DISCRETE STATE FEEDBACK CONTROL OF A FURUTA PENDULUM USING STATE ESTIMATOR

The Furuta Pendulum is a mechanical system designed to simulate the problem of self-balancing. It consists of a motor, an arm, and a rod connected by rotational joints. Its control challenge involves stabilizing the rod above its rotational axis in an equilibrium position. The Furuta Pendulum’s multivariable and highly nonlinear dynamics make it suitable for comparison to problems with significant connections to industry and society, such as stabilizing bipedal robots, individual transport vehicles, and modelling buildings to study the impact of earthquakes on their structures. This paper presents the construction of a Furuta Pendulum prototype and its mathematical modeling using the Lagrangian formulation. State feedback control designs were developed to stabilize the pendulum using Pole Placement and Linear Quadratic Regulator (LQR) techniques. Since the controllers are implemented via a digital computer, the Analog/Digital and Digital/Analog converters in the control loop were considered in the controller’s design by describing the system’s dynamics in discrete time and using discrete-time control techniques. State estimators were also implemented to estimate the state variables needed for feedback that are not physically measured in the prototype. The performances of the controllers were compared through graphical analysis and the ITAE (Integral of Time Multiplied by Absolute Error) index. The results indicated that both controllers were able to stabilize the pendulum’s rod in a vertical position and make the system arm follow a specific reference. The LQR controller showed a slightly more satisfactory performance than the Pole Placement controller, with smaller amplitudes of oscillation around the reference in the practical experiments and a shorter time to reach equilibrium in the simulations.