scholarly journals Regional Boundary Gradient Detectability in Distributed Parameter Systems

2018 ◽  
Vol 14 (2) ◽  
pp. 7818-7833 ◽  
Author(s):  
Raheam Al Saphory ◽  
Mrooj Al Bayati
Keyword(s):  
Hilbert Space ◽  
Domain Boundary ◽  
Distributed Parameter Systems ◽  
Distributed Parameter ◽  
System State ◽  
Infinite Dimensional ◽  
Infinite Dimensional Systems ◽  
Unknown System ◽  
Regional Boundary ◽  
Boundary Gradient

The aim of this paper is study and explore the notion of  the regional boundary gradient detectability in connection with the choice of strategic gradient sensors on sub-region of the considered system domain boundary. More precisely, the principal reason behind introducing this notion is that the possibility to design a dynamic system (may be called regional boundary gradient observer) which enable to estimate the unknown system state gradient. Then for linear infinite dimensional systems in a Hilbert space,  we give various new results related with different measurements. In addition, we provided a description of the regional boundary exponential gradient strategic sensors for completion the regional boundary exponential gradient observability and regional boundary exponential gradient detectability. Finally, we present and illustrate the some applications of sensors structures which relate by regional boundary exponential gradient detectability in diffusion distributed parameter systems.

scholarly journals On Regional Boundary Gradient Strategic Sensors In Diffusion Systems

2021 ◽  
Vol 20 ◽  
pp. 66-78
Author(s):  
Raheam Al-Saphory ◽  
Ahlam Y Al-Shaya
Keyword(s):  
Hilbert Space ◽  
Differential Equations ◽  
Distributed Parameter Systems ◽  
Distributed Parameter ◽  
Parabolic Differential Equations ◽  
Continuous Type ◽  
Diffusion Systems ◽  
Regional Boundary ◽  
Boundary Gradient

This paper is aimed at investigating and introducing the main results regarding the concept of Regional Boundary Gradient Strategic Sensors (RBGS-sensors  the in Diffusion Distributed Parameter Systems (DDP-Systems  . Hence, such a method is characterized by Parabolic Differential Equations (PDEs  in which the behavior of the dynamic is created by a Semigroup ( of Strongly Continuous type (SCSG  in a Hilbert Space (HS) . Additionally , the grantee conditions which ensure the description for such sensors are given respectively to together with the Regional Boundary Gradient Observability (RBG-Observability  can be studied and achieved . Finally , the results gotten are applied to different situations with altered sensors positions are undertaken and examined.

scholarly journals REGIONAL EXPONENTIAL REDUCED OBSERVABILITY IN DISTRIBUTED PARAMETER SYSTEMS

2015 ◽  
Vol 11 (4) ◽  
pp. 5058-5074 ◽  
Author(s):  
Shahad AL-MULLAH ◽  
Raheam Al-Saphory
Keyword(s):  
Sufficient Conditions ◽  
Distributed Parameter Systems ◽  
Distributed Parameter ◽  
Usual Sense ◽  
Two Phase ◽  
Linear Dynamical Systems ◽  
Infinite Dimensional ◽  
Infinite Dimensional Systems ◽  
New Concepts ◽  
Necessary And Sufficient

The regional exponential reduced observability concept in the presence for linear dynamical systems is addressed for a class of distributed parameter systems governed by strongly continuous semi group in Hilbert space. Thus, the existence of necessary and sufficient conditions is established for regional exponential reduced estimator in parabolic infinite dimensional systems. More precisely, the introduced approach is developed by using the decomposed system and reduced system in connection with various new concepts of (stability, detectability, estimator, observability and strategic sensors). Finally, we also show that there exists a dynamical system for two-phase exchange system described by the coupled parabolic equations is not exponentially reduced observable in usual sense, but it may be regionally exponentially reduced observable.

scholarly journals Regional Boundary Strategic Sensors Characterizations

2018 ◽  
Vol 14 (2) ◽  
pp. 7834-7850 ◽  
Author(s):  
Raheam Al-Saphory ◽  
Hind K. Kolaib
Keyword(s):  
Domain Boundary ◽  
Distributed Parameter ◽  
Usual Sense ◽  
Time Interval ◽  
Two Dimensional ◽  
Infinite Time ◽  
Infinite Dimensional ◽  
Infinite Time Interval ◽  
Boundary Observability ◽  
Regional Boundary

This paper, deals with the linear infinite dimensional distributed parameter systems in a Hilbert space where the dynamics of system is governed by strongly continuous semi-groups. More precisely, for parabolic distributed systems the characterizations of regional  boundary strategic sensors have been discussed and analyzed in different cases of regional  boundary observability in infinite time interval. Furthermore, the results so obtained are applied in two-dimensional systems and sensors studied under which conditions guarantee regional boundary observability in a sub-region of the system domain boundary.  Also, the authors show that, the existent of a sensor for the diffusion system is not strategic in the usual sense, but it may be regional  boundary strategic of this system.

Active Control of Mechanical Vibrations in a Circular Disk

1992 ◽  
Vol 114 (1) ◽  
pp. 104-112 ◽  
Author(s):  
C. Y. Kuo ◽  
C. C. Huang
Keyword(s):  
Mechanical Vibration ◽  
Circular Disk ◽  
Distributed Parameter Systems ◽  
Distributed Parameter ◽  
Sensors And Actuators ◽  
Mechanical Vibrations ◽  
Infinite Dimensional ◽  
Infinite Dimensional Systems ◽  
Finite Dimensional ◽  
And Control

Mechanical vibration is a common phenomenon observed in the operation of many machines and arises from the inertia effect of machine parts in motion. While many control system design methods for distributed parameter systems have already been proposed in the literature, generally they are either based on truncated models and, as a result, suffer from computational and “spillover” difficulties or require distributed parameter actuators which are rarely available in reality. Therefore, there is a definite need for the development of a class of controllers which can be realized by spatially discrete sensors and actuators and whose design specifically includes stabilization and control of all the higher frequency vibration modes. To address this need, we propose the design of linear compensators whose design is based on root locus arguments for infinite dimensional systems. Since the design is not based on finite dimensional models of the plant to be controlled, we expect it to perform well for those distributed parameter systems for which sufficiently accurate data on pole and zero locations can be obtained. In this paper we apply this approach to control mechanical vibrations in those physical systems which can be accurately modeled as a flexible circular disk. Computer simulation results indicate that all the predominant lower frequency vibrations can be efficiently eliminated by just a few pairs of colocated sensor and actuator.

The Description of a Distributed Parameter Process through a Finite Discrete Dimensional System

2014 ◽  
Vol 657 ◽  
pp. 874-878
Author(s):  
Sever Şerban ◽  
Doina Corina Şerban
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Industrial Process ◽  
Time Discretization ◽  
Distributed Parameter ◽  
Geometrical Parameters ◽  
Dimensional System ◽  
Infinite Dimensional ◽  
Infinite Dimensional Systems ◽  
Distributed Parameters

This article analyses the process of warming a metal by using a walking beam furnace. This process is meant to offer the technologist objective information that may allow him to produce eventual modifications of the temperature references from the furnaces zones. Thus making the metals temperature at the furnaces exit to have an imposed distribution, within precise limits, according to the technological requests. This industrial process has a geometrical parameters distribution, more precisely it can be described through a partial differential equation, by being attached to dynamic infinite dimensional systems (or with distributed parameters). Using a procedure called geometric-time discretization (in the condition of the solutions convergence), we have managed to obtain a representation under the form of a finite discrete dimensional linear system for a process with distributed parameters.

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