Robust nonlinear fractional order fuzzy PD plus fuzzy I controller applied to robotic manipulator

The aim of this article is to utilize fractional calculus for performance enhancement of nonlinear fuzzy PD + I controller. A fractional order fuzzy PD + I controller (FOFPD + I) is designed and implemented to control complex, uncertain and nonlinear robotic manipulator. FOFPD + I controller is derived from fractional order PD and fractional order I controller. The proposed control strategy has an adaptive capability due to its nonlinear gains and preserves the linear structure of fractional order PD + I controller. Further, integer-order fuzzy PD + I controller (FPD + I) and conventional PID controllers are also designed for comparative analysis. The optimum parameter values of FOFPD + I, FPD + I and PID controllers are obtained using non-dominated sorting genetic algorithm-II. The effectiveness of proposed controller is examined for reference tracking and disturbance rejection problems of robotic manipulator. The designed controllers are also validated experimentally on DC servomotor. Simulation and experimental results prove the superiority of FOFPD + I controller as compared to its integer-order equivalent and conventional PID controllers for control of robotic manipulator.

[1]  Guanrong Chen,et al.  A modified fuzzy PI controller for a flexible-joint robot arm with uncertainties , 2001, Fuzzy Sets Syst..

[2]  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.

[3]  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..

[4]  Asha Rani,et al.  Multi Objective PSO Tuned Fractional Order PID Control of Robotic Manipulator , 2016 .

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

[6]  Saptarshi Das,et al.  Chaos suppression in a fractional order financial system using intelligent regrouping PSO based fractional fuzzy control policy in the presence of fractional Gaussian noise , 2012 .

[7]  Robert W. Russell,et al.  Massive Swarm Migrations of Dragonflies (Odonata) in Eastern North America , 1998 .

[8]  H. T,et al.  The future of PID control , 2001 .

[9]  Lotfi A. Zadeh,et al.  Fuzzy Sets , 1996, Inf. Control..

[10]  I. S. Jesus,et al.  Genetic optimization of fuzzy fractional PD+I controllers. , 2015, ISA transactions.

[11]  I. Podlubny.  Fractional differential equations : an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications , 1999 .

[12]  Vineet Kumar,et al.  A fractional order fuzzy PID controller for binary distillation column control , 2015, Expert Syst. Appl..

[13]  YangQuan Chen,et al.  Tuning and auto-tuning of fractional order controllers for industry applications , 2008 .

[14]  Guanrong Chen,et al.  Fuzzy PID control of a flexible-joint robot arm with uncertainties from time-varying loads , 1997, IEEE Trans. Control. Syst. Technol..

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

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

[17]  Saptarshi Das,et al.  Fractional Order Fuzzy Control of Hybrid Power System with Renewable Generation Using Chaotic PSO , 2016, ISA transactions.

[18]  Francis L. Merat,et al.  Introduction to robotics: Mechanics and control , 1987, IEEE J. Robotics Autom..

[19]  Zwe-Lee Gaing.  A particle swarm optimization approach for optimum design of PID controller in AVR system , 2004, IEEE Transactions on Energy Conversion.

[20]  Saptarshi Das,et al.  Frequency Domain Design of Fractional Order PID Controller for AVR System Using Chaotic Multi-objective Optimization , 2013, ArXiv.

[21]  Asha Rani,et al.  An expert 2DOF fractional order fuzzy PID controller for nonlinear systems , 2019, Neural Computing and Applications.

[22]  Guanrong Chen,et al.  New design and stability analysis of fuzzy proportional-derivative control systems , 1994, IEEE Trans. Fuzzy Syst..

[23]  David H. Wolpert,et al.  No free lunch theorems for optimization , 1997, IEEE Trans. Evol. Comput..

[24]  Carlos Canudas de Wit,et al.  Adaptive eccentricity compensation , 2000, IEEE Trans. Control. Syst. Technol..

[25]  Guanrong Chen,et al.  Design and analysis of a fuzzy proportional-integral-derivative controller , 1996, Fuzzy Sets Syst..

[26]  Indrajit N. Trivedi,et al.  Optimization of problems with multiple objectives using the multi-verse optimization algorithm , 2017, Knowl. Based Syst..

[27]  A. Peterson,et al.  Discrete Fractional Calculus , 2016 .

[28]  S. Bennett,et al.  Development of the PID controller , 1993, IEEE Control Systems.

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

[30]  Vijander Singh,et al.  Robust adaptive fuzzy controller applied to double inverted pendulum , 2017, J. Intell. Fuzzy Syst..

[31]  Vijander Singh,et al.  Robust self-tuning fractional order PID controller dedicated to non-linear dynamic system , 2018, J. Intell. Fuzzy Syst..

[32]  Karl Johan Åström,et al.  PID Controllers: Theory, Design, and Tuning , 1995 .

[33]  Kalyanmoy Deb,et al.  A fast and elitist multiobjective genetic algorithm: NSGA-II , 2002, IEEE Trans. Evol. Comput..

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

[35]  Seyed Mohammad Mirjalili,et al.  Multi-Verse Optimizer: a nature-inspired algorithm for global optimization , 2015, Neural Computing and Applications.

[36]  Vijander Singh,et al.  Two degree of freedom PID based inferential control of continuous bioreactor for ethanol production. , 2017, ISA transactions.

[37]  Ahmet Dumlu,et al.  Trajectory Tracking Control for a 3-DOF Parallel Manipulator Using Fractional-Order $\hbox{PI}^{\lambda}\hbox{D}^{\mu}$ Control , 2014, IEEE Transactions on Industrial Electronics.

[38]  David Moskowitz,et al.  Simple rules guide dragonfly migration , 2006, Biology Letters.

[39]  Vijander Singh,et al.  A novel nature-inspired algorithm for optimization: Squirrel search algorithm , 2019, Swarm Evol. Comput..

[40]  Chang Chieh Hang,et al.  Towards intelligent PID control , 1989, Autom..

[41]  C. Lubich.  Discretized fractional calculus , 1986 .

[42]  Pradeep Jangir,et al.  Multi-objective ant lion optimizer: a multi-objective optimization algorithm for solving engineering problems , 2016, Applied Intelligence.

[43]  Omer Saleem,et al.  EKF-based self-regulation of an adaptive nonlinear PI speed controller for a DC motor , 2017 .

[44]  Choo Min Lim,et al.  Application of fuzzy logic control to a manipulator , 1991, IEEE Trans. Robotics Autom..

[45]  Vineet Kumar,et al.  Nonlinear adaptive fractional order fuzzy PID control of a 2-link planar rigid manipulator with payload , 2017, J. Frankl. Inst..

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

[47]  Robert LIN,et al.  NOTE ON FUZZY SETS , 2014 .

[48]  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..

[49]  Seyedali Mirjalili,et al.  Dragonfly algorithm: a new meta-heuristic optimization technique for solving single-objective, discrete, and multi-objective problems , 2015, Neural Computing and Applications.

[50]  Byung Kook Yoo,et al.  Adaptive control of robot manipulator using fuzzy compensator , 2000, IEEE Trans. Fuzzy Syst..

[51]  William Siler,et al.  Fuzzy control theory: A nonlinear case , 1990, Autom..