Academic Open Internet Journal

ISSN 1311-4360

www.acadjournal.com

Volume 17, 2006

 

 

 

FOR THE PLACE AND ROLE OF THE MATHEMATICAL MODELING IN CREATION

 OF AUTOMATED EQUIPMENT

 

Assos. Prof. PhD. Ivanka Georgieva

Department Electronic and communication technique and technologies

South-West University Neofit Rilski, Blagoevgrad, Bulgaria

E-mail: vanyakg@abv.bg

 

 

In the work is shared the personal experience of the author about the significance of the mathematical modeling in creation of new modernized automated equipment.

Created are general algorhytms for finding effective structural decisions and implementation in the production of automated equipment and systems.

 

  1. Introduction

The designing of automated equipment is a complex optimizing task. The solving of such a kind of task requires definite number of input data in order to choose optimal combination of technological, structural and component constructive decisions. One of the most responsible moments in designing of the automated equipment is the formulation of the technical offer.

The realization of a certain problem can be achieved by different variants of methods, technological routs, types of equipment, number of working positions, control systems etc. At the stage of technical offer, there should be selected one component structural variant to be used for further designing. The question for optimal combination of the parameters of new or modernized technological objects is actual for all spheres of the production. The optimization is based on the analysis of the mathematical methods, interrelations between technological, constructive and other parameters with features for reliability, capacity, and economical effectiveness of the created or modernized technological equipment.

The implementation during the last years of new technical means for automation, based on microprocessor technique brought about the creation of automated equipment, combining the production possibilities of the automated machines with the mobility and flexibility of the universal ones. In constructing and modernizing the equipment on lowest level (working process) today more and more are applied sensors able to process signals by themselves, to make preliminary assessment of the measured values, to compare normal and limit values or to receive and give several meanings of the values. These “intellectual” sensors can already exchange information between themselves as well as with the higher levels of the systems in this way changing the problems, which are solved on the first level (working process) in the hierarchy of the automated technological equipment. The exchange of information between the different components for automation in the contemporary automated machines and systems is carried out by the up to date communication Profibus or the interface AS-i.

In the work are revealed two stages: stage of analytic modeling of the object for automation and stage of technical assignment and work project.

 

2.Algorhytm for analytical modeling of the object for automation.

On Fig. 1 is presented algorhytm for development on the first stage. For obtaining full and maximum true information for the object for automation is needed to take into consideration all influencing factors. Otherwise every not recorded factor in the process of the experiment can start changing spontaneously its meaning and to encounter mistake during the experiments and from there mistakes in the automation of the relevant parameters.

On the stage preliminary and analytical investigation of the object for automation and modernization can be applied the mathematical methods according to the algorhytm on Fig.1.

 

The method of prior arrangement is based on survey investigation of opinions of specialists in this field and analysis of literature resources. Every factor is given a rank corresponding to its assumed influence on the investigated object and on the parameter of optimization. The aim of this method is to build arrangement order according to the significance of the factors and to remove the vague ones. The removal of the vague factors is carried out in compliance with definite technology. The application of this method is recommended in all cases when the object of automation is not known.

The precise investigation of the significance of the factors is carried out by the help of the method for removal of vague factors and their interactions by the method of random balance. Well known are two methods of removal by random balance – graphic and analytic. More precise is the analytical removal. The method is based on processing of experimental data from real measurements of the parameters of optimization by the relevant methodology. Investigated is the influence of all factors and their interactions, removed are the vague. The method requires considerable time for processing the experimental results but in working out a programme for automatic calculation is obtained correct and precise results.

The factors influencing one objective function are usually more than one and this is the reason why it is advisable to conduct multi-factor experiments with the aim shortening the time for their investigation. In such cases begins planning and conducting full factor experiment. The processing of the experimental results by the known in mathematics statistic methods can be done with the help of specialized software but if not available can be worked out a programme with Excel giving wonderful results. The obtained mathematical model is checked for adequacy. In the cases when it is not adequate, it is changed to planning on higher row and most convenient in these cases is conducting central-composing and rotating experiment with core of full factor experiment. After checking the adequacy of the model, done is the graphic interpretation and its optimization. These labor taking activities can be carried out with specialized software or with the possibilities offered by the integrated software package Microsoft Office 2000 – Microsoft Graph and Solver. With the help of Solver can be found not only the optimal values, but also all intermediate values needed in defining the relevant limits for regulation of the technological parameters in the systems for automation.

