A Study of the stability of solutions to inverse problems of dynamics of control systems under perturbations of initial data

2015 ◽  
Vol 291 (S1) ◽  
pp. 173-189 ◽  
Author(s):  
N. N. Subbotina ◽  
T. B. Tokmantsev
Keyword(s):  
Inverse Problems ◽  
Initial Data ◽  
Control Systems ◽  
Stability Of Solutions ◽  
Perturbations Of Initial Data ◽  
Inverse Problems Of Dynamics ◽  
The Stability

scholarly journals ABSOLUTE STABILITY OF A PROGRAM MANIFOLD OF NON-AUTONOMOUS BASIC CONTROL SYSTEMS

2018 ◽  
pp. 37-43
Author(s):  
Sailaubay Zhumatov
Keyword(s):  
Inverse Problem ◽  
Lyapunov Function ◽  
Control Systems ◽  
Absolute Stability ◽  
High Speed ◽  
Inverse Dynamics ◽  
Sufficient Conditions ◽  
System Of Differential Equations ◽  
Inverse Problems Of Dynamics ◽  
The Stability

In this paper the inverse dynamics problemisstudied: for a given manifold restore a force field, which lies in the tangent subspace to manifold. One of the general inverse problems of dynamics is solved: the corresponding system of differential equations is but as well as the stability is considered. This inverse problem is very important for a variety of mathematical models mechanics.Absolutestability of a program manifold of nonautonomous basic control systems with stationary nonlinearity is investigated.Theproblem of stability of the basic control systems is considered in the neighborhood of a program manifold. Nonlinearitysatisfies to conditions of local quadratic relations. The sufficient conditions of the absolute stability of the program manifold have been obtained relatively to a given vector-function by means of construction of Lyapunov function, in the form "quadratic form plus an integral from nonlinearity". The obtained results are used to solve the problem of the synthesis of high-speed regulators.

scholarly journals Solving a Class of Nonlinear Inverse Problems Using a Feedback Control Approach

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Mahmoud Tarokh
Keyword(s):  
Feedback Control ◽  
Inverse Problems ◽  
Control Systems ◽  
Stability And Convergence ◽  
Science And Engineering ◽  
New Approach ◽  
Control Approach ◽  
Highly Nonlinear ◽  
Feedback Control Systems ◽  
The Stability

Inverse problems have applications in many branches of science and engineering. In this paper we propose a new approach to solving inverse problems which is based on using concepts from feedback control systems to determine the inverse of highly nonlinear, discontinuous, and ill-conditioned input-output relationships. The method uses elements from least squares solutions that are formed within a control loop. The stability and convergence of the inverse solution are established. Several examples demonstrate the applicability of the proposed method.

TO THE STABILITY OF TANK VEHICLES IN THE BRAKE MODE

2019 ◽  
pp. 27-32
Author(s):  
Denys Popelysh ◽  
Yurii Seluk ◽  
Sergyi Tomchuk
Keyword(s):  
Mathematical Model ◽  
Control Systems ◽  
Distribution Systems ◽  
Traffic Accidents ◽  
Road Traffic ◽  
Center Of Mass ◽  
Dynamic Processes ◽  
Course Stability ◽  
The Stability ◽  
Tank Vehicles

This article discusses the question of the possibility of improving the roll stability of partially filled tank vehicles while braking. We consider the dangers associated with partially filled tank vehicles. We give examples of the severe consequences of road traffic accidents that have occurred with tank vehicles carrying dangerous goods. We conducted an analysis of the dynamic processes of fluid flow in the tank and their influence on the basic parameters of the stability of vehicle. When transporting a partially filled tank due to the comparability of the mass of the empty tank with the mass of the fluid being transported, the dynamic qualities of the vehicle change so that they differ significantly from the dynamic characteristics of other vehicles. Due to large displacements of the center of mass of cargo in the tank there are additional loads that act vehicle and significantly reduce the course stability and the drivability. We consider the dynamics of liquid sloshing in moving containers, and give examples of building a mechanical model of an oscillating fluid in a tank and a mathematical model of a vehicle with a tank. We also considered the method of improving the vehicle’s stability, which is based on the prediction of the moment of action and the nature of the dynamic processes of liquid cargo and the implementation of preventive actions by executive mechanisms. Modern automated control systems (anti-lock brake system, anti-slip control systems, stabilization systems, braking forces distribution systems, floor level systems, etc.) use a certain list of elements for collecting necessary parameters and actuators for their work. This gives the ability to influence the course stability properties without interfering with the design of the vehicle only by making changes to the software of these systems. Keywords: tank vehicle, roll stability, mathematical model, vehicle control systems.

