Mathematical modelling and quadratic optimal tuning based PID scheme for an inverted pendulum-cart system

Abstract

An Inverted Pendulum (IP) is one of pendulum-cart laboratory setup consisted of a pole mounted on a cart. The system encompasses complex control problems and greatly challenges the researchers in designing a better and optimal controller. This paper aims to model the IP and to design a PID control that using Quadratic Optimal Tuning (QOT) scheme for stabilization and position control of a single link IP. Firstly, a nonlinear model of IP is derived using Newtonian method. Then an augment model that include PID scheme is formulated. Lastly, the gains of PID scheme is tuned using QOT. Matlab-Simulink environment is utilized to simulate the balancing and position control performance of IP. The results show that the stability of the system had been confirmed and the system had a comparable performance with the one which controlled by LQR controller.