Skip to main content
Top
Published in: Neural Computing and Applications 7/2020

30-03-2019 | Original Article

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

Authors: Himanshu Chhabra, Vijay Mohan, Asha Rani, Vijander Singh

Published in: Neural Computing and Applications | Issue 7/2020

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

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.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Appendix
Available only for authorised users
Literature
1.
go back to reference Åström KJ, Hang CC, Persson P, Ho WK (1992) Towards intelligent PID control. Automatica 28:1–9CrossRef Åström KJ, Hang CC, Persson P, Ho WK (1992) Towards intelligent PID control. Automatica 28:1–9CrossRef
2.
go back to reference Bennett S (1993) Development of the PID controller. IEEE Control Syst 13:58–62 Bennett S (1993) Development of the PID controller. IEEE Control Syst 13:58–62
3.
go back to reference Åström KJ, Hägglund T (2001) The future of PID control. Control Eng Pract 9:1163–1175CrossRef Åström KJ, Hägglund T (2001) The future of PID control. Control Eng Pract 9:1163–1175CrossRef
4.
go back to reference Åström KJ, Hägglund T (2006) Advanced PID control. ISA—the instrumentation, systems, and automation society research Triangle park Åström KJ, Hägglund T (2006) Advanced PID control. ISA—the instrumentation, systems, and automation society research Triangle park
5.
go back to reference Mohan V, Chhabra H, Rani A, Singh V (2018) Robust self-tuning fractional order PID controller dedicated to non-linear dynamic system. J Intell Fuzzy Syst 34:1467–1478CrossRef Mohan V, Chhabra H, Rani A, Singh V (2018) Robust self-tuning fractional order PID controller dedicated to non-linear dynamic system. J Intell Fuzzy Syst 34:1467–1478CrossRef
7.
go back to reference Mohan V, Rani A, Singh V (2017) Robust adaptive fuzzy controller applied to double inverted pendulum. J Intell Fuzzy Syst 32:3669–3687CrossRef Mohan V, Rani A, Singh V (2017) Robust adaptive fuzzy controller applied to double inverted pendulum. J Intell Fuzzy Syst 32:3669–3687CrossRef
8.
go back to reference Lim CM, Hiyama T (1991) Application of fuzzy logic control to a manipulator. IEEE Trans Robot Autom 7:688–691CrossRef Lim CM, Hiyama T (1991) Application of fuzzy logic control to a manipulator. IEEE Trans Robot Autom 7:688–691CrossRef
9.
go back to reference Yoo BK, Ham WC (2000) Adaptive control of robot manipulator using fuzzy compensator. IEEE Trans Fuzzy Syst 8:186–199CrossRef Yoo BK, Ham WC (2000) Adaptive control of robot manipulator using fuzzy compensator. IEEE Trans Fuzzy Syst 8:186–199CrossRef
10.
go back to reference Sooraksa P, Chen G (1998) Mathematical modeling and fuzzy control of a flexible-link robot arm. Math Comput Model 27:73–93MATHCrossRef Sooraksa P, Chen G (1998) Mathematical modeling and fuzzy control of a flexible-link robot arm. Math Comput Model 27:73–93MATHCrossRef
11.
go back to reference Li W, Chang X, Wahl FM, Farrell J (2001) Tracking control of a manipulator under uncertainty by FUZZY P + ID controller. Fuzzy Sets Syst 122:125–137MathSciNetMATHCrossRef Li W, Chang X, Wahl FM, Farrell J (2001) Tracking control of a manipulator under uncertainty by FUZZY P + ID controller. Fuzzy Sets Syst 122:125–137MathSciNetMATHCrossRef
12.
go back to reference Tang W, Chen G, Lu R (2001) A modified fuzzy PI controller for a flexible-joint robot arm with uncertainties. Fuzzy Sets Syst 118:109–119MathSciNetCrossRef Tang W, Chen G, Lu R (2001) A modified fuzzy PI controller for a flexible-joint robot arm with uncertainties. Fuzzy Sets Syst 118:109–119MathSciNetCrossRef
13.
go back to reference Malki HA, Li H, Chen G (1994) New design and stability analysis of fuzzy proportional-derivative control systems. IEEE Trans Fuzzy Syst 2:245–254CrossRef Malki HA, Li H, Chen G (1994) New design and stability analysis of fuzzy proportional-derivative control systems. IEEE Trans Fuzzy Syst 2:245–254CrossRef
14.
go back to reference Malki HA, Misir D, Feigenspan D, Chen G (1997) Fuzzy PID control of a flexible-joint robot arm with uncertainties from time-varying loads. IEEE Trans Control Syst Technol 5:371–378CrossRef Malki HA, Misir D, Feigenspan D, Chen G (1997) Fuzzy PID control of a flexible-joint robot arm with uncertainties from time-varying loads. IEEE Trans Control Syst Technol 5:371–378CrossRef
