Self-Adaptive Stabilization Control of a Rotary Pendulum using Nonlinearly-Scaled Model-Reference Gain-Adaptation Law

This article presents the formulation of a novel self-adjusting model-reference-adaptive-control law to enhance the position-regulation and disturbance-rejection capability of Rotary-Inverted-Pendulum (RIP) systems. Initially, the baseline Linear-Quadratic-Regulator (LQR) is augmented with an online gain-Yadjustment law that modifies the state-compensator gains via pre-calibrated state-error dependent dissipative and anti-dissipative functions to improve the system's position-regulation capability. To further enhance the controller's robustness against exogenous disturbances, the baseline LQR is instead retrofitted with the proposed self-adjusting model-reference-adaptive-system that employs Lyapunov function to formulate a stable online state-compensator gain-adjustment law. The adaptability of the model-reference gain-adjustment law is increased by dynamically modifying the adaptation-gain of self-tuning law via a pre-calibrated Gaussian scaling function that is driven by the system's state-error variations. The hyperparameters associated with the aforementioned adaptive control systems variants are empirically tuned by minimizing an auxiliary quadratic cost function that captures the classical-state-error and control-input variations. The proposed adaptive control system variants are examined in the physical environment by conducting credible real-time hardware experiments on QNET Rotary Pendulum Board. The experimental outcomes validate the superior robustness of the self-adjusting model-reference-adaptive-control system against the bounded exogenous disturbances and modeling-errors.