Application of robust order reduction in modeling and control of real systems and objects in mechanical engineering

Дисертација „Примена робусне редукције реда система у моделовању и управљању реалним објектима у машинству“ је посвећена техникама и методама за редукцију реда линеарних модела, представљених у простору стања, као и условима и ограничењима за њихову примену. Приказан је концепт сингуларних пертурбација и његова примена у редукцији сложености модела система. Размотрене су различите карактеризације линеарних модела великог реда, чије репрезентације моделима у простору стања имају различите временске скале или и мали параметар (имају матрице великих димензија са пуно нула-елемената или са елементима, чији се редови величине веома разликују). Представљени су: сингуларно пертурбовани слабо повезани системи, слабо повезани системи, сингуларно пертурбовани системи, квази сингуларно пертурбовани системи и квази слабо повезани системи. Свака од ових класа представљена је одговарајућим моделом у простору стања неког реалног система. Детаљније је изложен прорачун регулатора за линеаран сингуларно пертурбован систем. Описана је метода балансирања, као и технике за редукцију реда линеарних модела, познате из литературе, које захтевају примену трансформације балансирања: балансирано одсецање, балансирана резидуализација, генералисана балансирана резидуализација, кориговано балансирано одсецање, метода заснована на брзом подсистему уз одбацивање спорог, модификована генералисана балансирана резидуализација, као и реверзна техника резидуализације. Свака од ових техника даје по један модел редукованог реда, полазећи од балансираног модела пуног реда. Технике изложене у овој тези, примењене су на редуковање реда четири модела реалних система. Први је модел бинарне дестилационе колоне са прегревачем и девет подова. Други је модел у простору стања борбене летелице L-1011. Трећи је математички модел каталитички контролисане реакције, из процесне технике. Четврти је математички модел дела електроенергетског система Србије, сачињен од две машине. Изложена је и редукција реда модела нестабилних линеарних система, на основу изабране литературе...The dissertation Application of Robust Order Reduction for Modeling and Control of Real Systems in Mechanical Engineering is dealing with techniques and methods of order reduction for linear models in the state space representation, as well as with conditions and limitations of their applicability. Well known concept of singular perturbations is described with its application in reduction of complexity of the system’s model. Different characterizations of large scale linear models are overviewed, having state space representations who exhibit different time scales or small parameter, too. These models have matrices of large dimensions with many zero-elements or elements with different size order, some very large and others very small. The singularly perturbed and weakly coupled systems, the weakly coupled systems, the singularly perturbed systems, the quasy singularly perturbed systems and the quasy weakly coupled systems are listed and represented here. Each class of these is represented with corresponding state space model of one real system. The design of the regulator for the linear singularly perturbed system is described in detail. The balancing method is analyzed, as well as techniques for the order reduction of linear model’s, known from the literature. These require application of the balancing transformation: the balancing truncation, the balancing residualization, the generalized balancing residualization, the corrected balancing truncation, the method based on the fast subsystem with rejection of the slow subsystem, the modified generalized balancing residualization, as well as the reversed residualization technique. Each of these techniques mentioned gives one model of reduced order, starting from the balanced full order model. Techniques represented in this thesis are applied on order reduction of four real system’s models. The first is the state space model of binary distillation column, with condenser, reboiler and nine plates. The second is the state space model of L-1011 fighter aircraft. The third is a mathematical model of the controlled catalytic reaction, from process engineering. The fourth part is a mathematical model of the part of electric power system of Serbia, consisting of two machines. Described here is the order reduction for models of unstable linear systems as well, based on the chosen references..

Essential oil composition of different parts of endemic species Seseli gracile Waldst. & Kit. (Apiaceae) from natural and cultivated conditions

The chemical composition of the essential oils of Seseli gracile Waldst. & Kit. from natural habitat (Derdap Gorge, Serbia) and from cultivated plants (Belgrade, Serbia) were characterized. The essential oils of the root, aerial parts, inflorescence and fruit were analyzed by GC/MS and GC/FID. Monoterpene hydrocarbons were the main compounds in the essential oil of aerial parts (45.2-93.0 %), inflorescences (84.1 and 90.0 %) and fruit (85.0 %). Polyacetylenes (38.8 and 87.6 %) were dominant in the essential oil of root. The cluster analysis revealed that there were significant differences in the chemical composition of the S. gracile oils at different phenological stages. On the other hand, essential oils from the aerial parts from natural and cultivated plants showed quite uniform qualitative composition. The aerial parts essential oil from natural habitat contained higher content of para-cymene (mean values 17.3 vs. 6.5 %) and lower amounts of terpinolene (mean values 23.1 vs. 49.9 %). Also polyacetylene falcarinol was present only in the aerial parts samples from natural habitat. The essential oil of inflorescences from natural habitat contained higher concentration of terpinolene, quite similar amount of para-cymene and lower content of a-pinene