15.
go back to reference Misir D, Malki HA, Chen G (1996) Design and analysis of a fuzzy proportional-integral-derivative controller. Fuzzy Sets Syst 79:297–314MathSciNetMATHCrossRef Misir D, Malki HA, Chen G (1996) Design and analysis of a fuzzy proportional-integral-derivative controller. Fuzzy Sets Syst 79:297–314MathSciNetMATHCrossRef
16.
go back to reference Dumlu A, Erenturk K (2014) Trajectory tracking control for a 3-DOF parallel manipulator using fractional-order control. IEEE Trans Ind Electron 61:3417–3426CrossRef Dumlu A, Erenturk K (2014) Trajectory tracking control for a 3-DOF parallel manipulator using fractional-order control. IEEE Trans Ind Electron 61:3417–3426CrossRef
17.
go back to reference Valerio D, da Costa JS (2012) An introduction to fractional control, vol 91. Institution of Engineering and Technology (IET), England Valerio D, da Costa JS (2012) An introduction to fractional control, vol 91. Institution of Engineering and Technology (IET), England
18.
go back to reference Pan I, Das S (2013) Frequency domain design of fractional order PID controller for AVR system using chaotic multi-objective optimization. Int J Electr Power Energy Syst 51:106–118CrossRef Pan I, Das S (2013) Frequency domain design of fractional order PID controller for AVR system using chaotic multi-objective optimization. Int J Electr Power Energy Syst 51:106–118CrossRef
19.
go back to reference Das S, Pan I, Das S, Gupta A (2012) A novel fractional order fuzzy PID controller and its optimal time domain tuning based on integral performance indices. Eng Appl Artif Intell 25:430–442CrossRef Das S, Pan I, Das S, Gupta A (2012) A novel fractional order fuzzy PID controller and its optimal time domain tuning based on integral performance indices. Eng Appl Artif Intell 25:430–442CrossRef
20.
go back to reference Chhabra H, Mohan V, Rani A, Singh V (2016) Multi Objective PSO tuned fractional order PID control of robotic manipulator. In: The international symposium on intelligent systems technologies and applications, pp 567–572 Chhabra H, Mohan V, Rani A, Singh V (2016) Multi Objective PSO tuned fractional order PID control of robotic manipulator. In: The international symposium on intelligent systems technologies and applications, pp 567–572
21.
go back to reference Bingül Z, Karahan O (2012) Fractional PID controllers tuned by evolutionary algorithms for robot trajectory control. Turk J Electr Eng Comput Sci 20:1123–1136 Bingül Z, Karahan O (2012) Fractional PID controllers tuned by evolutionary algorithms for robot trajectory control. Turk J Electr Eng Comput Sci 20:1123–1136
22.
go back to reference Monje CA, Vinagre BM, Feliu V, Chen Y (2008) Tuning and auto-tuning of fractional order controllers for industry applications. Control Eng Pract 16:798–812CrossRef Monje CA, Vinagre BM, Feliu V, Chen Y (2008) Tuning and auto-tuning of fractional order controllers for industry applications. Control Eng Pract 16:798–812CrossRef
23.
go back to reference Gaing Z-L (2004) A particle swarm optimization approach for optimum design of PID controller in AVR system. IEEE Trans Energy Convers 19:384–391CrossRef Gaing Z-L (2004) A particle swarm optimization approach for optimum design of PID controller in AVR system. IEEE Trans Energy Convers 19:384–391CrossRef
24.
go back to reference Wang P, Kwok D (1994) Optimal design of PID process controllers based on genetic algorithms. Control Eng Pract 2:641–648CrossRef Wang P, Kwok D (1994) Optimal design of PID process controllers based on genetic algorithms. Control Eng Pract 2:641–648CrossRef
25.
go back to reference Vasan A, Raju KS (2009) Comparative analysis of simulated annealing, simulated quenching and genetic algorithms for optimal reservoir operation. Appl Soft Comput 9:274–281CrossRef Vasan A, Raju KS (2009) Comparative analysis of simulated annealing, simulated quenching and genetic algorithms for optimal reservoir operation. Appl Soft Comput 9:274–281CrossRef
26.
