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Controller Analysis with Inverted Pendulum
KTH, School of Industrial Engineering and Management (ITM), Machine Design (Dept.).
KTH, School of Industrial Engineering and Management (ITM), Machine Design (Dept.).
2015 (English)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesisAlternative title
Regulatoranalys med Inverterad Pendel (Swedish)
Abstract [en]

The aim of this thesis is to examine if feedback of the angle from an inverted pendulum is sufficient to control its angle at an unstable equilibrium with statics and force impulses, and through different approaches and choice of controller find the most suitable one for these types of applications. The controllers that were tested was, the PID regulator and the state space regulator. The results would show that the mathematical approach to find a controller is difficult and time consuming, and it is often better to use a trial and error approach to find a regulator if repeated test on the system is possible. The core of the thesis lies in the mathematical approximations of the mechanical and electrical system, the analysis of the controller and the choice and usage of components. Analysis of the combined electrical and mechanical systems were made in Simulink and Matlab and was then generated to mechanical code to an micro controller controlling the voltage to a dc-motor. The system is non linear but can be linearised around the equilibrium point that we want to maintain, which is a good approximation for small angles. This thesis describes the electrical and mechanical components used to build a rotary inverted pendulum and how to produce an effective controller in detail.

Abstract [sv]

Målet med examensarbetet är att utvärdera om återkoppling av vinkeln frånen inverterad pendel är tillräcklig för att kontrollera denna kring en instabil jämviktspunkt med störningar samt pålagda kraftimpulser, och genom val av olika tillvägagångssätt och regulatorer finna den mest lämpliga för dessa typer av tillämpningar. De regulatorer som användes i projektet var PID-regulatorn samt state space regulatorn. Resultaten kom att visa att ett matematisk tillvägagångsätt att skapa en regulator är svårt och tidskrävande, och det är ofta mer effektivt att testa sig fram till en regulator om systemet tillåter. Kärnan i arbetet ligger i de matematiska approximationerna av de mekaniska och elektriska system, analysen av kontrollern och valet samt tillämpningen av komponenter. Analysen av det kombinerade elektriska och mekaniska systemen gjordes i Simulink och Matlab och var därefter genererad till mekanisk kod till en mikro-kontroller för att regulera spänningen till en likströmsmotor. Den inverterade pendeln är ett olinjärt system men kan med god approximation och litet fel linjariseras runt dess instabila jämnviktspunkt. Detta examensarbete kommer i huvudsak handla om hur man konstruerar en regulator genom simulering samt analys av systemet. Alla komponenter såväl elektriska som mekaniska kommer att beskrivas i detalj.

Place, publisher, year, edition, pages
2015.
Series
MMKB 2015:21 MDAB 074
National Category
Mechanical Engineering
Identifiers
URN: urn:nbn:se:kth:diva-184515OAI: oai:DiVA.org:kth-184515DiVA: diva2:916306
Supervisors
Examiners
Available from: 2016-04-08 Created: 2016-04-01 Last updated: 2016-04-08Bibliographically approved

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CiteExportLink to record
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