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

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. *Corresponding author: Sudarshan K. Valluru, Department of Electrical Engineering, Delhi Technological University, Delhi 110042, India E-mail: [email protected] Reviewing editor: Mohammed Chadli, University of Picardie Jules Verne, France Additional information is available at the end of the article ABOUT THE AUTHORS Sudarshan K. Valluru has been an associate professor of Electrical Engineering since 2009 at Delhi Technological University, New Delhi, India. His area of interests is Meta-Algorithms Applications to Control of Dynamical Systems, Intelligent, and Soft Computing Techniques. He is Fellow Member of Institution of Electronics and Telecommunication Engineers, Life Member of Institution of Engineers (I), and Life Member of Indian Society for Technical Education and also a member of IEEE (USA). Madhusudan Singh has been working as Professor of Electrical Engineering since 2007 at Delhi Technological University, New Delhi, India. His research interests are in the area of modeling and analysis of Electrical Machines and Dynamical Systems, Voltage control aspects of Self-Excited Asynchronous Generator, Power Electronics, and Drives. He is a Fellow Member of Institution of Electronics and Telecommunication Engineers, Fellow Member of Institution of Engineers (I), and Life Member of Indian Society for Technical Education and also a Senior member of IEEE (USA). PUBLIC INTEREST STATEMENT It is interesting to watch the rocket launching at the space center, many of us watching on television the launching process of the rocket/ satellites and their establishment in the orbit of the earth. Sometimes our mind stuck on certain aspects while watching the scenario of rocket flight. The aspects include what force is controlling the launching rocket which is carrying the satellite, how the rocket of such huge weight is projected upright, how the satellite is placed into the space orbit. All these aspects for a budding control engineer are hard to understand initially, but once we start embracing the results obtained from control engineering, to learn and design dynamic controllers are becoming inevitable nowadays. The nonlinear inverted pendulum system(IPS) is a challenging benchmark control problem to design and test such new dynamic controllers. It resembles the many real-world dynamical systems, such as self-erecting rocket, missile launchers, Segway robotic platforms. Received: 08 May 2017 Accepted: 16 July 2017 First Published: 20 July 2017 © 2017 The Author(s). This open access article is distributed under a Creative Commons Attribution (CC-BY) 4.0 license.