go back to reference Pan I, Das S (2016) Fractional order fuzzy control of hybrid power system with renewable generation using chaotic PSO. ISA Trans 62:19–29CrossRef Pan I, Das S (2016) Fractional order fuzzy control of hybrid power system with renewable generation using chaotic PSO. ISA Trans 62:19–29CrossRef
27.
go back to reference Mishra P, Kumar V, Rana K (2015) A fractional order fuzzy PID controller for binary distillation column control. Expert Syst Appl 42:8533–8549CrossRef Mishra P, Kumar V, Rana K (2015) A fractional order fuzzy PID controller for binary distillation column control. Expert Syst Appl 42:8533–8549CrossRef
28.
go back to reference Jesus IS, Barbosa RS (2015) Genetic optimization of fuzzy fractional PD + I controllers. ISA Trans 57:220–230CrossRef Jesus IS, Barbosa RS (2015) Genetic optimization of fuzzy fractional PD + I controllers. ISA Trans 57:220–230CrossRef
29.
go back to reference Pan I, Korre A, Das S, Durucan S (2012) Chaos suppression in a fractional order financial system using intelligent regrouping PSO based fractional fuzzy control policy in the presence of fractional Gaussian noise. Nonlinear Dyn 70:2445–2461MathSciNetCrossRef Pan I, Korre A, Das S, Durucan S (2012) Chaos suppression in a fractional order financial system using intelligent regrouping PSO based fractional fuzzy control policy in the presence of fractional Gaussian noise. Nonlinear Dyn 70:2445–2461MathSciNetCrossRef
30.
go back to reference Das S, Pan I, Das S (2013) Performance comparison of optimal fractional order hybrid fuzzy PID controllers for handling oscillatory fractional order processes with dead time. ISA Trans 52:550–566CrossRef Das S, Pan I, Das S (2013) Performance comparison of optimal fractional order hybrid fuzzy PID controllers for handling oscillatory fractional order processes with dead time. ISA Trans 52:550–566CrossRef
33.
go back to reference Craig JJ (2005) Introduction to robotics: mechanics and control, vol 3. Pearson Prentice Hall, Upper Saddle River Craig JJ (2005) Introduction to robotics: mechanics and control, vol 3. Pearson Prentice Hall, Upper Saddle River
34.
go back to reference Ayala HVH, dos Santos Coelho L (2012) Tuning of PID controller based on a multiobjective genetic algorithm applied to a robotic manipulator. Expert Syst Appl 39:8968–8974CrossRef Ayala HVH, dos Santos Coelho L (2012) Tuning of PID controller based on a multiobjective genetic algorithm applied to a robotic manipulator. Expert Syst Appl 39:8968–8974CrossRef
36.
go back to reference Kumar V, Rana K (2017) Nonlinear adaptive fractional order fuzzy PID control of a 2-link planar rigid manipulator with payload. J Frankl Inst 354:993–1022MathSciNetMATHCrossRef Kumar V, Rana K (2017) Nonlinear adaptive fractional order fuzzy PID control of a 2-link planar rigid manipulator with payload. J Frankl Inst 354:993–1022MathSciNetMATHCrossRef
39.
go back to reference Podlubny I (1998) Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications, vol 198. Academic Press, New YorkMATH Podlubny I (1998) Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications, vol 198. Academic Press, New YorkMATH
40.
go back to reference Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6:182–197CrossRef Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6:182–197CrossRef
41.
go back to reference Pachauri N, Singh V, Rani A (2017) Two degree of freedom PID based inferential control of continuous bioreactor for ethanol production. ISA Trans 68:235–250CrossRef Pachauri N, Singh V, Rani A (2017) Two degree of freedom PID based inferential control of continuous bioreactor for ethanol production. ISA Trans 68:235–250CrossRef
42.
go back to reference Mirjalili S, Jangir P, Saremi S (2017) Multi-objective ant lion optimizer: a multi-objective optimization algorithm for solving engineering problems. Appl Intell 46:79–95CrossRef Mirjalili S, Jangir P, Saremi S (2017) Multi-objective ant lion optimizer: a multi-objective optimization algorithm for solving engineering problems. Appl Intell 46:79–95CrossRef
43.
go back to reference Wolpert DH, Macready WG (1997) No free lunch theorems for optimization. IEEE Trans Evol Comput 1:67–82CrossRef Wolpert DH, Macready WG (1997) No free lunch theorems for optimization. IEEE Trans Evol Comput 1:67–82CrossRef
