Skip to main content
SpringerLink
Log in

Optimal control of hydraulically driven parallel robot platform based on firefly algorithm

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

A new cascade load force control design for a parallel robot platform is proposed. A parameter search for a proposed cascade controller is difficult because there is no methodology to set the parameters and the search space is broad. A parameter search based on firefly algorithm (FA) is suggested to effectively search the parameters of the cascade controller. We used unified mathematical model of hydraulic actuator of parallel robot platform. These equations are readily applicable to various types of proportional valves, and they unify the cases of critical center, overlapped and underlapped valves. These unified model equations are useful for nonlinear controller design. The optimal results are compared to those obtained from other metaheuristic algorithms: GA, PSO and CS. A comparative study is also made between proposed optimal tuned cascade control using FA and well-tuned PID controller. Simulation results show the advantages of the proposed optimal tuned cascade controller using FA to solve a formulated tracking problem.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

References

  1. Stewart, D.: platform with six degrees of freedom. Proceedings of the institution of mechanical engineers. J. Power Energy 180(15), 371–386 (1965)

    Google Scholar 

  2. Su, Y.X., Duan, B.Y., Zheng, C.H.: Nonlinear PID control of a six-DOF parallel manipulator. Control Theory Appl. IEE Proc. 151(1), 95–102 (2004)

    Article  Google Scholar 

  3. Pi, Y., Wang, X.: Trajectory tracking control of a 6-DOF hydraulic parallel robot manipulator with uncertain load disturbances. Control Eng. Pract. 19(2), 185–193 (2011)

    Article  Google Scholar 

  4. Stefanovic, M., Zhang, H.: Results on the robust observer-based position controller for parallel kinematic machines. J. Intell. Rob. Syst. 66(4), 417–428 (2012)

    Article  MATH  Google Scholar 

  5. Merritt, H.E.: Hydraulic Control Systems. Wiley, New York (1967)

    Google Scholar 

  6. Filipovic, V., Nedic, N., Stojanovic, V.: Robust identification of pneumatic servo actuators in the real situations. Forschung im Ingenieurwesen Eng. Res. 75(4), 183–196 (2011)

    Article  Google Scholar 

  7. Dihovicni, Dj, Nedic, N.: Simulation, animation and program support for a high performance pneumatic force actuator system. Math. Comput. Model. 48(5–6), 761–768 (2008)

    Article  Google Scholar 

  8. Tao, G., Kokotovic, P.V.: Adaptive control of plants with unknown dead-zones. IEEE Trans. Autom. Control 39(1), 59–68 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  9. Tao, G., Kokotovic, P.V.: Adaptive Control of Systems with Actuator and Sensor Nonlinearities. Wiley, New York (1996)

    MATH  Google Scholar 

  10. Soltanpour, M.R., Fateh, M.M.: Sliding mode robust control of robot manipulators in the task space by support of feedback linearization and backstepping control. World Appl. Sci. J. 6(1), 70–76 (2009)

    Google Scholar 

  11. Shafiei, S.E., Soltanpour, M.R.: Neural network slidingmodel-PID controller design for electrically driven robot manipulators. Int. J. Innov. Comput. Inf. Control 7(2), 3949–3960 (2011)

    Google Scholar 

  12. Spong, M.W., Hutchinson, S., Vidyasagar, M.: Robot Modeling and Control. Wiley, Hoboken (2006)

    Google Scholar 

  13. Heintze, J., Teerhuis, P.C., Van der Weiden, A.J.J.: Controlled hydraulics for a direct drive brick laying robot. Autom. Constr. 5(1), 23–29 (1996)

    Article  Google Scholar 

  14. Sepehri, N., Dumont, G.A.M., Lawrence, P.D., Sassani, F.: Cascade control of hydraulically actuated manipulators. Robotica 8(3), 207–216 (1990)

    Article  Google Scholar 

  15. Filipovic, V., Nedic, N.: PID regulators. Faculty of Mechanical Engineering, Kraljevo (2008)

  16. Guo, H.B., Liu, Y.G., Liu, G.R., Li, H.R.: Cascade control of a hydraulically driven 6-DOF parallel robot manipulator based on a sliding mode. Control Eng. Pract. 16(9), 1055–1068 (2008)

    Article  Google Scholar 

  17. Jelali, M., Kroll, A.: Hydraulic Servo-systems. Springer, Berlin (2002)

    Google Scholar 

  18. Rao, S.S.: Engineering Optimization: Theory and Practice. Wiley, New York (2009)

    Book  Google Scholar 

  19. Niknam, T., Farsani, E.A.: A hybrid self-adaptive particle swarm optimization and modified shuffled frog leaping algorithm for distribution feeder reconfiguration. Eng. Appl. Artif. Intell. 23(8), 1340–1349 (2010)

    Article  Google Scholar 

  20. Li, X., Yao, X.: Cooperatively coevolving particle swarms for large scale optimization. IEEE Trans. Evol. Comput. 16(2), 210–224 (2012)

    Article  MathSciNet  Google Scholar 

  21. Alfi, A.: Particle swarm optimization algorithm with dynamic inertia weight for online parameter identification applied to Lorenz chaotic system. Int. J. Innov. Comput. Inf. Control 8(2), 1191–1203 (2012)

    Google Scholar 

  22. Alfi, A.: PSO with adaptive mutation and inertia weight and its application in parameter estimation of dynamic systems. Acta Autom. Sinica 37(5), 541–549 (2011)

