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http://dx.doi.org/10.5370/JEET.2018.13.2.969

Fuzzy PID Control by Grouping of Membership Functions of Fuzzy Antecedent Variables with Neutrosophic Set Approach and 3-D Position Tracking Control of a Robot Manipulator  

Can, Mehmet Serhat (Dept. of Mechatronic, Gaziosmanpasa University, Zile Vocational School)
Ozguven, Omerul Faruk (Dept. of Biomedical Engineering, Inonu University)
Publication Information
Journal of Electrical Engineering and Technology / v.13, no.2, 2018 , pp. 969-980 More about this Journal
Abstract
This paper aims to design of the neutrosophic fuzzy-PID controller and it has been compared with the conventional fuzzy-PID controller for position tracking control in terms of robustness. In the neutrosophic fuzzy-PID controller, error (e) and change of error (ce) were assessed separately on two fuzzy inference systems (FISs). In this study, the designed method is different from the conventional fuzzy logic controller design, membership degrees of antecedent variables were determined by using the T(true), I(indeterminacy), and F(false) membership functions. These membership functions are grouped on the universe of discourse with the neutrosophic set approach. These methods were tested on three-dimensional (3-D) position-tracking control application of a spherical robot manipulator in the MATLAB Simulink. In all tests, reference trajectory was defined for movements of all axes of the robot manipulator. According to the results of the study, when the moment of inertia of the rotor is changed, less overshoot ratio and less oscillation are obtained in the neutrosophic fuzzy-PID controller. Thus, our suggested method is seen to be more robust than the fuzzy-PID controllers.
Keywords
Neutrosopy; Robust; Fuzzy logic controller; Grouping membership functions; Fuzzy-PID controller; 3-D position tracking control; Spherical robot manipulator;
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1 F. Smarandache, "Neutrosophy a new branch of philosophy," Multiple Valued Logic - Special Issue: Neutrosophy and Neutrosophic Logic, vol. 8, no. 3, pp. 297-384, Jan. 2002.
2 F. Smarandache, "Definition of neutrosophic logic, a generalization of the intuitionistic fuzzy logic," Proceeding of the Third Conference of the European Society for Fuzzy Logic and Technology, pp. 141-146, Sep. 2003.
3 E. Jahanshahi, et.al., "Industrial test setup for autotuning of PID controllers in large-scale processes: Applied to Tennessee Eastman process," IFAC-Papers On Line, vol. 48, no. 8, pp. 469-476, Jun. 2015.
4 P. Ponce, et.al., "Experimental study for FPGA PID position controller in CNC micro-machines," IFACPapers On Line, vol. 48, no. 3, pp. 2203-2207, Dec. 2015.
5 F. Reyes and A. Rosado, "Polynomial family of PDType controllers for robot manipulators," Control Engineering Practice, vol. 13, no. 4, pp. 441-450, Apr. 2005.   DOI
6 S. I. Sondhi and Y. V. Hote, "Fractional order PID controller for load frequency control," Energy Conversion and Management, vol. 85, pp. 343-353, Sep. 2014.   DOI
7 S. Jingzhuo, et.al., "Novel intelligent PID control of traveling wave ultrasonic motor," ISA Transactions, vol. 53, no. 5, pp. 1670-1679, Sep. 2014.   DOI
8 C. Mitsantisuk, et.al., "Design for sensorless force control of flexible robot by using resonance ratio control based on coefficient diagram method," Automatika, vol. 54, no. 1, special issue, selected papers from AMC2012 Conference, Mar. 2013.
9 W. L. Gau, and D. J. Buehrer, "Vague sets," IEEE Transactions on Systems, Man and Cybernetics, vol. 23, pp. 610-614, March/April 1993.   DOI
10 O. Karasakal, et.al., "Implementation of a new selftuning fuzzy PID controller on PLC," Turkish Journal of Electrical Engineering & Computer Sciences, vol. 13, no. 2, pp. 277-286, Oct. 2005.
11 K. Premkumar and B. V. Manikandan, "Fuzzy PID supervised online ANFIS based speed controller for brushless DC motor," Neurocomputing, vol. 157, pp. 76-90, 1 Jun 2015.   DOI
12 J. Lin, et.al., "Enhanced fuzzy sliding mode controller for active suspension systems," Mechatronics, vol. 19, no. 7, pp. 1178-1190, Oct. 2009.   DOI
13 C. Elmas, O. Deperlioglu and H. H. Sayan, "Adaptive fuzzy logic controller for DC-DC converters," Expert Systems with Applications, vol. 36, no. 2, Part 1, pp. 1540-1548, Mar. 2009.   DOI
14 M. El-Bardini and A. M. El-Nagar, "Interval Type-2 fuzzy PID controller for uncertain nonlinear inverted pendulum system," ISA Transactions, vol. 53, no. 3, pp. 732-743, May 2014.   DOI
15 M. Nie, and W. W. Tan, "Stable adaptive fuzzy PD plus PI controller for nonlinear uncertain systems," Fuzzy Sets and Systems, vol. 179, no. 1, pp. 1-19, Sep. 2011.   DOI
16 H. N. Wu, "Robust $H_2$ fuzzy output feedback control for discrete-time nonlinear systems with parametric uncertainties," International Journal of Approximate Reasoning, vol. 46, no. 1, pp. 151-165, Sep. 2007.   DOI
17 J. Godjevac, "Comparison between PID and fuzzy control, Internal Report R93.36I," Ecole Polytechnique Federale de Lausanne Departement d'Informatique Laboratoire de Microinformatique, 1993.
