This is the torque needed to start the rotational motion necessary to cause an object to rotate around an axis. In most cases, more torque is required to create the rotational motion than is needed to keep it going once it has begun. The amount of break-away torque required to move something is determined in part by static friction.
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.