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Algorithms 2017, 10(2), 68; doi:10.3390/a10020068

An Easily Understandable Grey Wolf Optimizer and Its Application to Fuzzy Controller Tuning

1
Department of Automation and Applied Informatics, Politehnica University of Timisoara, Bd. V. Parvan 2, 300223 Timisoara, Romania
2
School of Electrical Engineering and Computer Science, University of Ottawa, 800 King Edward, Ottawa,ON K1N 6N5 Canada
*
Author to whom correspondence should be addressed.
Academic Editor: Oscar Castillo
Received: 25 April 2017 / Revised: 7 June 2017 / Accepted: 8 June 2017 / Published: 10 June 2017
(This article belongs to the Special Issue Extensions to Type-1 Fuzzy Logic: Theory, Algorithms and Applications)
View Full-Text   |   Download PDF [660 KB, uploaded 13 June 2017]   |  

Abstract

This paper proposes an easily understandable Grey Wolf Optimizer (GWO) applied to the optimal tuning of the parameters of Takagi-Sugeno proportional-integral fuzzy controllers (T-S PI-FCs). GWO is employed for solving optimization problems focused on the minimization of discrete-time objective functions defined as the weighted sum of the absolute value of the control error and of the squared output sensitivity function, and the vector variable consists of the tuning parameters of the T-S PI-FCs. Since the sensitivity functions are introduced with respect to the parametric variations of the process, solving these optimization problems is important as it leads to fuzzy control systems with a reduced process parametric sensitivity obtained by a GWO-based fuzzy controller tuning approach. GWO algorithms applied with this regard are formulated in easily understandable terms for both vector and scalar operations, and discussions on stability, convergence, and parameter settings are offered. The controlled processes referred to in the course of this paper belong to a family of nonlinear servo systems, which are modeled by second order dynamics plus a saturation and dead zone static nonlinearity. Experimental results concerning the angular position control of a laboratory servo system are included for validating the proposed method. View Full-Text
Keywords: Grey Wolf Optimizer; Takagi-Sugeno proportional-integral fuzzy controllers; process parametric sensitivity; stability; convergence; parameter settings; angular position Grey Wolf Optimizer; Takagi-Sugeno proportional-integral fuzzy controllers; process parametric sensitivity; stability; convergence; parameter settings; angular position
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Precup, R.-E.; David, R.-C.; Szedlak-Stinean, A.-I.; Petriu, E.M.; Dragan, F. An Easily Understandable Grey Wolf Optimizer and Its Application to Fuzzy Controller Tuning. Algorithms 2017, 10, 68.

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