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

Saleem, Omer; Iqbal, Jamshed

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.

Citation

Saleem, O., & Iqbal, J. (2024). Phase-Based Adaptive Fractional LQR for Inverted-Pendulum-Type Robots: Formulation and Verification. IEEE Access, 12, 93185-93196. https://doi.org/10.1109/ACCESS.2024.3415494

• Journal Article Type: Article
• Acceptance Date: Jun 12, 2024
• Online Publication Date: Jun 17, 2024
• Publication Date: Jan 1, 2024
• Deposit Date: Jun 12, 2024
• Publicly Available Date: Jun 18, 2024
• Journal: IEEE Access
• Electronic ISSN: 2169-3536
• Publisher: Institute of Electrical and Electronics Engineers
• Peer Reviewed: Peer Reviewed
• Volume: 12
• Pages: 93185-93196
• DOI: https://doi.org/10.1109/ACCESS.2024.3415494
• Keywords: Adaptive control; Error phase; Fractional order control; LQR; Rotary inverted pendulum
• Public URL: https://hull-repository.worktribe.com/output/4708285