Stabilization of a Cart-Pendulum System Using the Pole Placement Technique

This study addresses the stabilization of the Cart Inverted Pendulum (CIP), a system widely recognized as a foundational challenge in control theory because of its unstable, nonlinear, and under controlled properties. Achieving stability in the CIP is essential for developing control methods for modern applications like robotics. This paper implements the Pole Placement method to ensure the system remains stable. The method begins by linearizing the nonlinear system dynamics about the unstable vertical configuration and expressing them in a state-variable form. After confirming the system's controllability, a state-feedback controller is designed by strategically assigning closed-loop pole locations. This placement dictates the system's performance, allowing for specific targets for damping and setting time. The controller's effectiveness is demonstrated through numerical simulations in MATLAB/Simulink, which confirm the system's successful transition from instability to stable, regulated control of both the angle of pendulum and the position of cart. This analysis also illuminates the essential trade-off between the system's response speed and the required energy control. The work ultimately affirms that Pole Placement is a highly effective, understandable, and computationally practical technique for stabilizing complex underactuated systems.