Modeliranje in vodenje invertiranega nihala z reakcijskim kolesom

Pečan, Žan (author), Tomažič, Simon (mentor)

V diplomskem delu so predstavljeni izdelava, modeliranje in vodenje invertiranega nihala z reakcijskim kolesom. V prvem delu je predstavljeno nihalo ter možnosti manipulacije njegovega naklona, od katerih sem izbral reakcijsko kolo. Za tem sledi izpeljava matematičnega modela dinamike sistema z uporabo Lagrangeeve funkcije ter Laplaceove transformacije, s katero sem nato določil prenosno funkcijo obravnavanega sistema. Drugi del predstavi realizacijo fizičnega modela. Opisuje modeliranje in 3D tiskanje sestavnih gradnikov sistema, kot so nihalo, kolo in stojalo. Prav tako se predstavi delovanje uporabljenega merilnega instrumenta, aktuatorja, električna vezja in mikroračunalnika. Zatem sledi postavitev fizičnega modela in programiranje funkcionalnosti, kjer je tudi natančneje opisana metoda filtriranja pridobljenih meritev. Tretji del pokriva simulacijo matematičnega modela v programskem okolju Matlab in Simulink, kjer se nekateri neznani parametri sistema določijo z metodo optimizacije. Po pridobitvi parametrov se analizirajo lastnosti izpeljanega modela, nato pa se vizualizira in primerja z realnim modelom za namen validacije ustreznosti matematičnega opisa sistema. Zadnji del naloge pa se poglobi v teorijo vodenja, kjer se predstavita PID in LQR regulator kot široko uporabljeni metodi vodenja sistemov. Obe metodi se implementirata na matematičnem modelu, njuni rezultati pa se med seboj primerjajo ter se določi njuna ustreznost za podani sistem.

• Language: Slovenian
• Keywords: Model, vodenje, Langrangeeva funkcija, Laplaceova transformacija, prenosna funkcija, prostor stanj, komplementarni filter, Matlab, Raspberry Pi, PID, LQR
• Work type: Bachelor thesis/paper
• Typology: 2.11 - Undergraduate Thesis
• Organization: FE - Faculty of Electrical Engineering
• Year: 2024
• PID: 20.500.12556/RUL-161591
• COBISS.SI-ID: 208079875
• Publication date in RUL: 12.09.2024

Secondary language

• Language: English
• Title: Modelling and control of an inverted pendulum with a reaction wheel

Abstract

The thesis presents the construction, modelling and control of an inverted pendulum with a reaction wheel. The first part introduces the pendulum and the possible methods for manipulating its tilt, from which I choose the reaction wheel. This is followed by the derivation of the mathematical description of the system's dynamics using the Lagrange function and Laplace transform, which I then used to determine the transfer function of the system. The second part presents the realization of the physical model. It describes the process of modelling and 3D printing of the system's components, such as the pendulum, wheel, and base. The operation of the measurement instrument, actuator, electrical circuits, and microcontroller used in the system is also described. This is followed by the assembly of the physical model and the programming of its functionalities, with a more detailed description of the method used to filter the obtained measurements. The third part covers the simulation of the mathematical model in the Matlab and Simulink environments, where some unknown system parameters are determined using an optimization method. The properties of the derived model are analysed based on the obtained parameters, and the model is then visualized and compared with the real model to validate the accuracy of the mathematical system. The final part of the thesis delves into control theory, where PID and LQR controllers are presented as widely used methods for system control. Both methods are implemented on the mathematical model, and their results are compared to determine their suitability for the given system.

• Keywords: Model, control, Lagrange function, Laplace transform, transfer function, state space, complementary filter, Matlab, Raspberry Pi, PID, LQR