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

Monika Rani¹, Sushma S Kamlu²

¹Department of EEE, Birla Institute of Technology, Mesra, Ranchi, India. monikarani815@gmail.com.

Scientific Reports

|February 7, 2025

Summary

This summary is machine-generated.

This study reviews control methods for nonlinear systems like the inverted pendulum. Linear Quadratic Gaussian (LQG) control demonstrates superior robustness and adaptability, effectively managing system uncertainties and disturbances.

Keywords:

Inverted pendulum Linear quadratic Gaussian control (LQG)Linear quadratic regulator design (LQR)Model predictive controller (MPC)Proportional-integral-derived (PID) control

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Area of Science:

Control Systems Engineering
Nonlinear Dynamics
Robotics

Background:

Controlling nonlinear systems, exemplified by the inverted pendulum on a moving cart, is challenging due to inherent nonlinearities and coupled states.
Existing control strategies include Proportional-Integral-Derivative (PID), Linear Quadratic Regulator (LQR), and Model Predictive Control (MPC).

Purpose of the Study:

To explore and develop control strategies for stabilizing nonlinear systems and enhancing their response to external disturbances.
To specifically analyze the efficacy of the Linear Quadratic Gaussian (LQG) control method for such applications.

Main Methods:

Linearization of system dynamics around the upright equilibrium position.
Detailed analysis of the Linear Quadratic Gaussian (LQG) control methodology.
Performance comparison via MATLAB simulations of various control strategies, emphasizing LQG.

Main Results:

LQG control exhibits significant robustness in managing system uncertainties and noise.
Simulations confirm LQG's effectiveness in ensuring system stability and performance under external disturbances.
LQG demonstrates adaptability to changing operational conditions.

Conclusions:

The Linear Quadratic Gaussian (LQG) control method is a highly promising approach for practical nonlinear control applications.
LQG's ability to handle uncertainties and disturbances makes it a strong candidate for real-world systems.
Further research into LQG for complex nonlinear systems is warranted.