Multimodeling Control via System Balancing

A new approach in multimodeling strategy is proposed. Multimodel strategies in which control agents use different simplified models of the same system are being developed using balancing transformation and the corresponding order reduction concepts. Traditionally, the multimodeling concept was studied using the ideas of multitime scales (singular perturbations) and weak subsystem coupling. For all reduced-order models obtained, a Linear Quadratic Gaussian (LQG) control problem was solved. Different order reduction techniques were compared based on the values of the optimized criteria for the closed-loop case where the full-order balanced model utilizes regulators calculated to be the optimal for various reduced-order models. The results obtained were demonstrated on a real-world example: a multiarea power system consisting of two identical areas, that is, two identical power plants

The system order reduction via balancing in view of the method of singular perturbation

U radu je predstavljeno nekoliko tehnika za redukciju reda sistema, poznatih iz literature, koje su sve zasnovane na uravnoteženju sistema uz primenu metode singularnih perturbacija. Ove tehnike imaju istu robusnost tačnosti izračunatu u skladu sa H∞ normom sistema redukovanog reda kao i dve tehnike poznate pod nazivom direktno odsecanje i metod balansirane rezidualizacije. Modifikacija ovih tehnika zadržava tačnu vrednost pojačanja jednosmernog signala kakva je kod originalnog sistema i daje aproksimaciju od veoma dobre do odlične tačnosti na nižim i srednjim učestanostima. Efikasnost prikazanih tehnika za redukciju reda modela data je na realnom primeru.This paper presents several techniques for system order reduction, known from literature, all of them based on system balancing by employing the method of singular perturbation. These techniques have the same robustness accuracy evaluated with respect to the H∞ norm of the reducedorder system like two techniques known as the direct truncation and the balancing residualization method. A modification of these techniques preserves the exact DC gain as the original system, and produces from very good to excellent accuracy at low and medium frequencies. To illustrate the efficiency of the order-reduction techniques here presented, a real simulation example is given

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

U radu je razvijen i prikazan digitalni merač kapaciteta akumulatora, sa integrisanim punjačem. Takođe, razvijen je i upravljačko / kontrolni softver za mikrokontroler ovog uređaja i PC računar, kako bi se podaci dobijeni merenjem, dalje mogli obrađivati i upoređivati, korišćenjem nekog od programa za tabelarna izračunavanja. Zbog široke primene elektro-hemijskih izvora, bilo primarnih, bilo akumulatorskih, izuzetno je važno poznavati i meriti njihov kapacitet. Merenje kapaciteta primarnih ćelija pomaže pri odabiru najpovoljnijeg rešenja (u skladu sa odnosom cene i kapaciteta) za napajanje prenosivih uređaja. Merenjem kapaciteta akumulatora, može se utvrditi njihovo stanje i da li su spremni za dalju eksploataciju, a i proveriti kapacitet novih akumulatora, na primer, radi upoređivanja sa podacima u tehničkoj dokumentaciji proizvođača.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

MAINTENANCE, TESTING AND AUTOMATIC CONTROL OF THE CUP FILLING MASCHINE

Industrial automation of the production process is based on the fusion of a CNC machine and an industrial robot. The industry of today requires skilled professionals and educators. Special attention is to be paid to the testing of the components and system operation and the maintenance of the system. Robots and automation are omnipresent nowadays and have also taken a significant role in education. The research presented here aims to overhaul the scaled model of the cup-filling machine to make it operate fully automated. The parts and subsystems of the cup-filling machine are explained in detail and their operation was tested. The cup-filling machine is fully automated using a programmable logic controller (PLC) SIEMENS S7 300. The machine can recognize two cup sizes and fills both types without overspilling. Filled cups are transported over a conveyor belt and classified according to their sizes PLCs have mainly replaced relays in industrial automation, bearing in mind that this way, scale-up is much more feasible, and alteration of control is done in PLC program code. This also has contributed to better maintenance and operation verification

Theoretical support of modern issues related to laser techniques, applications of coherent radiation and modern technologies

