerical example of solving the optimal control problem with phase constraints by the Adam gradient method and the evolutionary particle swarm method is given. In the example, a group of two symmetrical objects is used as a control object

scholarly journals The Mathematical Model for Research of the UAV Longitudinal Moving

2021 ◽  
Vol 13 (5) ◽  
pp. 29-39
Author(s):  
Sergii Zhdanov ◽  
◽  
Natalia Kadet ◽  
Valerii Silkov ◽  
Mariia Zirka ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Frequency Response ◽  
Unmanned Aerial Vehicles ◽  
Control Systems ◽  
Aerial Vehicles ◽  
General Mathematical Model ◽  
Logarithmic Frequency ◽  
The Impact ◽  
The Mathematical Model

The paper presents one of the perspective directions of the development to modern aviation, which is connected with designing and producing unmanned aerial vehicles (UAV) of various functionalities for applying in both military and civilian spheres. The syntheses of UAV control systems, regardless of their type and purpose presumes creation of adequate mathematical models, first of all adequate aerodynamic mathematical models. In the paper results that forms and justify the aerodynamic mathematical model and as well as the results of building a general mathematical model of the longitudinal movement of the perspective UAV are presented. Also factors that forms the mathematical model on given aerodynamic, geometric, mass and inertial data for a hypothetical perspective altitude long-range UAV are submitted. Assessment of the impact of these data on the dynamic, temporal, and logarithmic frequency response UAV also has been given in this paper.

A Knowledge-Based Controller Used in Process Control Systems

1997 ◽  
Vol 05 (01) ◽  
pp. 47-57
Author(s):  
Jin Wang ◽  
Fuli Wang ◽  
Mingzhong Li ◽  
Yingha Yang
Keyword(s):  
Mathematical Model ◽  
Process Control ◽  
Control Systems ◽  
Fuzzy Reasoning ◽  
Human Experience ◽  
Process Dynamics ◽  
Knowledge Based ◽  
Process Control Systems ◽  
Simulation Results ◽  
The Mathematical Model

A knowledge-based controller(KBC) used in process control systems is presented. It has three features: first, it does not need the mathematical model; secondly, the adjustable parameters of KBC have practical meanings, so they can be determined easily using human experience, and thirdly, the contribution of KBC to a controlled plant is separated into two parts: steady states contribution and transient contribution. A simple fuzzy reasoning is employed to tune the KBC parameters. The experimental and simulation results show that KBC is very effective especially when there are variations in the process dynamics.

ON UNIQUENESS OF FILIPPOV’S SOLUTIONS FOR NON-SMOOTH SYSTEMS HAVING MULTIPLE DISCONTINUITY SURFACES WITH APPLICATIONS TO ROBOTIC CONTROL SYSTEMS

2007 ◽  
Vol 31 (2) ◽  
pp. 191-206
Author(s):  
Q. Wu ◽  
H. Zeng
Keyword(s):  
Mathematical Model ◽  
Control Systems ◽  
Convex Sets ◽  
Numerical Solutions ◽  
Robotic Systems ◽  
Robotic Control ◽  
Physical Systems ◽  
Discontinuity Surfaces ◽  
The Mathematical Model

Analysis of the uniqueness of Filippov's solutions to non-smooth robotic control systems is important before the solutions can be sought. Such an analysis is extremely challenging when the discontinuity surface is the intersection of multiple discontinuity surfaces. The key step is to study the intersections of the convex sets from Filippov's inclusions and their associated sets containing vectors tangent to the discontinuity surfaces. For practical non-smooth robotic systems, due to their complexities, the determination of the intersections of these sets symbolically is extremely difficult if not impossible. In this paper, we propose a method such that the determinations of the intersections become feasible. Two examples of practical non-smooth robotic control systems are presented to demonstrate the efficacy of the method. The work contributes significantly to the analysis of non-smooth systems where the proof of the uniqueness of Filippov’s solution is crucial to keep the mathematical model relevant to physical systems and to ensure the numerical solutions can be sought.

scholarly journals Application of Fractional-Order Calculus to Improve the Mathematical Model of a Two-Mass System with a Long Shaft

Energies ◽  
2021 ◽  
Vol 14 (7) ◽  
pp. 1854
Author(s):  
Andriy Lozynskyy ◽  
Andriy Chaban ◽  
Tomasz Perzyński ◽  
Andrzej Szafraniec ◽  
Lidiia Kasha
Keyword(s):  
Mathematical Model ◽  
Fractional Order ◽  
Mass System ◽  
Electric Drives ◽  
Distributed Parameters ◽  
Time Space ◽  
Joint Coordinates ◽  
Sufficient Degree ◽  
Fractional Order Integrator ◽  
The Mathematical Model

Based on the general theory of fractional order derivatives and integrals, application of the Caputo–Fabrizio operator is analyzed to improve a mathematical model of a two-mass system with a long shaft and concentrated parameters. Thus, the real transmission of complex electric drives, which consist of long shafts with a sufficient degree of adequacy, is presented as a two-mass system. Such a system is described by ordinary fractional order differential equations. In addition, it is well known that an elastic mechanical wave, propagating along a drive transmission with a long stiff shaft, creates a retardation effect on distribution of the time–space angular velocity, the rotation angle of the shaft, and its elastic moment. The approach proposed in the current work helps to take in account the moving elastic wave along the shaft of electric drive mechanism. On this basis, it is demonstrated that the use of the fractional order integrator in the model for the elastic moment enables it to reproduce real transient processes in the joint coordinates of the system. It also provides an accuracy equivalent to the model with distributed parameters. The distance between the traditional model and the model in which the fractional integral is used for the elastic moment modelling in a two-mass system, with a long shaft, is analyzed.

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