Design of systems with extremal dynamic properties

2013 ◽  
Vol 61 (3) ◽  
pp. 563-567 ◽  
Author(s):  
H. Górecki ◽  
M. Zaczyk

Abstract In this article the problem of determination of coefficients a1, a2, . . . , an of the characteristic equation which yield required extremal values of the solution x(t) at extremal values τ of time is solved. The extremal values of x(t) and τ are treated as functions of the roots s1, s2, . . . , sn. The analytical formulae enable to design the systems with prescribed dynamic properties. The zeros and poles can be located using the known method. The extremal dynamic error x(t) is the most important property of the behaviour of the system. This extremal value of the dynamic error has fundamental role in the chemical industry where for example overrising temperature or pressure can lead to an explosion. A second very important property is the extremal time τ connected with the extremal value of the error. This property is essential in the electroenergetic system, which can be destroyed by the overvoltages waves.

2014 ◽  
Vol 62 (2) ◽  
pp. 241-253 ◽  
Author(s):  
H. Górecki ◽  
M. Zaczyk

Abstract In this article the problem of determination of such coefficients a1, a2, ..., an and eigenvalues s1, s2, ..., sn of the characteristic equation which yield required extremal values of the solution x(t) at the extremal value τ of time is solved. The extremal values of x(τ ) and τ are treated as functions of the roots s1, s2, ..., sn. The analytical formulae enable us to design the systems with prescribed dynamic properties. For solution of the problem the properties of symmetrical equations are used. The method is illustrated by an example of the equation of 4-th degree. The regions of the different kinds of the roots: real, with one pair of complex and two pairs of complex roots are illustrated. A practical problem is shown.


2016 ◽  
Vol 26 (4) ◽  
pp. 497-513
Author(s):  
Henryk Górecki ◽  
Mieczysław Zaczyk

AbstractIn the paper the extremal dynamic error x(τ) and the moment of time τ are considered. The extremal value of dynamic error gives information about accuracy of the system. The time τ gives information about velocity of transient. The analytical formulae enable design of the system with prescribed properties. These formulae are calculated due to the assumption that x(τ) is a function of the roots s1, ..., snof the characteristic equation.


2014 ◽  
Vol 24 (4) ◽  
pp. 771-784
Author(s):  
Henryk Górecki ◽  
Mieczysław Zaczyk

Abstract The maximal value of the error is the most important criterion in system design. It is also the most difficult one. For that reason there exist many other criteria. The extreme value of the error represents the attainable accuracy which can be obtained and the corresponding extreme time gives information about how fast the transients are. The extreme values of the error and the corresponding time are treated here as functions of the roots of the characteristic equation. The proposed analytical formulae allow designing systems with prescribed dynamic properties.


2013 ◽  
Vol 18 (2-3) ◽  
pp. 33-41
Author(s):  
Dominik Sankowski ◽  
Marcin Bakala ◽  
Rafał Wojciechowski

Abstract The good quality of several manufactured components frequently depends on solidliquid interactions existing during processing. Nowadays, the research in material engineering focuses also on modern, automatic measurement methods of joining process properties, i.a. wetting force and surface tension, which allows for quantitative determination of above mentioned parameters. In the paper, the brazes’ dynamic properties in high-temperatures’ measurement methodology and the stand for automatic determination of braze’s properties, constructed and implmented within the research grant nr KBN N N519 441 839 - An integrated platform for automatic measurement of wettability and surface tension of solders at high temperatures, are widely described


1980 ◽  
Vol 53 (3) ◽  
pp. 437-511 ◽  
Author(s):  
D. W. Brazier

Abstract An attempt has been made to review the development of thermoanalytical procedures as they have been applied to elastomers and elastomer systems over the past 10 years. For all rubber industry products, temperature and its effects, either alone or in conjunction with the chemical environment, play an important role from the production stage through to the final failure of the product in the field. It is thus not surprising that thermal analysis, in which temperature is the prime variable, has found such diverse applications in elastomer studies. The identification and quantitative analysis of rubber formulations have received most attention. Such formulations produce characteristic “fingerprints” when studied in DTA, DSC, TG, or TMA. In DSC, the determination of the glass transition characteristics, the observation and determination of crystallinity, the detection of cyclization reactions, and the monitoring of thermal and oxidative degradation characteristics can all be observed in a single experiment covering the temperature range from −150 to +600°C. At normal heating rates, e.g., 20°C/min, such information is available in 40 min. TG/DTG analysis can yield the elastomer or elastomers content, oil and plasticizer, carbon black (level and often type), and inorganic ash in less than 60 min. Processing and curing can also be studied. Blend compatibility can be assessed on the basis of both Tg and crystallinity measurements and the data used to determine optimum mixing times. Sulfur vulcanization and peroxide curing of elastomers is readily monitored by DSC and can be used for confirmation analysis of the presence of curatives. Limitations in such analysis exist, but as understanding and ability to interpret cure exotherms increase, valuable information about the mechanism and the nature of the cured network will be obtained. The testing of rubber compounds involves many hours of labor by current procedures. The rapidity of thermal analysis promises to offer some relief. In addition to DSC and TG, TMA, a relatively new technique, offers a rapid approach to low-temperature testing. Dynamic mechanical analysis (DMA) offers a rapid route to determining dynamic properties, but as yet, relatively little has been published on the application of this new technique to elastomers. As environmental concern increases, techniques such as evolved gas analysis (EGA) and combined techniques such as TG/gas chromatography are predicted to play an important role. As for the future, it is readily apparent that the principles of the methods have been established and, in several cases, it now remains to reduce them to a practical level. In some areas, such as vulcanization studies, much remains to be undertaken to improve our interpretive skills. Although there is some indication that certain industries have produced “in-house” standards for the analysis of rubber compounds by DSC and TG/DTG, it will only be when national and international standards organizations study and produce standard procedures, that the techniques will be generally adopted. Maurer's prediction in 1969 of increased applications of DTA and TG in elastomer studies has undoubtedly proved correct, and with the proliferation of reliable commercial instrumentation, significant developments can be anticipated in the next decade.


SPE Journal ◽  
2018 ◽  
Vol 23 (06) ◽  
pp. 2327-2338 ◽  
Author(s):  
Hojjat Kabirzadeh ◽  
Elena Rangelova ◽  
Gyoo Ho Lee ◽  
Jaehoon Jeong ◽  
Ik Woo ◽  
...  

Summary The safe and economical determination of a wellbore trajectory in directional drilling is traditionally achieved by measurement-while-drilling (MWD) methods, which implement magnetic north-seeking sensor packages. Inaccuracies in the determination of well path arise because of random and systematic errors in the measurements of the sensors. Multistation analysis (MSA) and magnetic in-field referencing (IFR) have already demonstrated the potential to decrease the effects of errors because of magnetization of drillstring components along with variable errors caused by irregularities in the magnetization of crustal rocks in the vicinity of wells. Advanced MSA methodologies divide a borehole into several sections and use the average reference values of the total magnetic field, declination, and dip angle for analysis of errors in each section. Our investigations indicate that the variable-reference MSA (VR-MSA) can lead to a better determination of errors, specifically in areas of high magnetization. In this methodology, magnetic reference values are estimated at each station using forward and inverse modeling of surface-magnetic observations from IFR surveys. The fixed errors in magnetometer components are then calculated by minimizing the variance of the difference between the measured and unique estimated reference values at each station. A Levenberg-Marquardt algorithm (LMA) is adopted to solve the nonlinear optimization problem. Examination of this methodology using MWD data confirms more than 20% improvement in well-path-determination accuracy by comparing the results with the corrected path from the conventional MSA method and gyro surveys.


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