The Fractional Order PID Controller for the 3-DOF Gyroscope System

This article presents a comparison between a classical PID controller and a fractional-order PID (FOPID) controller for a gyroscope with Cardan suspension (3 DOF). A gyroscope dynamics model accounting for gyroscopic couplings and viscous damping is adopted, while the FOPID controller is implemented in discrete form using the Grünwald–Letnikov (GL) operator, which reduces smoothly to the classical PID when λ = μ = 1. The effectiveness of both strategies is assessed in a moving-target tracking task using the IAE (tracking accuracy) and ISC (control effort) indices. MATLAB/Simulink R2025a simulations (ode4, Δt = 2 × 10−4 s) show that, under cross-axis couplings of the gyroscope suspension, FOPID yields smaller tracking errors and smoother control signals than PID. The results indicate the usefulness of fractional-order controllers in gyroscope control systems and provide a basis for further experimental studies.