Skip to main content

Advertisement

Log in

Local Model and Controller Network Design for a Single-Link Flexible Manipulator

  • Published:
Journal of Intelligent & Robotic Systems Aims and scope Submit manuscript

Abstract

This paper describes a new genetic learning approach to the construction of a local model network (LMN) and design of a local controller network (LCN) with application to a single-link flexible manipulator. A highly nonlinear flexible manipulator system is modelled using an LMN comprising Autoregressive–moving-average model with exogenous inputs (ARMAX) type local models (LMs) whereas linear Proportional-integral-derivative (PID) type local controllers (LCs) are used to design an LCN. In addition to allowing the simultaneous optimisation of the number of LMs and LCs, model parameters and interpolation function parameters, the approach provides a flexible framework for targeting transparency and generalisation. Simulation results confirm the excellent nonlinear modelling properties of an LM network and illustrate the potential benefits of the proposed LM control scheme.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Johansen, T.A., Foss, B.A.: Constructing NARMAX models using ARMAX models. Int. J. Control 58, 1125–1153 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  2. Johansen, T.A., Foss, B.A.: Semi-empirical modeling of nonlinear dynamic systems through identification of operating regimes and local models. In: Hunt, K.J., Irwin, G.R., Warwick, K. (eds.) Neural Network Engineering in Dynamic Control System, pp. 105–126. Springer-Verlag London Limited (1995)

  3. Brown, M.D., Lightbody, G., Irwin, G.W.: Non-linear internal model control using local model networks. IEE Proc. Control Theory Appl. 144(6), 505–514 (1997)

    Article  Google Scholar 

  4. Murray-Smith, R., Johansen, T.A.: Multiple Model Approaches to Modeling and Control. Taylor and Francis, New York (1997)

    Google Scholar 

  5. McLoone, S.F., Brown, M.D., Irwin, G.W., Lightbody, G.: A hybrid linear/nonlinear training algorithm for feedforward neural networks. IEEE Trans. Neural Netw. 9(4), 669–684 (1998)

    Article  Google Scholar 

  6. Nelles, O.: Orthogonal basis function for nonlinear system identification with local linear model trees (LOLIMOT). In: Proc. Of 11th IFAC Symposium on System Identification (Invited Session), Japan, vol. 2, pp. 667–672 (1997)

  7. Rippin, D.W.T.: Control of batch processes. In: Proceedings of the 3rd IFAC DYCORD + ’89 Symposium, pp. 115–125. Maastrict, Netherlands (1989)

    Google Scholar 

  8. Townsend, S., Lightbody, G., Brown, M.D., Irwin, G.W.: Nonlinear dynamic matrix control using local model networks. Trans. Inst. MC 20(1), 47–56 (1998)

    Article  Google Scholar 

  9. Tokhi, M.O., Azad, A.K.M.: Flexible Robot Manipulators—Modelling, Simulation and Control. The Institution of Engineering and Technology, London, UK (2008)

    Book  MATH  Google Scholar 

  10. Jie, L., Zhihui, G., Yushu, B., Jingjing, Y.: Modeling and modification of the flexible robot with single controllable local degree of freedom. In: 2012 International Conference on Mechatronics and Automation (ICMA), 5–8 Aug. 2012, pp. 1840–1844 (2012). doi:10.1109/ICMA.2012.6285101

  11. Sharma, S.K., McLoone, S., Irwin, G.W.: Genetic algorithms for local controller network construction. IEE Proc. Control Theory Appl. 152(5), 587–597 (2005)

    Article  Google Scholar 

  12. Michalewicz, Z.: Genetic Algorithms + Data Structures = Evolution Programs, 3rd edn. Springer, New York (1996)

    Book  MATH  Google Scholar 

  13. Poerwanto, H.: Dynamic simulation and control of flexible manipulator systems. PhD Thesis, Department of Automatic Control and System Engineering, The University of Sheffield, UK (1998)

  14. Sharma, S.K.: Soft computing for modelling and control of dynamic systems with application to flexible manipulators. PhD thesis, Department of Automatic Control and Systems Engineering, The University of Sheffield, UK (2000)

  15. Renato, V., Alessandro, G., Marco, G.: Design and implementation of an ERLS-based 3-D dynamic formulation for flexible-link robots. J. Robot. Comput. Integr. Manuf. 29(2), 273–282. issn = 0736-5845 (2013). doi:10.1016/j.rcim.2012.07.008