    Article  MATH  Google Scholar 

  23. Alfi, A., Fateh, M.M.: Intelligent identification and control using improved fuzzy particle swarm optimization. Expert Syst. Appl. 38(10), 12312–12317 (2011)

    Article  Google Scholar 

  24. Modares, H., Alfi, A., Fateh, M.M.: Parameter identification of chaotic dynamic systems through an improved particle swarm optimization. Expert Syst. Appl. 37(5), 3714–3720 (2010)

    Article  Google Scholar 

  25. Alfi, A., Modares, H.: System identification and control using adaptive particle swarm optimization. Appl. Math. Model. 35(3), 1210–1221 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  26. Shieh, C.S., Hung, R.T.: Hybrid control for synchronizing a chaotic system. Appl. Math. Model. 35(8), 3751–3758 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  27. Mohideen, K.A., Saravanakumar, G., Valarmathi, K., Devaraj, D., Radhakrishnan, T.K.: Real-coded Genetic Algorithm for system identification and tuning of a modified model reference adaptive controller for a hybrid tank system. Appl. Math. Model. 37(6), 3829–3847 (2013)

    Article  MathSciNet  Google Scholar 

  28. Karanki, S.B., Mishra, M.K., Kumar, B.K.: Particle swarm optimization-based feedback controller for unified power-quality conditioner. IEEE Trans. Power Deliv. 25(4), 2814–2824 (2010)

    Article  Google Scholar 

  29. Yang, X.S.: Nature-Inspired Metaheuristic Algorithms. Luniver Press, UK (2008)

    Google Scholar 

  30. Yang, X.S.: Firefly algorithms for multimodal optimization. Stochastic Algorithms: Foundations and Applications. Lecture Notes in Computer Science, Springer, Berlin 169-178 (2009)

  31. Lukasik, S., Zak, S.: Firefly algorithm for continuous constrained optimization tasks. Computational Collective Intelligence. Semantic Web, Social Networks and Multiagent Systems. Lecture Notes Comput. Sci. 5796, 97–106 (2009)

  32. Yang, X.S.: Firefly algorithm, stochastic test functions and design optimisation. Int. J. Bio-Inspired Comput. 2(2), 78–84 (2010)

    Article  Google Scholar 

  33. Arora, S., Singh, S.: A conceptual comparison of firefly algorithm, bat algorithm and cuckoo search. International Conference on Control, Computing, Communication and Materials (ICCCCM), 3-4 August 2013, 1-4, Allahabad (India) (2013)

  34. Yang, X.S.: Firefly algorithms for multimodal optimization. SAGA’09 Proceedings of 5th international conference on Stochastic algorithms: foundations and applications, Springer Berlin, 169–178 (2009)

  35. Gandomi, A.H., Yang, X.S., Alavi, A.H.: Computers and Structures 89(23–24), 2325–2336 (2011)

  36. Yang, X.S.: Nature-Inspired Optimization Algorithms. Elsevier, Amsterdam (2014)

  37. Blackburn, J.F., Reethof, G., Shearer, J.L.: Fluid Power Control. The MIT Press Cambridge, Massachusetts (1960)

    Google Scholar 

  38. Paul, R.: Robot Manipulators: Mathematics, Programming and Control. MIT Press, Cambridge (1981)

    Google Scholar 

  39. Omran, A., Kassem, A.: Optimal task space control design of a Stewart manipulator for aircraft stall recovery. Aerosp. Sci. Technol. 15, 353–365 (2011)

    Article  Google Scholar 

  40. Omran, A., Kassem, A., El-Bayoumi, G., Bayoumi, M.: Mission-based optimal control of Stewart manipulator. Aircr. Eng. Aerosp. Technol. J. 81(3), 147–153 (2009)

    Google Scholar 

  41. Huber, P.J.: Robust Statistics. Wiley, New York (1981)

    Book  MATH  Google Scholar 

  42. Bernzen, W.: Zur Regelung elastischer Roboter mit hydraulischen Antrieben. VDI Fortschritt-Berichte Reihe 8 Nr. 788, VDI-Verlag, Düsseldorf (1999)

  43. Cominos, P., Munro, N.: PID controllers: recent tuning methods and design to specification. IEEE Proc Control Theory Appl 149(1), 46–53 (2002)

    Article  Google Scholar 

Download references

Acknowledgments

The authors would like to express their gratitude to reviewers for their very useful comments and suggestions to improve this paper. This research has been supported by the Serbian Ministry of Education, Science and Technological Development through projects TR33026 and TR33027.

Author information

Authors and Affiliations

  1. Department of Automatic Control, Robotics and Fluid Technique, Faculty of Mechanical and Civil Engineering in Kraljevo, University of Kragujevac, Dositejeva 19, 36000, Kraljevo, Serbia

    Novak Nedic, Vladimir Stojanovic & Vladimir Djordjevic

Authors
  1. Novak Nedic
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Vladimir Stojanovic
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Vladimir Djordjevic
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Vladimir Stojanovic.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Nedic, N., Stojanovic, V. & Djordjevic, V. Optimal control of hydraulically driven parallel robot platform based on firefly algorithm. Nonlinear Dyn 82, 1457–1473 (2015). https://doi.org/10.1007/s11071-015-2252-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-015-2252-5

Keywords

Search

Navigation