Construção, Modelagem e Controle por Alocação de Polos e Regulador Quadrático Linear (Lqr) de UmPêndulo Furuta

Abstract

Rotational Inverted Pendulum, also known as Furuta Pendulum, is a mechanical system characterized by its highly nonlinear dynamics and unstable equilibrium point. These features are also found in systems relevant to industry and society such as the stabilization of bipedal robots and individual transport vehicles, the control in rocket launches, and the modeling of buildings for the study of the impact of earthquakes in these structures. In this context, the present work presents the construction and mathematical modeling, using the Lagrangian formulation, of a Furuta Pendulum. It is also presented state feedback control designs to stabilize the equipment’s rod in vertical position, using pole placement and Linear Quadratic Regulator (LQR). Considering that controller is implemented via a digital computer, the control designs take into account the Analog/Digital and Digital/Analog converters present in the control loop by representing the dynamics in discrete time. A state observer was also implemented since not all the state variables of the system, necessary for the state feedback, are physically measured in the equipment. The implementation of the controllers was done with the help of the Matlab/Simulink® software. Four tests were made, consisting of simulations and experiments, to validate the proposed mathematical model and compare the performance of the controllers in stabilizing the rod of the pendulum. The performance of the designed controllers was evaluated by graphical analysis, ITAE index, and transient response. The results indicate that both controllers were able to stabilize the pendulum’s rod in the vertical position despite disturbances applied to the system. In all the experiments, the response of the system presented an oscillatory characteristic. The LQR controller showed better results regarding ITAE index.