44.
go back to reference Mirjalili S, Mirjalili SM, Hatamlou A (2016) Multi-verse optimizer: a nature-inspired algorithm for global optimization. Neural Comput Appl 27:495–513CrossRef Mirjalili S, Mirjalili SM, Hatamlou A (2016) Multi-verse optimizer: a nature-inspired algorithm for global optimization. Neural Comput Appl 27:495–513CrossRef
45.
go back to reference Jain M, Singh V, Rani A (2018) A novel nature-inspired algorithm for optimization: Squirrel search algorithm. Swarm Evol Comput 44:148–175CrossRef Jain M, Singh V, Rani A (2018) A novel nature-inspired algorithm for optimization: Squirrel search algorithm. Swarm Evol Comput 44:148–175CrossRef
46.
go back to reference Mirjalili S (2016) Dragonfly algorithm: a new meta-heuristic optimization technique for solving single-objective, discrete, and multi-objective problems. Neural Comput Appl 27:1053–1073CrossRef Mirjalili S (2016) Dragonfly algorithm: a new meta-heuristic optimization technique for solving single-objective, discrete, and multi-objective problems. Neural Comput Appl 27:1053–1073CrossRef
47.
go back to reference Mirjalili S, Jangir P, Mirjalili SZ, Saremi S, Trivedi IN (2017) Optimization of problems with multiple objectives using the multi-verse optimization algorithm. Knowl-Based Syst 134:50–71CrossRef Mirjalili S, Jangir P, Mirjalili SZ, Saremi S, Trivedi IN (2017) Optimization of problems with multiple objectives using the multi-verse optimization algorithm. Knowl-Based Syst 134:50–71CrossRef
48.
go back to reference Russell RW, May ML, Soltesz KL, Fitzpatrick JW (1998) Massive swarm migrations of dragonflies (Odonata) in eastern North America. Am Midl Nat 140:325–342CrossRef Russell RW, May ML, Soltesz KL, Fitzpatrick JW (1998) Massive swarm migrations of dragonflies (Odonata) in eastern North America. Am Midl Nat 140:325–342CrossRef
49.
go back to reference Wikelski M, Moskowitz D, Adelman JS, Cochran J, Wilcove DS, May ML (2006) Simple rules guide dragonfly migration. Biol Lett 2:325–329CrossRef Wikelski M, Moskowitz D, Adelman JS, Cochran J, Wilcove DS, May ML (2006) Simple rules guide dragonfly migration. Biol Lett 2:325–329CrossRef
50.
go back to reference De Wit CC, Praly L (2000) Adaptive eccentricity compensation. IEEE Trans Control Syst Technol 8:757–766CrossRef De Wit CC, Praly L (2000) Adaptive eccentricity compensation. IEEE Trans Control Syst Technol 8:757–766CrossRef
51.
go back to reference Åström KJ, Hägglund T (1995) PID controllers: theory, design, and tuning, vol 2. Instrument society of America Research, Triangle Park Åström KJ, Hägglund T (1995) PID controllers: theory, design, and tuning, vol 2. Instrument society of America Research, Triangle Park
52.
go back to reference Saleem O, Omer U (2017) EKF-based self-regulation of an adaptive nonlinear PI speed controller for a DC motor. Turk J Electr Eng Comput Sci 25:4131–4141CrossRef Saleem O, Omer U (2017) EKF-based self-regulation of an adaptive nonlinear PI speed controller for a DC motor. Turk J Electr Eng Comput Sci 25:4131–4141CrossRef
53.
go back to reference Quanser Engineering Trainer for NI-ELVIS (2009) QNET Interactive learning Guide, Quanser Inc. Quanser Engineering Trainer for NI-ELVIS (2009) QNET Interactive learning Guide, Quanser Inc.
Metadata
Title
Robust nonlinear fractional order fuzzy PD plus fuzzy I controller applied to robotic manipulator
Authors
Himanshu Chhabra
Vijay Mohan
Asha Rani
Vijander Singh
Publication date
30-03-2019
Publisher
Springer London
Published in
Neural Computing and Applications / Issue 7/2020
Print ISSN: 0941-0643
Electronic ISSN: 1433-3058
DOI
https://doi.org/10.1007/s00521-019-04074-3

Other articles of this Issue 7/2020

Neural Computing and Applications 7/2020 Go to the issue

Deep Learning & Neural Computing for Intelligent Sensing and Control

Deep belief network-based support vector regression method for traffic flow forecasting

Deep Learning & Neural Computing for Intelligent Sensing and Control

Research on orthopedic auxiliary classification and prediction model based on XGBoost algorithm

Premium Partner