Simulink Model of LQR Controller for Inverted Pendulum System

This document presents a comprehensive model implementing a Linear Quadratic Regulator (LQR) controller designed for stabilizing an inverted pendulum system. The implementation utilizes Simulink, MATLAB's graphical programming environment for multi-domain simulation and model-based design. The LQR controller employs optimal control theory to minimize a quadratic cost function, balancing state regulation accuracy and control effort expenditure. Key implementation aspects include: state-space representation of the pendulum dynamics, design of the LQR gain matrix using MATLAB's lqr() function with appropriate weighting matrices Q and R, and real-time feedback control implementation. The model incorporates sensor measurements (pendulum angle and cart position) and calculates optimal control inputs to maintain the unstable equilibrium position. Through simulation analysis, this model enables thorough investigation of the system's transient response, stability margins, and disturbance rejection capabilities. The simulation framework allows parameter tuning of LQR weights to achieve desired performance specifications such as settling time, overshoot, and control effort limitations. This approach provides valuable insights for controller optimization and serves as a foundation for hardware implementation and real-time control applications.