Full-State Control of Rotary Pendulum Using LQR Controller

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.