Robust proportional–integral–derivative compensation of an inverted cart–pendulum system: an experimental study

This study designs a two-loop proportional–integral–derivative (PID) controller for an inverted cart–pendulum system via pole placement technique, where the (dominant) closed-loop poles to be placed at the desired locations are obtained from an Linear quadratic regulator (LQR) design. It is seen that in addition to yielding better responses (because of additional integral action) than this LQR (equivalent to two-loop PD controller) design, the proposed PID controller is robust enough. The performance and robustness of the PID compensation are verified through simulations as well as experiments.