Rotary Inverted Pendulum Control using Robust Generalized Dynamic Inversion with Adaptive Neural Estimation

Abstract

A novel robust generalized dynamic inversion control system with adaptive neural estimation (RGDI-ANE) is designed for trajectory tracking of the under actuated rotary inverted pendulum (RIP). The RGDI control design begins by prescribing a virtual differential constraint dynamics (VCD) that imitates the desired tracking control objectives. The baseline RGDI control law is derived by inverting the VCD using dynamically scaled Generalized Inversion, and then augmenting a sliding mode control (SMC) element to provide robustness against performance deterioration due to dynamic scaling of the Moore-Penrose generalized inverse. Furthermore, an adaptive estimator that is based on radial basis function neural networks (RBF-NN) is adopted to limit the dependency of RGDI control on the RIP mathematical model. The weighting matrices of the RBF-NN are updated using a Lyapunov control function. The closed loop RGDI-ANE control system is shown to guarantee semi-global asymptotic stability. Computer simulations along with experimental tests have been conducted on Quanser's RIP system to validate the performance of RGDI-ANE control, and the results are compared with the results obtained by using the SMC and the linear quadratic control methodologies.