Implementation and Control of an Inverted Pendulum on a Cart

An Inverted Pendulum on a Cart is a common system often used as a benchmark problem for control systems. The system consists of a cart that can move in one direction on the horizontal plane and a pendulum attached to the cart through a hinge point. The pendulum can rotate 360° on the plane made up of the vertical direction and the direction the cart can move. The system is controlled by applying a force to the cart, to make it move. This thesis consists of two goals. The first goal is to build a lab model of the Inverted Pendulum on a Cart system. The second goal is to create a controller that can swing the pendulum from a pendulum down position to a pendulum up position, and balance it in this position. The lab model is built using a track that the cart can move along, a stepper motor for applying force to the cart and a microcontroller for controlling the system. The pendulum angle and the cart position are measured using incremental encoders. A Mathematical model of the system have been derived. This forms the basis for the design of the controller and is also used for simulating and testing the system and controller in MATLAB/Simulink before it is implemented on the real system. The controller consists of three parts. An extended Kalman filter is implemented to estimate the non-measurable state. An energy-based controller is used to swing the pendulum from the down position to the up position. This controller regulates the energy in the pendulum to be close to the energy the pendulum should have when it is balanced in the upright position. When the pendulum is close to the upright position the controller will switch to a linear quadratic regulator to balance the pendulum. This controller is based on a linearized version of the mathematical system model. The lab model and the controllers have been successfully built and implemented

Modeling and control of nonlinear underactuated systems

Tato práce je zaměřena na návrh řízení nelineárních systémů. Předpokladem je nejen zajistit správnou funkčnost v okolí určitého pracovního bodu, ale především řešit přechod systému mezi dvěma stavy. Při přesouvání systému ve stavovém prostoru se často výrazně projevuje jeho nelineární chování. Návrh řízení je rozebírán jak ve variantě, kdy je požadováno pouhé splnění převodu mezi stavy, tak v podobě, u které se pomocí účelové funkce specifikují požadované vlastnosti daného přechodu a hledá se optimální řešení. V celém procesu návrhu řízení i při jeho ověřování se využívá v určité podobě model systému (model based design), tudíž modelování je nedílnou součástí této práce. Cílovou skupinou soustav, kterou se práce zabývá, jsou nelineární podaktuované systémy, byť většinu uvedených metod je možné použít obecně. Jako případová studie byl vybrán typický systém reprezentující tuto třídu – jednoramenné inverzní kyvadlo. Ověřování řízení pro realizaci jeho výšvihu probíhá nejen v simulaci, ale také na reálném laboratorním modelu. V závěrečné části práce probíhá návrh řízení pro víceramenná inverzní kyvadla, pomocí čehož se ověřuje univerzálnost celého návrhu a použitelnost metod pro extrémně složité systémy.This thesis focuses on the design of nonlinear system control. The idea is not only to ensure correct functionality around a certain operating point, but also to solve the transition of the system between two states. When moving the system in the state space, its nonlinear behavior is often significantly manifested. The control design is discussed both in a variant where the transition between states is only required and in a form where the desired properties of the transition are specified using an objective function and an optimal solution is searched for. A model of the system is used in some form throughout the control design and verification process (model based design), so modelling is an integral part of this thesis. The target group of systems addressed in this thesis are nonlinear underactuated systems, although most of the methods presented can be applied in general. A typical system representing this class, the single-arm inverted pendulum, was chosen as a case study. Verification of the control to realize its swing-up is carried out not only in simulation but also using a real laboratory model. In the final part of the thesis, the design of the control for multi-arm inverted pendulums is performed, through which the universality of the overall design and the applicability of the methods to extremely complex systems are verified.450 - Katedra kybernetiky a biomedicínského inženýrstvívyhově