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Licensed Unlicensed Requires Authentication Published by De Gruyter November 18, 2015

Design of Controller in Double Feedback Control Loop – An Analysis with Heuristic Algorithms

K. Suresh Manic, V. Rajinikanth, Sarath Ananthasivam and Uma Suresh

Abstract

In this paper, heuristic algorithm based optimization approach is proposed to design the PID controller in Double Feedback Control Loop (DFCL) for a class of stable and unstable Single Input Single Output (SISO) process models. In this work, a three dimensional search is attempted and the heuristic algorithm is employed to find the best possible values for inner loop proportional gain (Kp1), outer loop integral gain (Ki), and derivative gain (Kd). A weighted sum of Objective Function (OF) is considered to guide the optimization search in order to attain the global best values. A comparative analysis is presented between heuristic algorithms, such as Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Bacterial Foraging Optimization (BFO) and Firefly Algorithm (FA). From this experimental study, it is confirmed that, FA based DFCL offers better performance in reference tracking and disturbance rejection operations with reduced error values for most of the considered process models compared with the alternatives. The statistical significance of the FA is also verified using Wilcoxon’s rank test.

Nomenclature

Kp

Proportional gain

Ki

Integral gain

Kd

Derivative gain

Gp

Process model

Gc1

Inner loop (P) controller

Gc2

Outer loop (PID) controller

w1,... wn

Weighting parameter

Mp

Overshoot

ts

Settling time

R1,R2, rand

Random number [0, 1]

C1, C2

Cognitive and global parameters

D

Dimension of search

N

Population of agents

Jmin

Objective function to be minimized

Xit

Initial position

Xit+1

Updated position

Greek Symbols

α

randomization operator

γ

Light absorption coefficient

β

Attractiveness coefficient

β0

Attractiveness at r = 0

Ψ

Randomization parameter

Abbreviations

PID

Proportional + Integral + Derivative

SISO

Single Input Single Output

DOF

Degree Of Freedom

ACO

Ant Colony Optimization

GA

Genetic Algorithm

PSO

Particle Swarm Optimization

BFO

Bacterial Foraging Optimization

FA

Firefly Algorithm

ITAE

Integral Time Absolute Error

ITSE

Integral Time Square Error

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Published Online: 2015-11-18
Published in Print: 2015-12-1

©2015 by De Gruyter