  16. Book, W.J.: Recursive lagrangian dynamics of flexible manipulator arms. Int. J. Robot. 3, 87–101 (1984)

    Article  Google Scholar 

  17. Chang, L.W., Hamilton, J.F.: Dynamic robotic manipulators with flexible links. Trans. ASME J. Dyn. Syst. Meas. Control 113(1), 54–59 (1991)

    Article  Google Scholar 

  18. Gamarra-Rosado, V.O., Fernandez, G., Grieco, J.C., Armada, M., Alane, N.: Control of a flexible one-link manipulator. Autom. Cybern. 25(5), 38–47 (1996)

    Google Scholar 

  19. Shabana, A.: Flexible multibody dynamics review of past and recent developments. Multibody Syst. Dyn. 1, 189–222 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  20. Benosman, M., Boyer, F., Vey, G., Primautt, D.: Flexible links manipulators from modelling to control. J. Intell. Robot. Syst. 34(4), 381–414 (2002)

    Article  MATH  Google Scholar 

  21. Wasfy, T.M., Noor, A.K.: Computational strategies for flexible multibody systems. ASME Appl. Mech. Rev. 56(6), 553–613 (2003)

    Article  Google Scholar 

  22. Dwivedy, S., Eberhard, P.: Dynamic analysis of flexible manipulators, a literature review. Mech. Mach. Theory 41, 749–777 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  23. Benosman, M., Vey, G.: Control of flexible manipulators a survey. Robotica 22(22), 533–545 (2004)

    Article  Google Scholar 

  24. Caracciolo, R., Richiedei, D., Trevisani, A.: Design and experimental validation of piecewise-linear state observers for flexible link mechanisms. Meccanica 41(41), 623–637 (2006)

    Article  MATH  Google Scholar 

  25. Caracciolo, R., Richiedei, D., Trevisani, A.: Experimental validation of a model-based robust controller for multi-body mechanisms with flexible links. Multibody Syst. Dyn. 20(2), 129–145 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  26. Boscariol, P., Gasparetto, A., Zanotto, V.: Active position and vibration control of a flexible links mechanism using model-based predictive control. ASME J. Dyn. Syst. Meas. Control 132, 1–4 (2010)

    Article  Google Scholar 

  27. Dietz, S., Wallrapp, O., Wiedemann, S.: Nodal vs. modal representation in flexible multibody system dynamics. In: Proceedings of Multibody Dynamics 2003, IDMEC/IST 2003. Lisbon, Portugal (2003)

  28. Martins, J., Mohamed, Z., Tokhi, M., da Costa, J.S., Botto, M.: Approaches for dynamic modelling of flexible manipulator systems. In: Proceedings of the IEEE Conference on Control Theory and Applications, vol. 150 (2003)

  29. Ljung, L.: System Identification: Theory for the User, 2nd edn. Prentice Hall, Englewood Cliffs, NJ (1999)

  30. Alam, M.S., Tokhi, M.O.: Designing feedforward command shapers with multi-objective genetic optimisation for vibration control of a single-link flexible manipulator. Eng. Appl. Artif. Intell. 21(2), 229–246 (2008)

    Article  Google Scholar 

  31. Alam, M.S., Tokhi, M.O.: Hybrid fuzzy logic control with genetic optimisation of a single-link flexible manipulator. Eng. Appl. Artif. Intell. 21(6), 858–873 (2008)

    Article  Google Scholar 

  32. Alam, M.S., Tokhi, M.O.: Selecting and designing command shapers for vibration control of flexible manipulators: a multi-objective optimization approach. Int. J. Acoust. Vib. 14(4), 179–187 (2009)

    Google Scholar 

  33. Cannon, R.H., Schmitz, E.: Initial experiments on the end-point control of a flexible one link robot. Int. J. Robot. Res. 3(3), 62–75 (1984)

    Article  Google Scholar 

  34. Khorrami, F., Jain, S.: Non-linear control with end-point acceleration feedback for a two link flexible manipulator: experimental results. J. Robot. Syst. 10, 505–530 (1993)

    Article  Google Scholar 

  35. Md Zain, M.Z., Tokhi, M.O., Mohamed, Z.: Hybrid learning control schemes with input-shaping of a flexible manipulator system. Mechatronics 16, 209–219 (2006)

