Performance analysis of fractional order fuzzy PID controllers applied to a robotic manipulator

A two-link robotic manipulator is a Multi-Input Multi-Output (MIMO), highly nonlinear and coupled system. Therefore, designing an efficient controller for this system is a challenging task for the control engineers. In this paper, the Fractional Order Fuzzy Proportional-Integral-Derivative (FOFPID) controller for a two-link planar rigid robotic manipulator for trajectory tracking problem is investigated. Robustness testing of FOFPID controller for model uncertainties, disturbance rejection and noise suppression is also investigated. To study the effectiveness of FOFPID controller, its performance is compared with other three controllers namely Fuzzy PID (FPID), Fractional Order PID (FOPID) and conventional PID. For tuning of parameters of all the controllers, Cuckoo Search Algorithm (CSA) optimization technique was used. Two performance indices namely Integral of Absolute Error (IAE) and Integral of Absolute Change in Controller Output (IACCO) having equal weightage for both the links are considered for minimization. Numerical simulation results clearly indicate the superiority of FOFPID controller over the other controllers for trajectory tracking, model uncertainties, disturbance rejection and noise suppression.

[1]  Víctor Santibáñez,et al.  Fuzzy Self-Tuning PID Semiglobal Regulator for Robot Manipulators , 2012, IEEE Transactions on Industrial Electronics.

[2]  Zafer Bingul,et al.  Fractional PID controllers tuned by evolutionary algorithms for robot trajectory control , 2012, Turkish Journal of Electrical Engineering and Computer Sciences.

[3]  Ali R. Yildiz,et al.  Cuckoo search algorithm for the selection of optimal machining parameters in milling operations , 2012, The International Journal of Advanced Manufacturing Technology.

[4]  S. C. Neoh,et al.  Modified cuckoo search algorithm in weighted sum optimization for linear antenna array synthesis , 2012, 2012 IEEE Symposium on Wireless Technology and Applications (ISWTA).

[5]  Zwe-Lee Gaing,et al.  A particle swarm optimization approach for optimum design of PID controller in AVR system , 2004 .

[6]  Xin-She Yang,et al.  Cuckoo Search via Lévy flights , 2009, 2009 World Congress on Nature & Biologically Inspired Computing (NaBIC).

[7]  Hossein Nezamabadi-pour,et al.  A PSO-Based Optimum Design of PID Controller for a Linear Brushless DC Motor , 2007 .

[8]  S. Galvani,et al.  A particle swarm optimization approach for optimum design of PID controller in linear elevator , 2010, 2010 Conference Proceedings IPEC.

[9]  Aytekin Bagis,et al.  Tabu search algorithm based PID controller tuning for desired system specifications , 2011, J. Frankl. Inst..

[10]  Toshio Yoshimura,et al.  Fuzzy control of a manipulator using the concept of sliding mode , 1996, Int. J. Syst. Sci..

[11]  Nasser Sadati,et al.  Design of a fractional order PID controller for an AVR using particle swarm optimization , 2009 .

[12]  M. Y. Hassan,et al.  Allocation and sizing of DG using Cuckoo Search algorithm , 2012, 2012 IEEE International Conference on Power and Energy (PECon).

[13]  Han-Xiong Li,et al.  Conventional fuzzy control and its enhancement , 1996, IEEE Trans. Syst. Man Cybern. Part B.

[14]  Aytekin Bagis,et al.  Determination of the PID Controller Parameters by Modified Genetic Algorithm for Improved Performance , 2007, J. Inf. Sci. Eng..

[15]  Guanrong Chen,et al.  Mathematical modeling and fuzzy control of a flexible-link robot arm , 1998 .

[16]  Haluk Gozde,et al.  Comparative performance analysis of artificial bee colony algorithm for automatic voltage regulator (AVR) system , 2011, J. Frankl. Inst..

[17]  Arpita Sinha,et al.  Analytical structure and stability analysis of a fuzzy PID controller , 2008, Appl. Soft Comput..

[18]  Alain Oustaloup,et al.  Frequency-band complex noninteger differentiator: characterization and synthesis , 2000 .

[19]  Dervis Karaboga,et al.  A comparative study of Artificial Bee Colony algorithm , 2009, Appl. Math. Comput..

[20]  A. Vasan,et al.  Comparative analysis of Simulated Annealing, Simulated Quenching and Genetic Algorithms for optimal reservoir operation , 2009, Appl. Soft Comput..

[21]  Lixiang Li,et al.  Optimum design of fractional order PIλDμ controller for AVR system using chaotic ant swarm , 2012, Expert Syst. Appl..

[22]  Wei Li,et al.  Design of a hybrid fuzzy logic proportional plus conventional integral-derivative controller , 1998, IEEE Trans. Fuzzy Syst..

