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

Saleem, Omer; Iqbal, Jamshed


Omer Saleem


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.


Saleem, O., & Iqbal, J. (in press). Phase-Based Adaptive Fractional LQR for Inverted-Pendulum-Type Robots: Formulation and Verification. IEEE Access,

Journal Article Type Article
Acceptance Date Jun 12, 2024
Online Publication Date Jun 17, 2024
Deposit Date Jun 12, 2024
Publicly Available Date Jun 18, 2024
Journal IEEE Access
Publisher Institute of Electrical and Electronics Engineers
Peer Reviewed Peer Reviewed
Keywords Adaptive control; Error phase; Fractional order control; LQR; Rotary inverted pendulum
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