The next step is defining the functions of the system for automatic control based on designation and the principle of work of the machine or the line. Defined is the way of fitting and the orientation of the details, their reliable mounting and change of instruments, change of the instruments and the details one according to the other, change of the details to the next technological unit from the line etc. With the above actions ends the preliminary and analytical investigation of the objects for automation.

 

 

 

 

 

 

  1. Algorhytm for formulation of the technical assignment.

The problems solved on this stage are shown on Fig.2.

On the stage choice of criteria are defined the criteria for the basic technological parameters of the system. These are the criteria connected with the mistake of regulating the relevant parameter about the static and dynamic preciseness and special criteria. In the technical assignment for designing usually are requested: limit values of deviation of the output data, time of the transitional processes, and requirements to the transitional processes. The designer usually accepts such criteria about the dynamic preciseness of the system that guarantees satisfaction of the technical requirements or proves that they are objectively not reachable and should be corrected or made technological changes in the object for regulation. The special criteria could be of the type: max quick action, max preciseness, min expenditures of energy etc.

 

 

During the development of the architecture of the programme control must be made distinction between device and programme means, to be worked structural scheme; to be defined the functions of every block of the control system; to be chosen the form and the number of signals and commands, coming from one block to the other, to be chosen the technical means for automation.

On the stage logical designing of the system for programme control are developed functional-logical schemes with the chosen element basis; investigation of the different scheme decisions. In logical designing great significance has the analysis carried out under the form of mathematical modeling with the help of computer with basic aim finding out logical mistakes. In designing contemporary systems for automation based on microprocessor control, greater and greater application finds the method in which the blocks from the developed structure are standard.

The technical designing of the systems is the stage where is carried out choosing of devices, dislocation of modules, collecting components, working principle scheme for commands, blocks.

The work designing consists of working operative drawings, specifications, and exploitation documentation. After mounting the equipment, done is commissioning and worked out the test samples. The results from the experimental tests are used for analyses and corrections in the documentation if necessary.

The designing is one iterative procedure in which going back to previous stages is imposed by not right execution of the technical assignment and by new information for actual properties of the object and disturbances. Depending on the site conditions and a number of factors influencing the process of designing, the different stages can be changed or missed.

 

CONCLUSIONS

 

1. Systematized are the stages of designing of new or modernized automated technological equipment, about the applicability of the methods of mathematical modeling for every separate stage.

2. Offered are algorhytms for the development of the separate stages which are suitable for education in Higher Schools for Bachelor and Master’s Degrees as well as for young research workers at the beginning of their designing career.

 

REFERENCES

 

1.      Kuznesow M.M, etc, Projecting of the automated equipment for production., “Machine-building”, Moskva, 1987

2.      D.Vandev.K.Prodanova, V.Ruseva, New Mathematical Procedure for Analysis of Data obtained by Means of Circular Dichroism Titration Method, Arneim.-Forsch./Drug res.,Vol.48(11),12,1998, pp.1190-1193.

3.      D.Atanasov,K.Prodanova, D.Tersiiski,; Risk factors of Central Venous Catheter Related Infections in Intensive Care Patients, Pliska Stud.Math.Bulgar.,Vol.14, pp.15-22.

4.      Dolapchieva G., A choice the important factors in deformation tightly fit wear - Textil -obleclo, ¹6, pages 17-19, 2002.

5.      VakarelskaT, D. Chakyrski. Regression many-factor-containing analysis at the simulation modulation of the robotized producing machines AMTECH’03.

6.       Ovcharova Sn., Conditions for improvement of the innovational ability of the Bulgarian factories. Second scientific conference “Technical-economics analysis and forecasts”, 5-6 October, 2000, Varna

 

Personal data about the author: Ivanka Kostadinova Georgieva is Assos. Professor in Department Electronic and communications technique and technologies. She is Doctor in automation of the production. Works in the following trends: modeling and investigation of technological parameters influencing the productivity and quality of the operations in the discrete production; innovation and engineering of the automated discrete production; building control systems in the discrete production.

 

 

Technical College - Bourgas,

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