Stabilization and tracking control of the inverted pendulum on a cart via a modified PSO fractional order PID controller

Abstract

In this chapter, a fractional-order proportional integral derivative controller, PIλDμ, based super-twisting observer for the cart inverted pendulum system is proposed. The mathematical model of the underactuated robotic system is derived using Lagrange equation and Grunwald-Letnikov fractional calculus with the physical parameters of a commercial device, the Googol Technology experimental Laboratory. PIλDμ parameters are optimized using a modified Particle Swarm intelligence optimization approach with the help of a multiobjective fitness function. A comparative analysis with the classical Particle Swarm Optimization algorithm shows the superiority of the proposed approach.