Modern problems of the Earth’s population are increasing in the areas related to the basic concepts of survival of living beings, but also with opposite views, if parallels are made between energy and ecology. Many new technologies are searching for their way towards development and must be viewed from several points of view. Inthis paper, the issue is addressed through modern laser techniques in terms of obtaining energy for various purposes concerning selected roles in medicine, as well as the impact on flora, fauna and as a support to other technologies both classical and modern. Contemporary attributes of lasers and other quantum generators in termsof coherence, power and intensity densities have significantly increased, although some predictions from the time of the first quantum generator masers, like gammarasers (and X raser) are still relatively far from commercial concepts. Some of the possible contemporary implementations of quantum generators in measurements control and processing schemes, along with other possible applications of various laser types, have been estimated. The paper focuses on the characterization of today’s problems with Covid-19 virus, only from the engineering point of view. The lexical side of the issue is also included, as well as the social management needswith the application of modern technologies, including help from natural sciences

Analitički i numerički aparati za primene lasera u dijagnostičke svrhe u linearnoj i nelinearnoj oblasti

Primena lasera sa procesima rasejanja i interakcije zahteva rešavanje teorijskih problema, koji se razvojem računarskih alata svode na brze provere. Zadaci u vezi metroloških problematika pokrivaju zadatake sa angularnom raspodelom, monohromatskih i polihromatskih problema matrice rasejanja, specijalne funkcije ili komponentni prilaz definisanim geometrijama i koherentnih osobina snopa, rasejavača i ugla posmattranja. Laserski snopovi velikog intenziteta izazivaju niz efekata u atmosferi ili u prolazu kroz materijal, uključujući i disturbanse u rezonatorima zbog uticaja elastičnih i neelastičnih rasejanja i promene koeficijenata refleksije elemenata (ogledala), koji su u radnom prostoru kvantnog generatora-pojačavača. Rad se bavi izabranom problematikom teorijsko-analitičko-numeričke prirode i pored pozivanja na zadatke iz prakse, analizira podrške informacione tehnologije

Analitički i numerički aparati za primene lasera u dijagnostičke svrhe u linearnoj i nelinearnoj oblasti

Primena lasera sa procesima rasejanja i interakcije zahteva rešavanje teorijskih problema, koji se razvojem računarskih alata svode na brze provere. Zadaci u vezi metroloških problematika pokrivaju zadatake sa angularnom raspodelom, monohromatskih i polihromatskih problema matrice rasejanja, specijalne funkcije ili komponentni prilaz definisanim geometrijama i koherentnih osobina snopa, rasejavača i ugla posmattranja. Laserski snopovi velikog intenziteta izazivaju niz efekata u atmosferi ili u prolazu kroz materijal, uključujući i disturbanse u rezonatorima zbog uticaja elastičnih i neelastičnih rasejanja i promene koeficijenata refleksije elemenata (ogledala), koji su u radnom prostoru kvantnog generatora-pojačavača. Rad se bavi izabranom problematikom teorijsko-analitičko-numeričke prirode i pored pozivanja na zadatke iz prakse, analizira podrške informacione tehnologije

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..

Robust order reduction using system balancing with respect of the method of singular perturbation

Several techniques for system order reduction are presented here, known from literature, all of them based on system balancing and some of them employing the method of singular perturbation. These techniques are compared with the two techniques known as the direct truncation and the balancing residualization method for efficiency in approximating the model in two cases: when the system is in the open loop and when the system is working in the closed loop with negative unity gain. All of these techniques for order reduction have the same robustness accuracy evaluated with respect to the H-infinity norm of the reduced-order system. A modification of these techniques preserves the exact DC gain as the original system, and produce from very good to excellent accuracy at low and medium frequencies. To illustrate the efficiency of the order-reduction techniques here presented, a real simulation example is given. The closed loop case simulation shows that high frequency dynamics of the original system can be of more importance for more accurate approximation of the system behaviour in the closed loop even if the high frequency modes appear to be of less significance in the open loop