18 O. A. M. Ali, et.al., "Comparison between the effects of different types of membership functions on fuzzy logic controller performance," International Journal of Emerging Engineering Research and Technology, vol. 3, no. 3, pp. 76-83, Mar. 2015.
19 J. Zhao and B. K. Bose, "Evaluation of membership functions for fuzzy logic controlled induction motor drive," IEEE 2002 28th Annual Conference of the Industrial Electronics Society (IECON 02), vol. 1, pp. 229-234, 5-8 Nov. 2002.
20 K. S. Tang, et.al., "An optimal fuzzy PID controller," IEEE Transactions on Industrial Electronics, vol. 48, no. 4, pp. 757-765, Aug. 2001.   DOI
21 J. Carvajal, G. Chen and H. Ogmen, "Fuzzy PID controller: Design, performance evaluation, and stability analysis," Information Sciences, volume 123, issues 3-4, pp. 249-270, Apr. 2000.   DOI
22 A. P. Aguiar, et.al., "Position tracking for a nonlinear under actuated hovercraft: Controller design and experimental results," 42nd IEEE International Conference on decision and control, vol. 4, pp. 3858-3863, 9-12 Dec. 2003.
23 S. Yannier and A. Sabanovic, "Analog sliding mode controller for position tracking of piezoelectric actuators," Proceedings of the 18 th Mediterranean Conference on Control and Automation, Jul. 2007.
24 T. Dam and P. R. Ouyang, "Contour tracking control in position domain for CNC machines," Proceeding of the IEEE International Conference on Information and Automation Shenzhen, China, vol. 1, pp. 14-19, 6-8 Jun. 2011.
25 W. E. Dixon et.al., "Tracking control of robot manipulators with bounded torque inputs," Robotica, vol. 17, pp. 121-129, Mar. 1999.   DOI
26 M. P. S. Dos Santos and J. A. F. Ferreira, "Novel intelligent real-time position tracking system using FPGA and fuzzy logic," ISA Transactions, vol. 53, no. 2, pp. 402-414, Mar. 2014.   DOI
27 S. Aggarwal, et.al., "Neutrosophic modeling and control," International Conferans on Computer & Communication Technology (ICCCT), pp. 718-723, Sep. 2010.
28 J. G. Monicka, and N. O. G. Sekhar, "Performance evaluation of membership functions on fuzzy logic controlled AC voltage controller for speed control of induction motor drive," International Journal of Computer Applications, vol. 13, no. 5, pp. 8-12, Jan. 2011.   DOI
29 Q. Xu, et.al., "Fuzzy PID based trajectory tracking control of mobile robot and its simulation in Simulink," International Journal of Control and Automation, vol. 7, no. 8, pp. 233-244, Aug. 2014.   DOI
30 H. Wang, et.al., "Single valued neutrosophic sets," Multispace and Multistructure (4), pp. 410-413, 2010.
31 S. Miao, et.al., "Comparison of fuzzy membership functions for value of information determination," Proceedings of the 25th Modern Artificial Intelli gence and Cognitive Science Conference, pp. 53-60, 2014.
32 H. Ahmed, et.al., "Controlling of D.C. Motor using fuzzy logic controller," Conference on Advances in Communication and Control Systems (CAC2S2013), 2013.
33 A. Q. Ansari, et.al., "Extension to fuzzy logic representation: Moving towards neutrosophic logic -A new laboratory rat," IEEE International Conference on Fuzzy Systems, 7-10 Jul. 2013.
34 F. Smarandache and L. Vladareanu, "Applications of neutrosophic logic to robotics: An Introduction," IEEE International Conference on Granular Computing (GrC), 8-10 Nov. 2011.
35 M. Arora, U. S. Pandey, "Generalization of functional dependencies in total of functional dependencies in total neutrosophic relation," International Journal of Computer Science, vol. 9, no. 3, no. 2, pp. 294-302, May 2012.
36 E. H. Mamdani, "Application of fuzzy logic algorithms for control of simple dynamic plant," Proceedings of the Institution of Electrical Engineers, vol. 121, no. 12, pp. 1585-1588, Dec. 1974.   DOI
37 M. W. Spong, et.al., "Robot modeling and control," First Edition, John Wiley& Sons, Inc., 2005.
38 J. A. Goguen, "L-Fuzzy sets," Journal of Mathematical Analysis and Applications, vol. 18, no. 1, pp. 145-174, Apr. 1967.   DOI
39 Z. Yunusa, et.al., "Effects of the number of rules on the quality of fuzzy logic control of induction motor," International Journal of Applied Electronics in Physics & Robotics, vol. 1, pp. 14-17, no. 1, Jul. 2013.