Symmetrizable Difference Dchemes

2005 ◽  
Vol 5 (1) ◽  
pp. 3-50 ◽  
Author(s):  
Alexei A. Gulin
Keyword(s):  
Initial Data ◽  
Difference Scheme ◽  
Difference Schemes ◽  
Time Dependent ◽  
Stability Boundaries ◽  
Typical Representative ◽  
Variable Weight ◽  
The Stability ◽  
Conditions Of Stability ◽  
The Right

AbstractA review of the stability theory of symmetrizable time-dependent difference schemes is represented. The notion of the operator-difference scheme is introduced and general ideas about stability in the sense of the initial data and in the sense of the right hand side are formulated. Further, the so-called symmetrizable difference schemes are considered in detail for which we manage to formulate the unimprovable necessary and su±cient conditions of stability in the sense of the initial data. The schemes with variable weight multipliers are a typical representative of symmetrizable difference schemes. For such schemes a numerical algorithm is proposed and realized for constructing stability boundaries.

scholarly journals Implicit nonlinear fractional differential equations of variable order

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Amar Benkerrouche ◽  
Mohammed Said Souid ◽  
Kanokwan Sitthithakerngkiet ◽  
Ali Hakem
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Fractional Differential Equations ◽  
Boundary Value ◽  
Variable Order ◽  
Stability Of Solutions ◽  
Nonlinear Fractional Differential Equations ◽  
Caputo Fractional Differential Equations ◽  
Fractional Differential ◽  
The Stability

AbstractIn this manuscript, we examine both the existence and the stability of solutions to the implicit boundary value problem of Caputo fractional differential equations of variable order. We construct an example to illustrate the validity of the observed results.

scholarly journals The Application of an Impedance-Passivity Controller in Haptic Stability Analysis

2021 ◽  
Vol 11 (4) ◽  
pp. 1618
Author(s):  
Ping-Nan Chen ◽  
Yung-Te Chen ◽  
Hsin Hsiu ◽  
Ruei-Jia Chen
Keyword(s):  
Control Systems ◽  
Force Feedback ◽  
Training System ◽  
Considerable Time ◽  
Virtual Training ◽  
Control Gain ◽  
Negative Damping ◽  
The Stability ◽  
Time Required ◽  
Stable Control

This paper proposes a passivity theorem on the basis of energy concepts to study the stability of force feedback in a virtual haptic system. An impedance-passivity controller (IPC) was designed from the two-port network perspective to improve the chief drawback of haptic systems, namely the considerable time required to reach stability if the equipment consumes energy slowly. The proposed IPC can be used to achieve stability through model parameter selection and to obtain control gain. In particular, haptic performance can be improved for extreme cases of high stiffness and negative damping. Furthermore, a virtual training system for one-degree-of-freedom sticking was developed to validate the experimental platform of our IPC. To ensure consistency in the experiment, we designed a specialized mechanical robot to replace human operation. Finally, compared with basic passivity control systems, our IPC could achieve stable control rapidly.

Device for the Experimental Determination of Control Objects' Mathematical Models

2013 ◽  
Vol 650 ◽  
pp. 493-497 ◽  
Author(s):  
Valerij I. Goncharov ◽  
Vadim A. Onufriev ◽  
Ilya O. Ilyin
Keyword(s):  
Control Systems ◽  
Computer Technology ◽  
Interpolation Method ◽  
Facilities Management ◽  
Operational Conditions ◽  
Automatic Control Systems ◽  
Interpolation Procedure ◽  
Real Interpolation Method ◽  
Inverse Problems Of Dynamics

Authors review methods of determining a plant’s mathematical model. Then, they show a numerical method of pulse automatic control systems’ (ACS) identification, focused on computer technology, the interpolation procedure and iterative methods of approximation to the desired solution. The basis of the approach is the method of inverse problems of dynamics and real interpolation method for calculating the linearized dynamical systems. An algorithm and the mobile device designed for the identification of facilities management in operational conditions are proposed. There is results’ application in the conclusion.

Sign in / Sign up

Export Citation Format

Share Document