An integrated controller for stabilizing an inverted pendulum: LQR and Fuzzy Logic Control with Observer-Based State Estimation

Abstract

This paper addresses the challenging control problem of stabilizing an inverted pendulum on a cart. The inherent nonlinearity, instability, and under actuation of the system pose significant difficulties in achieving simultaneous pendulum stabilization and cart movement. To overcome these challenges, we propose an integrated approach that combines Linear Quadratic Regulator (LQR) and fuzzy logic control methods. This integrated control strategy effectively stabilizes the pendulum and controls the cart’s position. Notably, the integrated control outperforms the LQR control in terms of convergence speed. Furthermore, we explore the use of observers for state estimation, specifically the high-order integral-chain differentiator and the extended state observer, to accurately estimate pendulum angular velocity. Simulation results, along with detailed discussions, are presented to validate the accuracy and effectiveness of the proposed control methods and observers.

Keywords

• inverted pendulum
• fuzzy logic control
• linear quadratic regulator
• extended state observer
• high-order integral-chain differentiator