Control de prototipo de planta de péndulo invertido.
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Date
2025
Journal Title
Journal ISSN
Volume Title
Publisher
Universidad de Concepción
Abstract
El objetivo de este trabajo es diseñar, implementar y validar de forma experimental estrategias de control para un sistema de péndulo invertido montado sobre un carro móvil. Se abordan los problemas de swing-up y estabilización del movimiento del péndulo.
Para esto, se desarrolló un modelo fenomenológico del sistema mediante dos enfoques: el método de Euler-Lagrange y mediante un análisis de fuerzas basado en las Leyes de Newton. El primero permite un tratamiento desde el punto de vista energético, mientras que el segundo permite una interpretación a partir de las fuerzas involucradas. Ambos métodos entregan el mismo modelo dinámico, demostrando su correcta formulación. Este modelo es linealizado en torno a los puntos de operación estable e inestable, para obtener representaciones del sistema como funciones de transferencia y de espacio de estados.
A partir del modelo, se diseñaron dos estrategias a para abordar el problema de swing-up: una basada en el control de energía del péndulo y otra en el control de la posición del carro. Para el problema de estabilización se diseñaron otras dos estrategias: un controlador óptimo Regulador Cuadrático Lineal (LQR) y un esquema basado en controladores PID en cascada.
Cada uno de los controladores diseñados fueron validados utilizando simulaciones en el entorno Simulink de MATLAB y posteriormente implementadas en un prototipo físico diseñado y construido en el laboratorio.
Los resultados experimentales muestran que el controlador por posición para el problema de swing-up y el controlador LQR para el problema de estabilización ofrecen un desempeño superior a las otras estrategias presentadas.
The objective of this work is to design, implement and experimentally validate control strategies for an inverted pendulum system mounted on a movable cart. This study addresses both the swing-up and stabilization problems of the pendulums motion. For this purpose, a phenomenological model of the system was developed using two different approaches: the Euler-Lagrange method and a force-based analysis derived from Newton’s laws. Th first one provides an energy-based formulation, while the second one provides an interpretation based on the acting forces. Both methods result in the same dynamic model, demonstrating its correct formulation. The model was then linearized around both the stable and unstable equilibrium points to obtain system representations in the form of transfer functions and state-space models. Based on the obtained model, two strategies were developed to solve the swing-up problem: one based on the energy control of the pendulum, and another based on controlling the position of the cart. For the stabilization phase, two additional strategies were designed: an optimal Linear Quadratic Regulator (LQR) and a control scheme based on cascaded PID controllers. Each of the proposed controllers was validated through simulations in MATLAB’s Simulink environment and then implemented on a physical prototype designed and built in the laboratory. The experimental results show that the position-based swing-up controller and the LQR stabilization controller outperform the other presented strategies.
The objective of this work is to design, implement and experimentally validate control strategies for an inverted pendulum system mounted on a movable cart. This study addresses both the swing-up and stabilization problems of the pendulums motion. For this purpose, a phenomenological model of the system was developed using two different approaches: the Euler-Lagrange method and a force-based analysis derived from Newton’s laws. Th first one provides an energy-based formulation, while the second one provides an interpretation based on the acting forces. Both methods result in the same dynamic model, demonstrating its correct formulation. The model was then linearized around both the stable and unstable equilibrium points to obtain system representations in the form of transfer functions and state-space models. Based on the obtained model, two strategies were developed to solve the swing-up problem: one based on the energy control of the pendulum, and another based on controlling the position of the cart. For the stabilization phase, two additional strategies were designed: an optimal Linear Quadratic Regulator (LQR) and a control scheme based on cascaded PID controllers. Each of the proposed controllers was validated through simulations in MATLAB’s Simulink environment and then implemented on a physical prototype designed and built in the laboratory. The experimental results show that the position-based swing-up controller and the LQR stabilization controller outperform the other presented strategies.
Description
Tesis presentada para optar al título de Ingeniero/a Civil Electrónico/a.
Keywords
Control automático, Péndulo, Estabilidad