Real-Time Adaptive Linear Quadratic Regulator Control for the QUBE–2 Rotary Inverted Pendulum

This paper presents a real-time adaptive Linear Quadratic Regulator (LQR) control strategy for the rotary inverted pendulum. The state weighting matrix of the LQR cost function is continuously adapted online based on real-time tracking error, state dynamics, and sliding-mode-inspired robustness measures. Unlike conventional LQR controllers with fixed weighting matrices or hybrid schemes that apply sliding mode control directly to the control input, the proposed approach modulates the LQR cost function itself, enabling dynamic reshaping of controller behavior while preserving smooth control action. The real-time adaptive controller is implemented using a continuous-time Riccati differential equation solved online, making the method suitable for real-time deployment. Experimental validation is conducted on two Quanser QUBE-Servo 2 rotary inverted pendulum platforms under square, sinusoidal, and sawtooth reference trajectories. Performance is compared against a fixed-gain LQR controller using multiple quantitative metrics, including tracking error and control effort. Experimental results demonstrate substantial improvements in tracking accuracy, with reductions exceeding 70–90% in error metrics, while simultaneously achieving over 94% reduction in control effort. These findings verify that adaptive cost shaping provides an effective and practical mechanism for enhancing LQR performance in underactuated experimental systems.