Application of robust order reduction in modeling and control of real systems and objects in mechanical engineering

Дисертација „Примена робусне редукције реда система у моделовању и управљању реалним објектима у машинству“ је посвећена техникама и методама за редукцију реда линеарних модела, представљених у простору стања, као и условима и ограничењима за њихову примену. Приказан је концепт сингуларних пертурбација и његова примена у редукцији сложености модела система. Размотрене су различите карактеризације линеарних модела великог реда, чије репрезентације моделима у простору стања имају различите временске скале или и мали параметар (имају матрице великих димензија са пуно нула-елемената или са елементима, чији се редови величине веома разликују). Представљени су: сингуларно пертурбовани слабо повезани системи, слабо повезани системи, сингуларно пертурбовани системи, квази сингуларно пертурбовани системи и квази слабо повезани системи. Свака од ових класа представљена је одговарајућим моделом у простору стања неког реалног система. Детаљније је изложен прорачун регулатора за линеаран сингуларно пертурбован систем. Описана је метода балансирања, као и технике за редукцију реда линеарних модела, познате из литературе, које захтевају примену трансформације балансирања: балансирано одсецање, балансирана резидуализација, генералисана балансирана резидуализација, кориговано балансирано одсецање, метода заснована на брзом подсистему уз одбацивање спорог, модификована генералисана балансирана резидуализација, као и реверзна техника резидуализације. Свака од ових техника даје по један модел редукованог реда, полазећи од балансираног модела пуног реда. Технике изложене у овој тези, примењене су на редуковање реда четири модела реалних система. Први је модел бинарне дестилационе колоне са прегревачем и девет подова. Други је модел у простору стања борбене летелице L-1011. Трећи је математички модел каталитички контролисане реакције, из процесне технике. Четврти је математички модел дела електроенергетског система Србије, сачињен од две машине. Изложена је и редукција реда модела нестабилних линеарних система, на основу изабране литературе...The dissertation Application of Robust Order Reduction for Modeling and Control of Real Systems in Mechanical Engineering is dealing with techniques and methods of order reduction for linear models in the state space representation, as well as with conditions and limitations of their applicability. Well known concept of singular perturbations is described with its application in reduction of complexity of the system’s model. Different characterizations of large scale linear models are overviewed, having state space representations who exhibit different time scales or small parameter, too. These models have matrices of large dimensions with many zero-elements or elements with different size order, some very large and others very small. The singularly perturbed and weakly coupled systems, the weakly coupled systems, the singularly perturbed systems, the quasy singularly perturbed systems and the quasy weakly coupled systems are listed and represented here. Each class of these is represented with corresponding state space model of one real system. The design of the regulator for the linear singularly perturbed system is described in detail. The balancing method is analyzed, as well as techniques for the order reduction of linear model’s, known from the literature. These require application of the balancing transformation: the balancing truncation, the balancing residualization, the generalized balancing residualization, the corrected balancing truncation, the method based on the fast subsystem with rejection of the slow subsystem, the modified generalized balancing residualization, as well as the reversed residualization technique. Each of these techniques mentioned gives one model of reduced order, starting from the balanced full order model. Techniques represented in this thesis are applied on order reduction of four real system’s models. The first is the state space model of binary distillation column, with condenser, reboiler and nine plates. The second is the state space model of L-1011 fighter aircraft. The third is a mathematical model of the controlled catalytic reaction, from process engineering. The fourth part is a mathematical model of the part of electric power system of Serbia, consisting of two machines. Described here is the order reduction for models of unstable linear systems as well, based on the chosen references..

Digital battery capacity meter with battery charger

In this paper, a digital battery capacity meter with an integrated battery charger is developed and built. Also, the software used to control and monitor the microcontroller of the device from the PC has been developed, so that the data obtained from measurement can be processed and compared further using one of the available spreadsheet software packages. Due to the widespread use of electrochemical energy sources, whether primary ones or of the battery type, it is extremely important to know and measure their actual capacity. Primary cell capacity measurement helps in selecting the most appropriate solution (with respect to the cost/ capacity ratio) for powering portable or mobile devices. By measuring the capacity of the used battery, its condition and capability of further exploitation can be determined. Measuring capacity can provide verification of the data in the manufacturer's specifications, for example, in order to compare measurements and confirm statements in technical documentation

Essential oil composition of different parts of endemic species Seseli gracile Waldst. & Kit. (Apiaceae) from natural and cultivated conditions

