Cascade PID control of some processes with distributed parameters through the (Mpdx) method with approximating solutions

Coloşi, Tiberiu; Abrudean, Mihai; Ungureşan, Mihaela-Ligia; Mureşan, Vlad

doi:10.3182/20130522-3-ro-4035.00004

Cited by 9 publications

(12 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The tabular method may be considered an ideal method whenever experimentally can be completed tables such as the one below, both from to and from to , either for a real process or for an approximating solution, which corresponds, for example, with the relation (23) Table I, for the line the following curve could be represented [4], [5]: (24) Also, for column the following curve could be represented [4], [5]: (25) where and Thus, it can be observed that from the relations (24) and (25) days to days, and from to meters, both and evolutions are exponentially increasing, resulting that the phenomenon is cumulative, both in relation to time and in relation to the propagation space.…”

Section: Approximation Of Structure Parameters By Tabular Methodsmentioning

confidence: 99%

“…In addition, it can also be shown that for the decreasing evolutions of and defined by the relations (7) and (8) and exemplified in figure 2, where and , the inflection abscises respectively correspond to those defined in the relations (5) and (6) (2), (3), (5) and (6) there are taken into consideration the following notations [1]- [3], [6]- [8]:…”

Section: Introductionmentioning

confidence: 99%

“…Considering the final values and The approximating solution represented in relation (1) may be rewritten considering relations (2) and (3) such as [1]- [5]: (4) The inflection abscises correspond to the following relations [1]- [3], [5]- [7]:…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Preliminaries of Structural Parameters Approximation Through Transcendence Equations for an 15N Isotope Separation Column

Mureșan¹,

D.²,

Clitan³

et al. 2017

IJMO

View full text Add to dashboard Cite

Abstract-Theisotope separation column process presented in this article represents a space propagation process modeled by second-order quasi-linear equations with two independent variables. The new approach of Cohen's equation using a second-order differential equation in relation to time variable t and spatial variable s is presented. For this stage of development, for variables and there is a limitation of two time constants ( ), or space constants ( ). Also, and evolutions are exponentially increasing, resulting that the phenomenon is cumulative, both in relation to time and in relation to the propagation space. In this case, results a family of curves of the concentration.Index Terms-Isotopic separation process, cohen's equation, transcendent equations, structural parameters approximation. I. INTRODUCTIONThe space propagation process presented in this article represents an isotope separation column process which is modeled by second-order quasi-linear equations with two independent variables.Using a second-order differential equation in relation with both time and space variables, a new approach of Cohen's equation is presented.In the following equation, it is considered the overdamped version of approximating solutions associated with the isotopic separation phenomena [1]-[3]:(1) For this stage of development, for variables and there is a limitation of two time constants ( ), or space constants ( ). The evolution of and is represented in the following figure:Also, and evolutions are exponentially increasing, resulting that the phenomenon is cumulative, both in relation to time and in relation to the propagation space. In this case, results a family of curves of the concentration.Considering the final values and In addition, it can also be shown that for the decreasing evolutions of and defined by the relations (7) and (8) and exemplified in figure 2, where and , the inflection abscises respectively correspond to those defined in the relations (5) and (6) [1-2].(7) (8) Further, in this paper it will be presented only the case for increasing evolution of the and .Preliminaries of Structural Parameters Approximation Through Transcendence Equations for an Isotope Separation Column Muresan V., Sas D., Clitan I., and Unguresan M.-L.International Journal of Modeling and Optimization, Vol. 7, No. 5, October 2017 305 DOI: 10.7763/IJMO.2017.V7.603 Based on knowing the abscises ( , and ordinate , but also the abscises , and ordinate the aproximating parameters noted above determine the aproximation of both and , respectively and . It will be considered the following transcendentwhere:Calculations start with for providing iterative increasing for until the difference (DIF) changes its mark and fulfills to the solution of the transcendent equation.The following relations corresponds to the approximation of space constants ( ) and ( with an error, as low as the step (At the same time, it can be shown that there is only one value ( for which the curve represented in the following figure passes simultaneously through t...

show abstract

Section: Approximation Of Structure Parameters By Tabular Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Preliminaries of Structural Parameters Approximation Through Transcendence Equations for an 15N Isotope Separation Column

Mureșan¹,

D.²,

Clitan³

et al. 2017

IJMO

View full text Add to dashboard Cite

show abstract

“…Taking into consideration the relations (2) respectively (3), (1) is presented as follows [2], [4]: (4) Considering the elements of the Cartesian system, namely p = 0 and q = 0, it follows that s = r corresponds to the height of the column, respective represents the final height of the column. With and are noted the initial and final moments of the isotopic separation process.…”

Section: Introductionmentioning

confidence: 99%

“…(1), the partial derivatives expressed in relation (6) lead to much more unitary and systematized expressions than those resulting in , presented in [3], directly associated with Cohen's equation. (6) As a result, the following relations will be presented as follows [1], [2], [4]: (7) ) (…”

Section: Introductionmentioning

confidence: 99%

Analytical Modeling of an 15N Isotope Separation Column by Second-Order Quasi-Linear Equations with Two Independent Variable

Sas¹,

Clitan²,

M-L.³

et al. 2017

IJMO

View full text Add to dashboard Cite

Abstract-The presented process is an isotope separation column for , which represents a space propagation process modeled by the proposed method. Cohen's equation was approached by a second-order differential equation in relation to time t and also second-order in relation to the spatial variable s. This second order partial derivative equation was developed at an initial stage for which the variables and have been limited to two time constants ( ), or space ( ), resulting a family of curves of the concentration.

show abstract

Process modeling and simulation of distributed parameter using (M<inf>pdx</inf>) method with approximating solutions

Sas

Ungureşan

Coloşi

et al. 2014

2014 IEEE International Conference on Automation, Quality and Testing, Robotics

View full text Add to dashboard Cite

This paper presents a control system where the controlled plant is a distributed parameter process. Numerical simulation of the control system is accomplished using the method of Matrix of Partial Derivatives of the State Vector associated with Taylor Series. By including a process modeled by a partial differential equation of second order with two independent variables, this presents method with approximate solutions, which are needed to ensure the start of the calculations and to check the results.

show abstract

Cascade PID control of some processes with distributed parameters through the (Mpdx) method with approximating solutions

Cited by 9 publications

References 0 publications

Preliminaries of Structural Parameters Approximation Through Transcendence Equations for an 15N Isotope Separation Column

Preliminaries of Structural Parameters Approximation Through Transcendence Equations for an 15N Isotope Separation Column

Analytical Modeling of an 15N Isotope Separation Column by Second-Order Quasi-Linear Equations with Two Independent Variable

Process modeling and simulation of distributed parameter using (M<inf>pdx</inf>) method with approximating solutions

Contact Info

Product

Resources

About