Stability Analysis of LQR-ANFIS Control Schemes on 2-degree-of-freedom Inverted Pendulum Systems

The concepts of stability and balance represent many critical problems faced by engineering today. The inverted pendulum on a cart is one such non-linear, unstable, multivariate system whose goal is to determine a suitable control action given to the cart such that it stabilizes the pendulum in an upright vertical position. This paper therefore, aims to design and study a highly robust MISO control structure using Linear Quadratic Regulation, Fuzzy logic and Neural Networks called Two-Stage LQR-based-ANFIS (referred to as TS-LA) for the stabilization of Inverted Pendulums. The proposed controller is implemented on a Simulink model of the Inverted Pendulum constructed through relevant mathematical and state space modelling using Newtonian and Lagrangian mechanics. Applying external disturbances, transient parameters are obtained and are benchmarked against standard conventional controllers to perform comparative analysis and showcase its disturbance rejection capabilities.