Reduced-Order Observer-Based LQR Controller Design for Rotary Inverted Pendulum

Abstract

The Rotary Inverted Pendulum (RIP) is a widely used underactuated mechanical system in various applications such as bipedal robots and skyscraper stabilization where attitude control presents a significant challenge. Despite the implementation of various control strategies to maintain equilibrium, optimally tuning control gains to effectively mitigate uncertain nonlinearities in system dynamics remains elusive. Existing methods frequently rely on extensive experimental data or the designer's expertise, presenting a notable drawback. This paper proposes a novel tracking control approach for RIP, utilizing a Linear Quadratic Regulator (LQR) in combination with a reduced-order observer. Initially, the RIP system is mathematically modeled using the Newton-Euler-Lagrange method. Subsequently, a composite controller is devised that integrates an LQR for generating nominal control signals and a reduced-order observer for reconstructing unmeasured states. This approach enhances the controller's robustness by eliminating differential terms from the observer, thereby attenuating unknown disturbances. Thorough numerical simulations and experimental evaluations demonstrate the system's capability to maintain balance below 50 Hz and achieve precise tracking below 1.4 rad, validating the effectiveness of the proposed control scheme.