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

Abstract

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 a stable online gain-adjustment law that modifies the state-feedback gains online 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 and parametric variations, the baseline LQR is instead retrofitted with the proposed self-adjusting model-reference-adaptive-system that employs Lyapunov theory to formulate a stable online state-feedback gain-adjustment law. The adaptability and flexibility of the model-reference gain-adjustment law is increased by dynamically modifying the adaptation-gains via pre-calibrated Gaussian scaling functions that are driven by the system’s state-error variations. The hyper-parameters associated with each control strategy are tuned offline by iteratively minimizing an auxiliary quadratic cost function that captures the state-error and control-input variations. The proposed adaptive control strategies are examined in the physical environment by conducting credible real-time hardware experiments on QNET Rotary Pendulum Board. The experimental outcomes validate the superior reference-tracking and robustness of the proposed adaptive controller even under the influence of exogenous disturbances and modeling-errors.