LQR Simulation Model for Single Inverted Pendulum Control

The LQR simulation model for single inverted pendulum control can achieve outstanding control performance. In this model, since the pendulum rod can only rotate in one direction, it requires mastery of feedback control theory to ensure the pendulum maintains its vertical position. The implementation typically involves designing a state-space controller where the system dynamics are represented using matrices A, B, C, and D, followed by computing optimal feedback gains using the lqr() function in MATLAB/Simulink. Additionally, dynamic control algorithms need to be implemented to promptly detect and adjust the system's state. This involves real-time state estimation through sensor data processing and applying control inputs calculated using the LQR optimal control law: u = -Kx, where K represents the optimized gain matrix and x is the state vector containing pendulum angle, angular velocity, cart position, and cart velocity. Finally, to ensure the control system operates reliably under various conditions, multiple simulations and tests are necessary to identify and resolve potential issues. This includes parameter tuning, robustness testing against disturbances, and validating performance metrics such as settling time and overshoot. In summary, by comprehensively applying feedback control theory, dynamic control algorithms, and systematic simulation testing, we can successfully implement the LQR simulation model for single inverted pendulum control and achieve excellent control results.