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

Sudarshan K Valluru,Madhusudan Singh,Mohammed Chadli

doi:10.1080/23311916.2017.1357314

Sudarshan K Valluru, Madhusudan Singh + Show 1 more

Open Access

https://doi.org/10.1080/23311916.2017.1357314

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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 o...

Highlights

Most of the physical systems are nonlinear dynamic systems which exhibit multiple equilibrium points
The inverted pendulum system (IPS) is one of the established benchmark problems in control literature as well as one of the most complicated dynamical systems according to report of the International Federation of Automatic Control (IFAC) theory committee
The present study focuses on detailed investigations, and performance evaluation of the nonlinear PID (NL-PID) controlled IPS for optimal gain tuning by new variants of metaheuristics i.e. multi-objective genetic algorithm (MOGA) and adaptive particle swarm optimization (APSO) based optimization of controller parameters

Summary

Introduction

Most of the physical systems are nonlinear dynamic systems which exhibit multiple equilibrium points. The variants of MOGA and Adaptive Particle Swarm Optimization Algorithm (APSO) have been considered here for the tuning of NL-PID controllers for IPS. 8. Decode the binary strings and visualize the new values of Kp, Ki, Kd. The size of the population, dimension, mutation rate, selection rate, maximum iterations used in the MOGA process to find best optimizing tuning parameters of NL-PID controllers for IPS taken as 10, 3, 0.2, 0.3, 100 respectively. The block diagram of APSO tuned NL-PID for cart pendulum system is shown in Figure 7 which uses the step reference signal to the IPS, the error between actual output and the reference signal along with proportional (Kp), integral (Ki), derivative (Kd) gains generated the control signal u(t). While stopping criteria is not reached do for every particle i do Generate innovative velocity vi,j(n + 1) according to Equation (16) Generate new positions pi,j(n + 1) according to Equation (17)

Output the final results of optimized global best

Conclusion