Pole Placement Method for Controlling a Single Inverted Pendulum System

To control a single inverted pendulum system, we employ the pole placement method. This approach achieves system equilibrium by modifying system parameters, particularly the gain coefficient K. In control engineering, pole placement is widely utilized not only for inverted pendulum systems but also for various other control applications. The implementation typically involves calculating the state feedback gain matrix K using algorithms like Ackermann's formula or directly solving the pole placement equation via MATLAB's `place` or `acker` functions. This requires deriving the system's state-space representation and ensuring controllability. In practical applications, thorough analysis of system characteristics is essential for selecting appropriate parameters. Additionally, considerations for system stability and robustness are crucial to ensure reliable operation under diverse conditions. Therefore, control system design must comprehensively account for multiple factors to guarantee both performance and reliability, including simulation-based validation of the closed-loop system response.