Stabilization of nonlinear inverted pendulum system using MOGA and APSO tuned nonlinear PID controller

Abstract

An inverted pendulum system (IPS) is a highly nonlinear dynamical open loop unstable system, typically used as a benchmark to verify the performance of controllers. The IPS emulates the behaviour of an altitude control of a space booster or rocket on take-off. The problem is to develop suitable controllers to maintain the stabilization and swing up of an inverted pendulum on a cart. This paper presents the evolutionary tuning methods of nonlinear PID (NL-PID) controller for IPS with the multi-objective genetic algorithm (MOGA) and adaptive particle swarm optimization (APSO) algorithm. The function of NL-PID controllers is to keep the pendulum in an upright position by maintaining the pendulum at same state and angle at zero degrees. The comparison of responses and performance of MOGA tuned NL-PID and APSO tuned NL-PID controllers for an IPS are described. The mathematical modeling and simulation analysis of the IPS is presented in detail to test the effectiveness of controller tuning algorithm. The APSO based tuning of the NL-PID controller has lesser chattering, noise and fast settling time than MOGA based tuning of the controller.

Keywords

• inverted pendulum system
• nl-pid controller
• tuning
• multi-objective genetic algorithm
• adaptive particle swarm optimization algorithm