A new and robust control strategy for a class of nonlinear power systems: Adaptive general type-II fuzzy

In this article, a robust direct adaptive general type-2 fuzzy logic controller is introduced for a class of nonlinear power systems. The proposed controller uses the advantages of general type-2 fuzzy logic system in handling dynamic uncertainties to approximate unknown nonlinear actions. Implementing general type-2 fuzzy system is computationally costly; however, by using a recently introduced α-plane representation, general type-2 fuzzy logic system can be seen as a composition of several interval type-2 fuzzy logic systems with a corresponding level of α for each. Linguistic rules are directly incorporated into the controller. In addition, an H ∞ compensator is corrupted to attenuate external disturbance and fuzzy approximation error. General type-2 fuzzy adaptation laws are also derived using Lyapunov approach. It is worth noting that mathematical analysis proves the stability of the closed-loop system. In order to evaluate the performance of the proposed controller, the results are compared with those obtained by direct adaptive type-1 fuzzy logic controller, a direct adaptive interval type-2 fuzzy logic controller and adaptive proportional–integral–derivative, which are the latest researches in the problem in hand. The proposed controller is applied to a chaotic power system as a case study. Simulation reveals the effectiveness of the proposed controller in presence of dynamic uncertainties and external disturbances.

[1]  Mohammed Chadli,et al.  Fuzzy model based multivariable predictive control of a variable speed wind turbine: LMI approach , 2012 .

[2]  Caoyuan Ma,et al.  Chaos of a power system model and its control , 2012 .

[3]  Alireza Alfi,et al.  Chaos suppression on a class of uncertain nonlinear chaotic systems using an optimal H∞ adaptive PID controller , 2012 .

[4]  Seyyed Kamal Hosseini-Sani,et al.  Direct adaptive general type-2 fuzzy control for a class of uncertain non-linear systems , 2014 .

[5]  Taher Niknam,et al.  A robust and simple optimal type II fuzzy sliding mode control strategy for a class of nonlinear chaotic systems , 2014, J. Intell. Fuzzy Syst..

[6]  Yang Liu,et al.  A New Fuzzy Impulsive Control of Chaotic Systems Based on T–S Fuzzy Model , 2011, IEEE Transactions on Fuzzy Systems.

[7]  Jerry M. Mendel,et al.  $\alpha$-Plane Representation for Type-2 Fuzzy Sets: Theory and Applications , 2009, IEEE Transactions on Fuzzy Systems.

[8]  Meng Joo Er,et al.  Fire-rule-based direct adaptive type-2 fuzzy H∞ tracking control , 2011, Eng. Appl. Artif. Intell..

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

[10]  Robert Ivor John,et al.  Geometric Type-1 and Type-2 Fuzzy Logic Systems , 2007, IEEE Transactions on Fuzzy Systems.

[11]  Jerry M. Mendel,et al.  Introduction to uncertainty bounds and their use in the design of interval type-2 fuzzy logic systems , 2001, 10th IEEE International Conference on Fuzzy Systems. (Cat. No.01CH37297).

[12]  J. Mendel,et al.  α-Plane Representation for Type-2 Fuzzy Sets: Theory and Applications , 2009 .

[13]  Haibo Zhou,et al.  Adaptive control using interval type-2 fuzzy logic , 2009, 2009 IEEE International Conference on Fuzzy Systems.

[14]  Tsung-Chih Lin.  Based on interval type-2 fuzzy-neural network direct adaptive sliding mode control for SISO nonlinear systems , 2010 .

[15]  Tzuu-Hseng S. Li,et al.  Design of interval type-2 fuzzy sliding-mode controller , 2008, Inf. Sci..

[16]  R. Rakkiyappan,et al.  Impulsive controller design for exponential synchronization of chaotic neural networks with mixed delays , 2013, Commun. Nonlinear Sci. Numer. Simul..

[17]  R. N. Banavar,et al.  A chaotic phenomenon in the damped power swing equation , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[18]  Feilong Liu,et al.  An efficient centroid type-reduction strategy for general type-2 fuzzy logic system , 2008, Inf. Sci..

[19]  M. Khooban,et al.  An optimal type II fuzzy sliding mode control design for a class of nonlinear systems , 2013, Nonlinear Dynamics.

[20]  Chi-Hsu Wang,et al.  Dynamical optimal training for interval type-2 fuzzy neural network (T2FNN) , 2003, SMC'03 Conference Proceedings. 2003 IEEE International Conference on Systems, Man and Cybernetics. Conference Theme - System Security and Assurance (Cat. No.03CH37483).

[21]  Edward Ott,et al.  Controlling chaos , 2006, Scholarpedia.

[22]  Jerry M. Mendel,et al.  Type-2 fuzzy logic systems: type-reduction , 1998, SMC'98 Conference Proceedings. 1998 IEEE International Conference on Systems, Man, and Cybernetics (Cat. No.98CH36218).

[23]  Eyad H. Abed,et al.  Bifurcations, chaos, and crises in voltage collapse of a model power system , 1994 .

