Fractional Gradient-Based Model Reference Adaptive Control Applied on an Inverted Pendulum-Cart System
Year: 2025
Type: article
Abstract: This study introduces a novel model reference adaptive control (MRAC) framework that incorporates fractional-order gradients (FGs) to regulate the displacement of an inverted pendulum-cart system. Fractional-order gradients have been shown to significantly improve convergence rates in domains such as machine learning and neural network optimization. Nevertheless, their integration with fractional-order error models within adaptive control paradigms remains unexplored and represents a promising avenue for research. The proposed control scheme extends the classical MRAC architecture by embedding Caputo fractional derivatives into the adaptive law governing parameter updates, thereby improving both convergence dynamics and control flexibility. To ensure optimal performance across multiple criteria, the controller parameters are systematically tuned using a multi-objective Particle Swarm Optimization (PSO) algorithm. Two fractional-order error models (FOEMs) incorporating fractional gradients (FOEM2-FG, FOEM3-FG) are investigated, with their stability formally analyzed via Lyapunov-based methods under conditions of sufficient excitation. Validation is conducted through both simulation and real-time experimentation on a physical pendulum-cart setup. The results demonstrate that the proposed fractional-order MRAC (FOMRAC) outperforms conventional MRAC, proportional-integral-derivative (PID), and fractional-order PID (FOPID) controllers. Specifically, FOMRAC-FG achieved superior tracking performance, attaining the lowest Integral of Squared Error (ISE) of 2.32×10−5 and the lowest Integral of Squared Input (ISI) of 6.40 in simulation studies. In real-time experiments, FOMRAC-FG maintained the lowest ISE (5.11×10−6). Under real-time experiments with disturbances, it still achieved the lowest ISE (1.06×10−5), highlighting its practical effectiveness.
Source: Fractal and Fractional
Language: English
Subfield: Control and Systems Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,258
Awards: G2103440617, MULTIMODAL CONTEXT-AWARE PROGNOSTIC METHODS FOR INFORMED REAL-TIME DECISION-MAKING IN DYNAMIC SYSTEMS, ADVANCED CENTER FOR ELECTRICAL AND ELECTRONIC ENGINEERING, DISENO Y AJUSTE DE OBSERVADORES DE ESTADO CONMUTADOS PARA LA ESTIMACION DE VARIABLES CRITICAS NO MEDIBLES CON APLICACION A SISTEMAS BIOTECNOLOGICOS
OpenAlex ID: W4412630766