The simplest interval type-2 fuzzy PID controller: Structural analysis

In this paper, we will present analytical derivations of the simplest the Interval Type-2 Fuzzy PID (IT2-FPID) controller output which is composed of only 4 rules. Thus, we will first propose a new visualizing method called Surface of the Switching Points (S-MAP) in order to better analyze the derivation of the Switching Points (SPs) of the Karnik-Mendel algorithms. We presented mathematical explanation of the S-MAP and showed that the SPs are determined by only two Boundary Functions (BFs) for the simplest IT2-FPID controller. We will then give the simplified analytical derivation of the simplest IT2-FPID controller around the steady state via the employed BFs and S-MAP. We have illustrated that the simplest IT2-FPID controller is in fact analogous to a conventional PID controller around the steady state. We presented the simplest IT2-FPID controller output in terms of the parameters of the antecedent IT2-FSs. We examined the effect of the design parameter over IT2-FPID control system performance. In the light of the observations, we presented a simple self-tuning mechanism to enhance the transient state and disturbance rejection performance.

[1]  Tufan Kumbasar,et al.  A simple design method for interval type-2 fuzzy pid controllers , 2014, Soft Comput..

[2]  Engin Yesil,et al.  Interval type-2 fuzzy PID load frequency controller using Big Bang-Big Crunch optimization , 2014, Appl. Soft Comput..

[3]  Woei Wan Tan,et al.  Analytical Structure and Characteristics of Symmetric Karnik–Mendel Type-Reduced Interval Type-2 Fuzzy PI and PD Controllers , 2012, IEEE Transactions on Fuzzy Systems.

[4]  Jerry M. Mendel,et al.  Interval type-2 fuzzy logic systems , 2000, Ninth IEEE International Conference on Fuzzy Systems. FUZZ- IEEE 2000 (Cat. No.00CH37063).

[5]  Jerry M. Mendel,et al.  On the Stability of Interval Type-2 TSK Fuzzy Logic Control Systems , 2010, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[6]  Jerry M. Mendel,et al.  Interval Type-2 Fuzzy Logic Systems Made Simple , 2006, IEEE Transactions on Fuzzy Systems.

[7]  Sung-Kwun Oh,et al.  A comparative experimental study of type-1/type-2 fuzzy cascade controller based on genetic algorithms and particle swarm optimization , 2011, Expert Syst. Appl..

[8]  Hak-Keung Lam,et al.  Stability Analysis of Interval Type-2 Fuzzy-Model-Based Control Systems , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[9]  M. Furkan Dodurka,et al.  Boundary function based Karnik-Mendel type reduction method for Interval Type-2 Fuzzy PID controllers , 2014, 2014 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE).

[10]  Dongrui Wu,et al.  On the Fundamental Differences Between Interval Type-2 and Type-1 Fuzzy Logic Controllers , 2012, IEEE Transactions on Fuzzy Systems.

[11]  Jerry M. Mendel,et al.  Centroid of a type-2 fuzzy set , 2001, Inf. Sci..

[12]  Oscar Castillo,et al.  Systematic design of a stable type-2 fuzzy logic controller , 2008, Appl. Soft Comput..

[13]  Jerry M. Mendel,et al.  Uncertainty bounds and their use in the design of interval type-2 fuzzy logic systems , 2002, IEEE Trans. Fuzzy Syst..

[14]  Dongrui Wu,et al.  Interval Type-2 Fuzzy PI Controllers: Why They are More Robust , 2010, 2010 IEEE International Conference on Granular Computing.

[15]  I. Eksin,et al.  Type-2 fuzzy model based controller design for neutralization processes. , 2012, ISA transactions.

[16]  Engin Yesil,et al.  Interval type-2 fuzzy inverse controller design in nonlinear IMC structure , 2011, Eng. Appl. Artif. Intell..

[17]  Hao Ying,et al.  Derivation and Analysis of the Analytical Structures of the Interval Type-2 Fuzzy-PI and PD Controllers , 2010, IEEE Transactions on Fuzzy Systems.

[18]  Dongrui Wu,et al.  Design of Type-Reduction Strategies for Type-2 Fuzzy Logic Systems using Genetic Algorithms , 2007, Advances in Evolutionary Computing for System Design.

[19]  Dongrui Wu,et al.  Genetic learning and performance evaluation of interval type-2 fuzzy logic controllers , 2006, Eng. Appl. Artif. Intell..

[20]  Hani Hagras,et al.  A hierarchical type-2 fuzzy logic control architecture for autonomous mobile robots , 2004, IEEE Transactions on Fuzzy Systems.

[21]  Jerry M. Mendel,et al.  Enhanced Karnik--Mendel Algorithms , 2009, IEEE Transactions on Fuzzy Systems.