Backstepping Linear Quadratic Gaussian Controller Design for Balancing an Inverted Pendulum

Abstract

Numerous real-time implementations such as a robust balancing process, segway and hover board riding, and rocket propeller operation are done with the control principle of Inverted Pendulum (IP). Dynamically, the IP is considered as an extremely unstable, non-linear in nature, and under-actuated system. Thus, the control strategy formulation for its equilibrium is generally accepted as an initial attempt for any new control technique as a proof towards further application in the control system engineering. This paper presents a novel Backstepping Linear Quadratic Gaussian Controller (BLQGC) based on the Lyapunov function to control the cart position x(t) and angular displacement θ(t) of the pendulum. The justification of enhanced control performance of BLQGC is demonstrated by comparative result analysis with optimal PID control, Linear Quadratic Gaussian (LQG) control, and other robust control techniques suggested by different authors. The simulations are carried out through MATLAB/SIMULINK environment and the results indicate comparatively better control ability of the proposed method in terms of accuracy, stability, quick damping, and robustness.