[23]  P. Wang,et al.  Optimal Design of PID Process Controllers based on Genetic Algorithms , 1993 .

[24]  Leonid Reznik,et al.  PID plus fuzzy controller structures as a design base for industrial applications , 2000 .

[25]  Meng Joo Er,et al.  Hybrid fuzzy proportional-integral plus conventional derivative control of linear and nonlinear systems , 2001, IEEE Trans. Ind. Electron..

[26]  Xin-She Yang,et al.  Bat algorithm: a novel approach for global engineering optimization , 2012, 1211.6663.

[27]  Saptarshi Das,et al.  Chaotic multi-objective optimization based design of fractional order PIλDμ controller in AVR system , 2012, ArXiv.

[28]  Kai-Yuan Cai,et al.  An improved robust fuzzy-PID controller with optimal fuzzy reasoning , 2005, IEEE Trans. Syst. Man Cybern. Part B.

[29]  Ivo Petraÿs,et al.  FRACTIONAL - ORDER FEEDBACK CONTROL OF A DC MOTOR , 2009 .

[30]  Guanrong Chen,et al.  A robust fuzzy PI controller for a flexible-joint robot arm with uncertainties , 1994, Proceedings of 1994 IEEE 3rd International Fuzzy Systems Conference.

[31]  Chuen-Chien Lee.  FUZZY LOGIC CONTROL SYSTEMS: FUZZY LOGIC CONTROLLER - PART I , 1990 .

[32]  Shantanu Das,et al.  A novel fractional order fuzzy PID controller and its optimal time domain tuning based on integral performance indices , 2012, Eng. Appl. Artif. Intell..

[33]  Deacha Puangdownreong,et al.  Obtaining an Optimum PID Controller Via Adaptive Tabu Search , 2007, ICANNGA.

[34]  Shantanu Das,et al.  Performance Comparison of Optimal Fractional Order Hybrid Fuzzy PID Controllers for Handling Oscillatory Fractional Order Processes with Dead Time , 2013, ISA transactions.

[35]  Leandro dos Santos Coelho,et al.  Tuning of PID controller based on a multiobjective genetic algorithm applied to a robotic manipulator , 2012, Expert Syst. Appl..

[36]  Jianqiang Yi,et al.  A computed torque controller for uncertain robotic manipulator systems: Fuzzy approach , 2005, Fuzzy Sets Syst..

[37]  Zhong Guo,et al.  An Improved Ant Colony Algorithm for PID Parameters Optimization , 2009, 2009 Second International Conference on Intelligent Computation Technology and Automation.

[38]  Amir Hossein Gandomi,et al.  Cuckoo search algorithm: a metaheuristic approach to solve structural optimization problems , 2011, Engineering with Computers.

[39]  Reza Ghaderi,et al.  Fuzzy fractional order sliding mode controller for nonlinear systems , 2010 .

[40]  Radovan R. Bulatović,et al.  Cuckoo Search algorithm: A metaheuristic approach to solving the problem of optimum synthesis of a six-bar double dwell linkage , 2013 .

[41]  Daobo Wang,et al.  Novel approach to nonlinear PID parameter optimization using ant colony optimization algorithm , 2006 .

[42]  O. Ibidapo-Obe,et al.  On Development of Fuzzy Controller: The Case of Gaussian and Triangular Membership Functions , 2011 .

[43]  Jih-Gau Juang,et al.  PID Control Using Presearched Genetic Algorithms for a MIMO System , 2008, IEEE Trans. Syst. Man Cybern. Part C.

[44]  Jay A. Farrell,et al.  Tracking control of a manipulator under uncertainty by FUZZY P+ID controller , 2001, Fuzzy Sets Syst..

[45]  Ajith Abraham,et al.  Design of fractional-order PIlambdaDµ controllers with an improved differential evolution , 2009, Eng. Appl. Artif. Intell..

[46]  Jin-Jye Lin,et al.  A fuzzy PID controller being like parameter varying PID , 1999, FUZZ-IEEE'99. 1999 IEEE International Fuzzy Systems. Conference Proceedings (Cat. No.99CH36315).

[47]  Ramin Rajabioun,et al.  Cuckoo Optimization Algorithm , 2011, Appl. Soft Comput..

[48]  Engin Yesil,et al.  Self-tuning of PID-type fuzzy logic controller coefficients via relative rate observer , 2003 .

[49]  David Harel,et al.  Drawing graphs nicely using simulated annealing , 1996, TOGS.

[50]  Vineet Kumar,et al.  Real-Time Performance Evaluation of a Fuzzy PI + Fuzzy PD Controller for Liquid-Level Process , 2008 .