This consists of a driven arm that rotates horizontally inside the XY plane and a pendulum attached to the edge of the driven arm. The pendulum is free to turn in a plane that is perpendicular to the pendulum’s arm and coincides with the edge of said arm. It is an example of a complex non-linear oscillator. Such systems are of interest in control system theory. The rotary pendulum is underactuated and highly non-linear due to the gravitational forces and the coupling arising from the Coriolis and centripetal forces.
Published in Chapter:
Full-State Control of Rotary Pendulum Using LQR Controller
Horacio Alain Millan-Guerrero (Universidad Autónoma de Baja California, Mexico), Jose Antonio Nuñez-Lopez (Autonomous University of Baja California, Mexico),
Fabian N. Murrieta-Rico (Universidad Politécnica de Baja California, Mexico),
Lars Lindner (Universidad Autónoma de Baja California, Mexico),
Oleg Sergiyenko (Universidad Autónoma de Baja California, Mexico), Julio C. Rodríguez-Quiñonez (Universidad Autónoma de Baja California, Mexico), and
Wendy Flores-Fuentes (Universidad Autónoma de Baja California, Mexico)
Copyright: © 2022
|Pages: 43
DOI: 10.4018/978-1-7998-9795-8.ch007
Abstract
In this chapter, the authors design, simulate, and implement an optimal controller for a rotary pendulum while addressing real-world phenomena. The controller, called linear-quadratic-regulator (LQR), minimizes a cost function based on weights that penalize the system's state error and controller effort. The control objective is to reach the desired system state in an optimal way. The rotary pendulum consists of a pendulum attached to a rotary arm actuated by a motor. It is a great system to design and analyze different types of controllers. This system is underactuated, nonlinear, sensitive to initial conditions, and has 2 DOF. This chapter's main contributions are the mathematical modeling of the system taking into account nonlinear friction, the characterization of the plant using measured data from the physical system using the nonlinear squares and the trust-region reflective algorithms, comparison of linear and nonlinear behaviors, and implementation on real hardware considering discrete phenomena while using hardware-provided tools such as position decoding and PWM generation.