The chemical composition of the essential oils of Seseli gracile Waldst. & Kit. from natural habitat (Đerdap Gorge, Serbia) and from cultivated plants (Belgrade, Serbia) were characterized. The essential oils of the root, aerial parts, inflorescence and fruit were analyzed by GC/MS and GC/FID. Monoterpene hydrocarbons were the main compounds in the essential oil of aerial parts (45.2–93.0 %), inflorescences (84.1 and 90.0 %) and fruit (85.0 %). Polyacetylenes (38.8 and 87.6 %) were dominant in the essential oil of root. The cluster analysis revealed that there were significant differences in the chemical composition of the S. gracile oils at different phenological stages. On the other hand, essential oils from the aerial parts from natural and cultivated plants showed quite uniform qualitative composition. The aerial parts essential oil from natural habitat contained higher content of para-cymene (mean values 17.3 vs. 6.5 %) and lower amounts of terpinolene (mean values 23.1 vs. 49.9 %). Also polyacetylene falcarinol was present only in the aerial parts samples from natural habitat. The essential oil of inflorescences from natural habitat contained higher concentration of terpinolene, quite similar amount of para- -cymene and lower content of α-pinene. [Project of the Serbian Ministry of Education, Science and Technological Development, Grant no. 173021 Grant no. 173030

Variations in Chemical Composition, Vasorelaxant and Angiotensin I-Converting Enzyme Inhibitory Activities of Essential Oil from Aerial Parts of Seseli pallasii Besser (Apiaceae)

The present paper describes environmental and seasonal-related chemical composition variations, vasorelaxant and angiotensin I-converting enzyme (ACE) activities of essential oil from aerial parts of Seseli pallasii BESSER. The composition was analyzed by GC and GC/MS. Monoterpenes were found to be the most abundant chemical class with alpha-pinene (42.7 - 48.2%) as the most prevalent component. Seseli pallasi essential oil relaxed isolated endothelium-intact mesenteric arteries rings precontracted with phenylephrine with IC50 = 3.10 nl/ml (IC50 = 2.70 mu g/ml). Also, S. pallasii essential oil was found to exhibit a dose-dependent ACE inhibitory activity with an IC50 value of 0.33 mg/ml. In silico evaluation of ACE inhibitory activity of the individual components showed that spathulenol exhibited the best binding affinity with ACE, and the lowest binding energy of -7.5 kcal/mol. The results suggested that combination of vasorelaxing and ACE inhibitory effects of the analyzed S. pallasii essential oil might have the potential therapeutic significance in hypertension

The method of “external spiral” for solving a large system of linear equations / Применение метода «внешней спирали» при решении систем линейных уравнений с большим количеством неизвестных / Metoda 'spoljašnje spirale" za rešavanje linearnog sistema sa velikim brojem nepoznatih

Solving a linear system of n × n equations can be very difficult for the computer, especially if one needs the exact solution, even when the number n - of equations and of unknown variables is relatively small (a few thousands). All existing methods have to overcome at least one of the following problems: 1. Computational complexity, which is expressed with the number of arithmetic operations required in order to determine a solution; 2. The possibility of overflow and underflow problems; 3. Causing variations in the values of some coefficients in the initial system, which may be leading to instability of the solution; 4. Requiring additional conditions for convergence; 5. In cases of a large number of equations and unknown variables it is often required that the systems matrix be: either sparse, or symmetrical, or diagonal, etc. This paper presents a method for solving a system of linear equations of arbitrary order (any number of equations and unknown variables) to which the problems listed above do not reflect. / Решение систем линейных уравнений n × n может представлять проблему для компьютера, особенно в тех случаях, когда требуется точное решение, и даже в тех случаях, когда количество уравнений и неизвестных относительно невелико (всего несколько тысяч). Все существующие методы сталкиваются с наименее одной из следующего ряда проблем: 1. сложность вычисления, выраженная количеством соответствующих операций, которые необходимо произвести для получения решения; 2. потенциальная возможность неограниченного роста значений результатов, что приводит к проблемам: overflow и underflow; 3. изменение значений некоторых коэффициентов в исходной системе, что приводит к неустойчивости решения; 4. дополнительные требования вследствие конвергенции; 5. в случаях большого количества уравнений и неизвестных необходимо, чтобы матрица системы была или не слишком наполнена, или была симметричной, либо диагональной, и т.д. В данной работе представлены методы решения системы линейных уравнений с произвольным количеством уравнений и неизвестных, на которых не отражаются перечисленные проблемы. / Rešavanje linearnog sistema jednačina n × n može biti problem i za računar, pogotovo ako je potrebno tačno rešenje, čak i kada je broj jednačina i nepoznat i relativno mali (par hiljada). Sve postojeće metode su opterećene bar jednim od sledećih problema: 1. složenošću računanja izraženim kroz broj potrebnih operacija koje je potrebno izvršiti kako bi se došlo do rešenja; 2. potencijalnom mogućnošću neograničenog rasta veličina među rezultata, što uzrokuje probleme prekoračenja opsega (overflow) i nedovoljne osetljivosti odnosno preciznosti (underflow); 3. promenom vrednosti nekih koeficijenata u polaznom sistemu, što uzrokuje nestabilnost rešenja; 4. dodatnim zahtevima, zbog konvergencije; 5. slučajevima velikog broja jednačina i nepoznatih koji zahtevaju da matrica sistema bude: ili slabo popunjena, ili simetrična, ili dijagonalna, itd. U ovom radu prezentuje se metoda za rešavanje sistema linearnih jednačina sa proizvoljnim brojem jednačina i nepoznatih na koju se navedeni problemi ne reflektuju

