Relative Stability Analysis of Perturbed Cart Inverted Pendulum: An Experimental Approach

Abstract

In this paper, generalized form of transfer function model of a cart inverted pendulum system is presented. Furthermore, robustness analysis of PID-based cart inverted pendulum using LQR approach and SBL approach are carried out using Krishnamurthi's corollary on Routh criterion by considering variations in cart mass, pendulum length, and also applied force to the cart. Here, the mathematical formula is developed which provides limit for the mass of cart before the pendulum becomes unstable. The most important advantage of the proposed approach is that the analysis is carried using classical approach without using advanced robust control techniques. The results have been verified on a hardware set-up of cart inverted pendulum system. Finally, practical issues have been identified by comparing simulation and hardware results. The results can be expected to be useful in other real-time applications. © 2017, © 2017 IETE.