[24]  Jerry M. Mendel,et al.  Type-2 fuzzy logic systems , 1999, IEEE Trans. Fuzzy Syst..

[25]  Du Qu Wei,et al.  Passivity-based adaptive control of chaotic oscillations in power system , 2007 .

[26]  Reza Shahnazi,et al.  PI Adaptive Fuzzy Control With Large and Fast Disturbance Rejection for a Class of Uncertain Nonlinear Systems , 2008, IEEE Transactions on Fuzzy Systems.

[27]  Mokhtar Sha Sadeghi,et al.  Parallel distributed compensator design for process control based on fuzzy Takagi-Sugeno model , 2011, 2011 IEEE Power Engineering and Automation Conference.

[28]  Mohammad Hassan Khooban,et al.  Control of a class of non-linear uncertain chaotic systems via an optimal Type-2 fuzzy proportional integral derivative controller , 2013 .

[29]  Guodong Zhang,et al.  New Algebraic Criteria for Synchronization Stability of Chaotic Memristive Neural Networks With Time-Varying Delays , 2013, IEEE Transactions on Neural Networks and Learning Systems.

[30]  Hao Ying,et al.  Adaptive control using interval Type-2 fuzzy logic for uncertain nonlinear systems , 2011 .

[31]  Yang Liu,et al.  T-S fuzzy model-based impulsive control for chaotic systems and its application , 2011, Math. Comput. Simul..

[32]  Taher Niknam,et al.  Fuzzy sliding mode control scheme for a class of non-linear uncertain chaotic systems , 2013 .

[33]  Jerry M. Mendel,et al.  Type-2 fuzzy sets made simple , 2002, IEEE Trans. Fuzzy Syst..

[34]  I. Kar,et al.  Contraction theory-based recursive design of stabilising controller for a class of non-linear systems , 2010 .

[35]  Tao Yang,et al.  In: Impulsive control theory , 2001 .

[36]  Tsung-Chih Lin,et al.  Direct adaptive interval type-2 fuzzy control of multivariable nonlinear systems , 2009, Eng. Appl. Artif. Intell..

[37]  Francisco Chiclana,et al.  Type‐Reduction of General Type‐2 Fuzzy Sets: The Type‐1 OWA Approach , 2013, Int. J. Intell. Syst..

[38]  Shouming Zhong,et al.  Design of sliding mode controller for a class of fractional-order chaotic systems , 2012 .

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

[40]  T. Guerra,et al.  Motion control of planar parallel robot using the fuzzy descriptor system approach. , 2012, ISA transactions.

[41]  Prem Kalra,et al.  Chaotic oscillations in power system under disturbances , 1993 .

[42]  Zoubir Ahmed-Foitih,et al.  A self-tuning fuzzy inference sliding mode control scheme for a class of nonlinear systems , 2012 .

[43]  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).

[44]  V. Ajjarapu,et al.  Bifurcation theory and its application to nonlinear dynamical phenomena in an electrical power system , 1991, [Proceedings] Conference Papers 1991 Power Industry Computer Application Conference.

[45]  Shaocheng Tong,et al.  Direct adaptive fuzzy output tracking control of nonlinear systems , 2002, Fuzzy Sets Syst..

[46]  Lotfi A. Zadeh,et al.  The Concepts of a Linguistic Variable and its Application to Approximate Reasoning , 1975 .

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

[48]  Felix F. Wu,et al.  Chaos in a simple power system , 1993 .

[49]  N. Vafamand,et al.  Non-quadratic exponential stabilisation of non-linear hyperbolic partial differential equation systems , 2014 .

[50]  Hak-Keung Lam,et al.  Chaotic synchronisation using output/full state-feedback polynomial controller , 2010 .

[51]  赵辉,et al.  Controlling chaos in power system based on finite-time stability theory , 2011 .

[52]  Robert Ivor John,et al.  A Fast Geometric Method for Defuzzification of Type-2 Fuzzy Sets , 2008, IEEE Transactions on Fuzzy Systems.

[53]  Woei Wan Tan,et al.  A simplified type-2 fuzzy logic controller for real-time control. , 2006, ISA transactions.

[54]  Behrooz Safarinejadian,et al.  Parallel distributed compensator design of tank level control based on fuzzy Takagi-Sugeno model , 2014, Appl. Soft Comput..

[55]  Xiaohong Zhang,et al.  Unified impulsive fuzzy-model-based controllers for chaotic systems with parameter uncertainties via LMI , 2010 .

[56]  S. C. Srivastava,et al.  Elimination of dynamic bifurcation and chaos in power systems using FACTS devices , 1998 .

[57]  Zhidong Teng,et al.  General impulsive control of chaotic systems based on a TS fuzzy model , 2011, Fuzzy Sets Syst..

[58]  Tzuu-Hseng S. Li,et al.  Controlling a Time-Varying Unified Chaotic System via Interval Type 2 Fuzzy Sliding-Mode Technique , 2009 .

[59]  Jerry M. Mendel,et al.  Interval type-2 fuzzy logic systems: theory and design , 2000, IEEE Trans. Fuzzy Syst..