  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.
