Hybrid Mamdani Fuzzy Logic Swing-Up and LQR Stabilization Control of a Rotary Inverted Pendulum: Design, Simulation, and Analysis

This paper presents the design, simulation, and analysis of a hybrid control system for a rotary inverted pendulum (RIP) combining a Mamdani-type fuzzy logic controller (FLC) for energy-based swing-up with a linear quadratic regulator (LQR) for upright stabilization. A 25-rule Mamdani FIS with energy error ΔE and pendulum angular velocity α˙ inputs implements energy pumping toward Eref ≈15.19mJ. The LQR, designed via the algebraic Riccati equation with Q=diag(1,200,1,5) and R=0.1, stabilizes the pendulum from 17.2° within 0.5 s. A 20° angle-threshold switching logic transitions smoothly between controllers. Extended robustness analyses covering varied initial conditions, disturbance rejection, switching-threshold sensitivity, rule-count variation, LQR weight sensitivity, offset tracking, power consumption, and simulation-hardware consistency confirm the architecture's suitability for QUARC deployment on a Qube-Servo 3.