Optimal LQG controller design for inverted pendulum systems using a comprehensive approach

Controlling nonlinear systems, such as the inverted pendulum on a moving cart, presents a well-known challenge due to the system's nonlinearities and highly coupled states. This paper explores the control methodology of the system by linearizing the dynamics around the pendulum's upright position. The primary objective of this review article is to develop control strategies that can not only stabilize the system but also respond effectively to external disturbances. Although control techniques like Proportional-Integral-Derivative (PID), Linear Quadratic Regulator (LQR), and Model Predictive Control (MPC) are commonly used, this research places particular emphasis on the Linear Quadratic Gaussian (LQG) control method. LQG, known for its capacity to handle uncertainties and system noise, is analyzed in detail. MATLAB simulations are conducted to compare the performance of various control strategies, with a specific focus on LQG's ability to ensure stability and performance under disturbance. The findings highlight LQG's robustness in managing system uncertainties and its adaptability to changing conditions, making it a strong candidate for practical nonlinear control applications.