Inverted Pendulum Control Using LQR (Linear Quadratic Regulator) Methodology

The inverted pendulum represents a classical control theory benchmark problem frequently employed to investigate and validate various control algorithms. In this project, we implement pendulum stabilization using LQR (Linear Quadratic Regulator) methodology, which constitutes an optimal control strategy that balances system dynamics against control cost functions through quadratic performance indices. The implementation typically involves linearizing the nonlinear pendulum dynamics around the upright equilibrium point using Jacobian matrices, then solving the algebraic Riccati equation to obtain optimal feedback gain coefficients. Key implementation steps include constructing state-space matrices [A,B,C,D] from the derived linearized model, designing appropriate Q (state weighting) and R (control effort weighting) matrices based on performance requirements, and computing the gain matrix K using MATLAB's lqr() function. Practical considerations must account for sensor inaccuracies, environmental disturbances, and actuator saturation to ensure controller stability and robustness. Through this hands-on project, developers gain deeper comprehension of control theory fundamentals, including state-space representation, pole placement techniques, and real-time controller implementation, establishing a solid foundation for future control system applications.