40 M. S. B. M. Aras, et.al., "Study of the effect in the output membership function when tuning a fuzzy logic controller," IEEE International Conference on Control System, Computing and Engineering, pp. 1-6, 25-27, Nov. 2011.
41 Lotfi Zadeh, "The concept of a linguistic variable and its application to approximate reasoning," Journal of Information Sciences, vol. 8, no. 3, pp. 199-249, Jan. 1975.   DOI
42 I. Grattan-Guiness, "Fuzzy membership mapped onto interval and many-valued quantities," Mathematical Logic Quarterly, vol. 22, no. 1, pp. 149-160, 1975.
43 K. U. Jahn, "Intervall-wertigemengen," Mathematische Nachrichten, vol. 68, no. 1, pp. 115-132, 1975.   DOI
44 N. Belnap, "A useful four-valued logic," Modern Uses of Multiple-Valued Logics, vol. 2, pp. 5-37, 1977
45 K. Atanassov, "Intuitionistic fuzzy sets," Fuzzy Sets & Systems, vol. 20, pp. 87-96, Aug. 1986.   DOI
46 K. Atanassov and G. Gargov, "Interval-valued intuitionistic fuzzy sets," Fuzzy Sets and Systems, vol. 31, pp. 343-349, 20 Jul. 1989.   DOI
47 Konstantinos A. Chrysafis, et.al., "On the fuzzy difference equations of finance," Fuzzy Sets and Systems, vol. 159, no. 24, pp. 3259-3270, 16 Dec. 2008.   DOI
48 Lotfi Zadeh, "Fuzzy sets," Information & Control, vol. 8, pp. 338-353, Jun. 1965.   DOI
49 Isabelle Bloch, "Fuzzy sets for image processing and understanding,"Fuzzy Sets and Systems, vol. 281, pp. 280-291, 15 Dec. 2015.   DOI
50 Jerry Mendel, "Uncertainty, fuzzy logic, and signal processing," Signal Processing, vol. 80, no. 6, pp. 913-933, Jun. 2000.   DOI
51 Mansoir Baig M., et.al., "Fuzzy logic based anaesthesia monitoring systems for the detection of absolute hypovolaemia," Computers in Biology and Medicine, vol. 43, no. 6, pp. 683-692, 1 Jul. 2013.   DOI
52 J. M. Sánchez-Lozano, et.al., "Evaluating military training aircrafts through the combination of multicriteria decision making processes with fuzzy logic. A case study in the Spanish Air Force Academy," Aerospace Science and Technology, vol. 42, pp. 58-65, April-May 2015.   DOI
53 M. S. Can and O. F. Ozguven, "PID tuning with neutrosophic similarity measure," International Journal of Fuzzy Systems, vol. 19, no. 2, pp. 489-503, Apr. 2017.   DOI
54 L. Vladareanu, et.al., "Robot control intelligent interfaces using the DSmT and the neutrosophic logic," International Journal of Advanced Mechatronic Systems, vol. 6, no. 2-3, pp. 128-135, Jan. 2015.   DOI
55 L. Vladareanu, et.al., "Improvement of the walking robot dynamic stability using the DSmT and the neutrosophic logic," Advanced Mechatronic Systems (ICAMechS), 10-12 Aug. 2014
56 A. Gal, et.al., "Neutrosophic Logic Approaches Applied to "RABOT" Real Time Control," Neutrosophic theory and its applications, collected papers, vol. 1, pp. 55-60, (2014).
57 M. S. Can and O. F. Ozguven, "Design of the neutrosophic membership valued fuzzy-PID controller and rotation angle control of a permanent magnet direct current motor," Journal of New Results in Science, vol. 5, no. 12, pp. 126-138, Oct. 2016.
58 H. A. Malki, et.al., "Fuzzy PID control of a flexible joint robot arm with uncertainties from time-varying loads," IEEE Transactions On Control Systems Technology, vol. 5, no. 3, pp. 371 - 378, May 1997.   DOI
59 I. Rodríguez-Fdez, et.al., "Learning fuzzy controllers in mobile robotics with embedded preprocessing," Applied Soft Computing, vol. 26, pp. 123-142, Jan 2015.   DOI
60 R. Thompson, and A. Dexter, "A fuzzy decisionmaking approach to temperature control in airconditioning systems," Control Engineering Practice, vol. 13, no. 6, pp. 689-698, Jun 2005.   DOI
61 C. W. Tao and J. S. Taur, "An approach for the robustness comparison between piecewise linear PID-like fuzzy and classical PID controllers," Soft Computing, vol. 9, pp. 430-438, Jun. 2005.   DOI
62 S. Saha, et.al., "A Comparison between the performance of fuzzy logic-based PD controller and general PD controller," International Journal of Advance Innovations, Thoughts & Ideas, vol. 1, no. 2, ISSN: 2277-1891, March/April 2012.
63 B. Akbiyik, et.al., "Evalution of the performance of various fuzzy PID controller structures on Benchmark systems," 4th International Conf. on Electrical and Electronics Engineering (ELECO), Jan. 2005.