Introduction

System description
The inverted pendulum task resembles a self-erecting control problem, relevant in applications like missile launching and control. The inverted cart-pendulum exemplifies an under-actuated, non-minimum phase and highly unstable system, posing significant challenges for controller design. Complicating matters are physical constraints on track length and pendulum angle. To address these challenges, a two-loop PID controller utilizing pole placement technique is employed here, strategically positioning dominant closed-loop poles at desired locations to generate control signals that aid in system stabilization.
Fig. 1 explains how the control system is organised.