FORMALISMS, ANALYSIS, RESULTS AND ACCOMPLISHMENTS WITH POPULATION INVERSION OF MATERIALS

During six decades of quantum electronics, a vast majority of new types of quantum generators have been developed. Although the principle of population inversion has united different ranges of electromagnetic spectra (and respective quantum generators), the existence of the title laser without the population inversion, makes that the exception had confirmed the rule, i. e. that this title deserves to be discussed further. Developing of formalisms describing the operation of quantum generators, by now have produced several approaches, which must have a quantum mechanics base. For the practical reasons, negative coefficient of absorption is acquired using classic electromagnetics as well, however for the population purposes, quantum representation must be entered.A few levels of formalisms will be set in this paper, linked to quantum generators accenting the optical portion of the spectra. The lowest level descriptions are based on lumped circuits. This could be expanded to equivalents of other physical problems, using program packages developed for the electrical engineering application purposes (Spice, etc.). Schematics are defined at the macro as well as micro equivalent levels (atomic – electronic levels). The kinetic equations with simpler approach will be considered as well as simplified laser equations based on quantum/ semi-quantum approach. The use of Fourier analysis or other appropriate transformations leads to formulating the main five laser equations which serve as the base for various working regimes of quantum generators and amplifiers (free generation regime, Q switch, synchronization, operation with filters, two modes regime, regime with losses, etc.). The Lyapunov stability theorem has to be included here, etc.For some of the chosen types of quantum generator, analytical modeling will be analyzed as well as the results of program packages developed for the lasers dynamics, regimes and parameters. The systems pumped with electronic beams (relativistic) will be considered and the nuclear physics statements discussed which must be included at the beginning, in order to consider further necessary parts of the condensed – solid state theory and laser techniques, after slowing down towards thermal energies.Existing program packages provide fast modeling and visualization of laser energy distribution, temperature, modes, etc. in active material with or without the resonator. A modeling will be performed for the specified geometries and a temperature distribution in active material will be captured during operation of a chosen laser system. Different pump geometries will be compared. Contemporary lasers with the shortest existing pulse durations demand new formalisms. Areas of nonlinear optics and quantum electrody-namics, Glauber states and similar, are areas that have to be included. Two main formalisms thermodynamical and quantum mechanical with transition probabilities using perturbation methods and secondary quantization naturally had to be complemented if the Brillouin, Raman, Compton, soliton, fiber and other lasers are included more generally

Assessment of depression and anxiety in patients with chronic liver disease

Background/Aim. In recent years mental health of patients including those with chronic liver disease (CLD), has become interesting because its disturbance leads to reduced quality of life, that is associated with worsening of clinical outcome, reduced compliance and increased mortality. The aim of the study was to determinate the frequency and severity of depression and frequency of anxiety in patients with CLD and to assess the contribution of selected socio-demographic, clinical and laboratory risk factors for depression and anxiety. Methods. In this cross-sectional study, we used the Hamilton depression rating scale (HDRS) and Hamilton anxiety rating scale (HARS) in patients with CLD. Results. The study included 54 male and 43 female patients. Depression was present in 62.9%, and anxiety in 13.4% of the patients. A higher HDRS was noted in the patients older than 50 years (p = 0.022) and unemployed patients (p = 0.043). The patients with at least one episode of gastrointestinal bleeding had a significantly higher frequency of anxiety than those without bleeding (p = 0.018). A higher HARS score was present in the women (p = 0.011), unemployed patients (p = 0.008) and those with non-alcoholic liver disease (p = 0.007). There was a significant correlation between the mean corpuscular volume (MCV) and the value of the HDRS score, and between serum potassium and sodium levels and HDRS score. Conclusion. Age and the mean corpuscular volume have significant influence on the HDRS score while unemployment, gastrointestinal bleeding, serum potassium and serum sodium have predictive value for HARS score