LQR Controller Design for Single Inverted Pendulum System - With Research Papers and MATLAB Implementation

For the design of an LQR controller for a single inverted pendulum system, several key aspects must be considered. First, we need to conduct in-depth research on the theoretical knowledge presented in inverted pendulum papers, covering fundamental principles, physical characteristics, and control methodologies. This involves understanding the system's mathematical model derivation, state-space representation, and LQR optimal control theory. Second, we must analyze the MATLAB code implementation, including parameter definitions (such as system matrices A, B, Q, and R), function calls (like lqr() for controller gain calculation), and simulation setup procedures. The MATLAB implementation typically involves creating state-space models, computing optimal gain matrices using the algebraic Riccati equation, and simulating the closed-loop system response.

Based on this foundation, we can implement controller enhancements such as adding feedback control loops, optimizing control algorithms through parameter tuning, and implementing real-time stabilization techniques. These improvements aim to enhance the pendulum's control performance metrics like settling time, overshoot, and disturbance rejection. Key MATLAB functions involved may include ode45 for system dynamics integration, feedback() for control loop implementation, and custom scripts for performance analysis. Therefore, designing an effective LQR controller for a single inverted pendulum requires comprehensive understanding of both theoretical concepts and practical implementation through systematic simulation and debugging processes in MATLAB environment.