Phase-Based Adaptive Fractional LQR for Inverted-Pendulum-Type Robots: Formulation and Verification

Abstract

The underlying principles of inverted pendulums are widely applied to develop stabilization control strategies for under-actuated robotic systems in various applications. This article methodically designs an adaptive fractional-order linear quadratic regulator to optimize the position regulation and disturbance compensation ability of an inverted-pendulum-like robot. The proposed adaptive controller is realized by employing fractional-order differentiation operators in the baseline linear-quadratic-regulator. These fractional orders are adaptively modulated via an error-phase-based online adaptation law. The AFO modulation supplements the controller’s agility to efficiently steer the input trajectory as the state error’s phase changes, aiding the closed-loop system in robustly rejecting the external perturbations while maintaining a time-optimal behavior. The said propositions are verified by conducting customized experimental trials on the Quanser rotary pendulum platform. The proposed adaptive controller reduces the system’s transient recovery time by 35.8%, overshoots by 35.1%, control-energy expenditure by 37.2%, and offsets by 38.2% under transient disturbances, in comparison to the baseline linear quadratic regulator. The experimental data validates the superior time optimality and disturbance compensation of the proposed control law.

Keywords

• Adaptive control
• error phase
• fractional order control
• LQR
• rotary inverted pendulum