A simplified adaptive interval Type-2 fuzzy control in practical industrial application

Abstract

Adaptive Type-2 fuzzy control possesses control performance better than the traditional adaptive fuzzy control. However, heavy computation burden obviously blocks the utilization of adaptive Type-2 fuzzy control in industrial application. By adopting novel piecewise fuzzy sets and center-average type-reduction, a simplified adaptive interval Type-2 fuzzy controller involving less computation is developed for practical industrial application. In the proposed controller, the inputs are divided into several subintervals and then two piecewise fuzzy sets are used for each subinterval. With the manner of piecewise fuzzy sets and a novel fuzzy rules inference engine, only part of fuzzy rules are simultaneously activated in one control loop, which exponentially decreases the computation and makes the controller appropriate in industrial application. The simulation and experimental study, involving the popular magnetic levitation platform, shows the predicted system with theoretical stability and good tracking performance. The analysis indicates that there is far less computation of the proposed controller than the traditional adaptive interval Type-2 fuzzy controller, especially when the number of fuzzy rules and fuzzy sets is large, and the controller still maintains good control performance as the traditional one.

Keywords

Type-2 fuzzy control / piecewise fuzzy set / adaptive fuzzy control / center-average type-reduction

References

[1] MendelJ MUncertain rule-based fuzzy logic systems: introduction and new directions [M], 2001, Upper Saddle River, NJ, Prentice-Hall: 10-120

[2] JohnR I, CouplandS. Type-2 fuzzy logic: A historical view [J]. IEEE Computational Intelligence Magazine, 2007, 2(1): 57-62

[3] HagrasH. Type-2 FLCs: A new generation of fuzzy controllers [J]. IEEE Computational Intelligence Magazine, 2007, 2(1): 30-43

[4] CaoJ-t, JiX-f, LiP, LiuH-hai. Design of adaptive interval type-2 fuzzy control system and its stability analysis [J]. International Journal of Fuzzy Systems, 2011, 13(4): 335-343

[5] GalluzzoM, CosenzaB. Adaptive type-2 fuzzy logic control of a bioreactor [J]. Chemical Engineering Science, 2010, 65(14): 4208-4221

[6] HsiaoM-y, ChenC-y, LiT-hseng. Interval Type-2 adaptive fuzzy sliding-mode dynamic control design for wheeled mobile robots [J]. International Journal of Fuzzy Systems, 2008, 10(4): 268-275

[7] ZhouH-b, YingH, DuanJ-an. Adaptive Type-2 fuzzy control for uncertain nonlinear system [J]. Journal of Central South University of Technology, 2011, 18: 760-766

[8] WuH W, MendelJ M. Uncertainty bounds and their use in the design of interval Type-2 fuzzy logic systems [J]. IEEE Transactions on Fuzzy Systems, 2002, 10(5): 622-639

[9] LiH X, TongS C. A hybrid adaptive fuzzy control for a class of nonlinear MIMO systems [J]. IEEE Transactions on Fuzzy Systems, 2003, 11(1): 24-34

[10] YingH. Deriving analytical input-output relationship for fuzzy controllers using arbitrary input fuzzy sets and Zadeh fuzzy and operator [J]. IEEE Transactions on Fuzzy Systems, 2006, 14(5): 654-662

[11] ZhouH B, YingH. A method for deriving the analytical structure of a broad class of typical interval Type-2 mamdani fuzzy controllers [J]. IEEE Transactions on Fuzzy Systems, 2013, 21(3): 447-458

[12] DuX-y, YingHao. Derivation and analysis of the analytical structures of the interval Type-2 fuzzy-PI and PD controllers [J]. IEEE Transactions on Fuzzy Systems, 2010, 18(4): 802-814

[13] YingH. General interval type-2 mamdani fuzzy systems are universal approximators [C]. 2008 Annual Meeting of the North American Fuzzy Information Processing Society, 2008, New York, IEEE: 294-299

[14] YingH. Interval Type-2 takagi-sugeno fuzzy systems with linear rule consequent are universal approximators [C]. 2009 Annual Meeting of the North American Fuzzy Information Processing Society, 2009, Cincinnati, USA, IEEE: 541-545

[15] KarnikN N, MendelJ M, LiangQ L. Type-2 fuzzy logic systems [J]. IEEE Transactions on Fuzzy Systems, 1999, 7(6): 643-658

[16] WuD R, MendelJ M. Enhanced karnik-mendel algorithms [J]. IEEE Transactions on Fuzzy Systems, 2009, 17(4): 923-934

[17] MendelJ M, LiuF L. Super-exponential convergence of the Karnik-Mendel algorithms for computing the centroid of an interval type-2 fuzzy set [J]. IEEE Transactions on Fuzzy Systems, 2007, 15(2): 309-320

[18] ChenM Y, WangM J, FuL C. Modeling and controller design of a maglev guiding system for application in precision positioning [J]. IEEE Transactions on Industrial Electronics, 2003, 50(3): 493-506

[19] FulfordC, MaggioreM, ApkarianJ. Control of a 5DOF magnetically levitated positioning stage [J]. IEEE Transactions on Control Systems Technology, 2009, 17(4): 844-852

[20] JingM-q, LiuH, LianJ-x, YuLie. Two-dimensional high precision positioning maglev stage [J]. Journal of Xi’an Jiaotong University, 2008, 42(11): 1377-1380

[21] ShanX M, KuoS K, ZhangJ H, MenqC H. Ultra precision motion control of a multiple degrees of freedom magnetic suspension stage [J]. IEEE-ASME Transactions on Mechatronics, 2002, 7(1): 67-77

[22] WaiR J, LeeJ D. Adaptive fuzzy-neural-network control for maglev transportation system [J]. IEEE Transactions on Neural Networks, 2008, 19(1): 54-70

[23] ZhouH B, DuanJ A. Levitation mechanism modelling for maglev transportation system [J]. Journal of Central South University of Technology, 2010, 17(6): 1230-1237

[24] ZhouH B, DuanJ A. A novel levitation control strategy for a class of redundant actuation maglev system [J]. Control Engineering Practice, 2011, 19(12): 1468-1478

[25] SinhaP K, PechevA N. Model reference adaptive control of a maglev system with stable maximum descent criterion [J]. Automatica, 1999, 358: 1457-1465

[26] DuanJ A, ZhouH B, GuoN P. Electromagnetic design of a novel linear maglev transportation platform with finite-element analysis [J]. IEEE Transactions on Magnetics, 2011, 47(1): 260-263