Mathematical Modelling of Hydraulic Systems

V okviru diplomske naloge smo prikazali razvoj matematičnih modelov hidravličnih sistemov različne strukture. Pri tem smo uporabili kombiniran pristop k modeliranju, saj smo pri gradnji modelov izvajali tudi meritve, ki so potekale na realnem sistemu, točneje na pilotni napravi AMIRA DTS 200. Delo je organizirano na naslednji način. V prvem poglavju smo opisali motivacijo za izdelavo pričujoče naloge, predstavili pa smo tudi osnovne načine modeliranja. Poglavja 2 do 6 opisujejo pet različno definiranih problemov modeliranja hidravličnih sistemov, ki se razlikujejo po redu in številu vhodnih, oziroma izhodnih signalov. V drugem poglavju smo predstavili v zaporedju značilnih korakov načrtovanja matematično modeliranje hidravličnega sistema prvega reda. Rezultata modeliranja sta pravzaprav dva, nelinearni in linearizirani model, ki dobro opisuje delovanje sistema v bližini izbranih delovnih pogojev. V naslednjih poglavjih opisujemo izvedene meritve in razvoje nelinearnih modelov za univariabilni sistem drugega in tretjega reda ter za multivariabilni sistem tretjega reda. Pri modeliranju teh sistemov linearizacije nismo izvajali. Vse razvite modele in izvedene meritve je mogoče na uporabniško prijazen način opazovati s pomočjo razvitega grafičnega vmesnika, prav tako pa le-ta zaradi svoje preglednosti omogoča tudi enostavno nadaljevanje dela in sicer tako v kontekstu modeliranja, kot načrtovanja vodenja.Within the framework of our thesis we presented the development of mathematical models and hydraulic systems of different structure. In doing so, we used a combined approach to modeling. In the construction of models we also performed measurements that were performed on a real system, namely on the AMIRA DTS 200 pilot device. The work is organized as follows. In the first section we described the motivation for this task and the basic modeling methods. Chapters 2 to 6 describe the five differently defined problems of hydraulic systems modeling, that differ in the order and number of input or output signals. In the second section, we presented and described mathematical modeling of the first order hydraulic system in a series of typical design steps. The modeling results are actually two, a non-linear and linearized model that describe the performance of the system near the selected operating conditions. The following sections describes the experiments made and the development of nonlinear models for a univariable second and third-order system and for a multivariable third-order system. We have not implemented linearization in modeling these systems. All developed models and measurements can be viewed in a user-friendly way with the help of a developed graphical interface, and because of their transparency it also allows easy continuation of work, both in the context of modeling and control planning