Design of Optimal and Fuzzy Controllers for Balancing an Inverted Pendulum System

Abstract

The inverted pendulum represents a challenging control problem. Since, inverted pendulum is inherently unstable i.e. if it is left without a stabilizing controller it will not be able to remain in upright position when disturbed. The aim of this study is to stabilize the inverted pendulum such that position of the cart is controlled quickly and accurately so that pendulum is always maintained its upright position. This thesis includes description of Cart Inverted Pendulum System (CIPS) and its linearized state space model. The proposed controllers in this study are Linear Quadratic Regulator (LQR), Linear Quadratic Gaussian (LQG) and Fuzzy Logic (FLC) controllers. The LQR controller designed by assuming all the states of the system available for feedback. The LQG controller, which is a combination of LQR and Kalman filter has been designed. It aims in providing a proper control input to obtain a desired output in terms of the pendulum angle and cart position. The fuzzy logic controller is a nonlinear control method provides better control performance than other traditional control methods without any need of mathematical modelling. The fuzzy logic controller has been designed based on state variable combination method. All the simulations are done in MATLAB/Simulink environment.