Control of rotary inverted pendulum

Inverzno rotacijsko njihalo predstavlja primjer standardnog edukacijskog mehaničkog sustava s dva rotacijska stupnja slobode gibanja, opisanog složenom nelinearnom dinamikom. Ovaj rad prikazuje metode regulacije takvog sustava koristeći različite vrste regulatora. Za slučaj potpuno upravljivog sustava, dizajnirani su standardni PD i PID regulatori koji asimptotski stabiliziraju sustav u proizvoljnom položaju. Uveden je predfilter referentne pozicije radi poboljšanja performansi regulacije te filter brzine pod pretpostavkom da brzine nisu mjerljive. Za slučaj podupravljanog inverznog njihala, provedena je linearizacija dinamičkog modela te sinteza linearnog kvadratičnog regulatora. S obzirom da linearni regulator nije u mogućnosti, za dovođenje njihala iz ravnotežnog položaja u područje oko inverznog položaja gdje regulaciju preuzima linearni regulator, dizajniran je swing-up algoritam. Dodatno, za stabilizaciju njihala u inverznom položaju dizajniran je i neizraziti regulator.Inverted rotational pendulum is an example of a standard educational mechanical system with two rotational degrees of freedom, described by complex nonlinear dynamics. This work presents the control methods of such a system using various types of controllers. In case of a fully actuated system, standard PD and PID controllers for asymptotic stabilization at a desired position are designed. To improve the controller performance, a desired position pre-filter and, assuming the speeds are not measurable, a speed filter are introduced. In case of an underactuated rotational inverted pendulum, the model has been linearized and a linear quadratic controller has been designed. Since it is not possible using the linear controller, a swing-up algorithm has been designed to drive the pendulum from the downward, hanging position towards the inverted position where the linear controller takes over. Additionally, a fuzzy regulator has also been designed to stabilize the pendulum in its upright position