Development of Fractional-Order Model Reference Adaptive Control of a Higher-Order Ball and Beam System with Actuator Dynamics

Abstract

This study develops a fractional-order model reference adaptive controller (FOMRAC) for a higher-order balland-beam system in which actuator behaviour is explicitly represented. The experimental platform comprises a 0.60 m beam, a 2.7 g ball with a 20 mm radius, a Hitec HS-645MG servo, an Arduino UNO controller, and a VL53L1 time-of-flight position sensor. The ball dynamics are obtained from the rolling constraint and then linearised about the horizontal equilibrium. Recalculation from the parameters gives an effective rolling mass of 7.02 × 10⁻³ kg and a nominal ballposition/beam-angle gain of −0.25154 s⁻². Actuator dynamics are retained in the higher-order representation rather than being treated as instantaneous. A Caputo fractional-order adaptation law is incorporated into a Lyapunov-based MRAC structure. PID, integer-order MRAC, and FOMRAC are compared using the performance measures, while four recorded laboratory PID trajectories are used to illustrate the sensitivity of the physical platform to gain selection. Under the model, FOMRAC gives a settling time of 1.880 s and the smallest IAE and ITAE among the three controllers. The results support the use of fractional adaptation as an additional tuning dimension for practical ball-and-beam control.