    Article  Google Scholar 

  36. Mohamed, Z., Tokhi, M.O.: Hybrid control schemes for input tracking and vibration suppression of a flexible manipulator. Proc. IMechE-I J. Syst. Control Eng. 217(I1), 23–34 (2003)

    Article  Google Scholar 

  37. Mohamed, Z., Tokhi, M.O.: Command shaping techniques for vibration control of a flexible robot manipulator. Mechatronics 14, 69–90 (2004)

    Article  Google Scholar 

  38. Mohamed, Z., Martins, J., Tokhi, M.O., Sa Da Costa, J., Botto, M.A.: Vibration control of a very flexible manipulator system. Control Eng. Pract. 13(3), 267–277 (2005)

    Article  Google Scholar 

  39. Mohamed, Z., Chee, A.K., Mohd Hashim, A.W.I., Tokhi, M.O., Shamsudin, H.M.A., Mamat, R.: Techniques for vibration control of a flexible manipulator. Robotica 24(4), 499–511 (2006)

    Article  Google Scholar 

  40. Siciliano, B., Book, W.J.: A Singular perturbation approach to control of light-weight flexible manipulators. Int. J. Robot. Res. 7(4), 79–90 (1988)

    Article  Google Scholar 

  41. Siddique, M.N.H., Tokhi, M.O.: GA-based neural fuzzy control of flexible-link manipulators. Eng. Lett. 13(2), 148–157 (2006)

    Google Scholar 

  42. Tokhi, M.O., Md Zain, M.Z.: Hybrid learning control schemes with acceleration feedback of a flexible manipulator system. Proc. IMechE-I J. Syst. Control Eng. 220(I4), 257–267(2006)

    Article  Google Scholar 

  43. Tzes, A., Yurkovich, S.: An adaptive input shaping control scheme for vibration suppression in slewing flexible structures. IEEE Trans. Control Syst. Technol. 1, 114–121 (1993)

    Article  Google Scholar 

  44. Lin, L.C.: State feedback H ∞  control of manipulators with flexible joints and links. In: IEEE International Conference on Robotics and Automation, pp. 218–223. Sacramento, California (1991)

  45. Lucibello, P.: Nonlinear regulation with internal stability of a two link flexible robot arm. In: IEEE Conference on Decision and Control, pp. 1645–1650. Florida, USA (1989)

  46. Khorrami, F., Ozguner, U.: Perturbation methods in control of flexible link manipulators. In: IEEE Conference on Robotics and Automation, pp. 310–315. Philadelphia, PA (1988)

  47. Nathan, P.J., Singh, S.N.: Sliding mode control and elastic mode stabilization of a robotic arm with flexible link. ASME Trans. Dyn. Syst. Meas. Control 113, 669–676 (1991)

    Article  MATH  Google Scholar 

  48. Yurkovich, S., Garcia-Benitez, E., Watkins, J.: Feedback linearization with acceleration feedback for a two-link flexible manipulator. In: Proceedings of American Control Conference, vol. 2, pp. 1360–1365. Evanston, IL (1991)

  49. Siciliano, B., Yuan, B.S., Book, W.J.: Model reference adaptive control of a one link flexible arm. In: Proc. 25th IEEE Conference on Decision and Control, pp. 91–95. Athens, Greece (1986)

  50. Feliu, V., Rattan, K.S., Brown, H.B.: Adaptive control of a single-link flexible manipulator. IEEE Control Syst. Mag. 10(2), 29–33 (1990)

    Article  Google Scholar 

  51. Menq, C.H., Chen, J.S.: Dynamic modelling and payload-adaptive control of a flexible manipulator. In: IEEE Conference on Robotics and Automation, pp. 488–493. Philadelphia, PA (1988)

  52. Cetinkunt, S., Wu, S.: Tip position control of a flexible one arm robot with predictive adaptive output feedback implemented with lattice filter parameter identifier. Comput. Struct. 36(3), 429–441 (1990)

    Article  MATH  Google Scholar 

  53. Yang, T.C., Yang, J.C., Kudva, P.: Adaptive control of a single-link flexible manipulator with unknown load. Int. Electr. Eng. Proc. 138(2), 153–159 (1991)

    Google Scholar 

  54. Nemir, D.C., Koivo, A.J., Kashyap, R.L.: Pseudolinks and the self-tuning control of a non rigid link mechanism. IEEE Trans. Syst. Man Cybern. 18(1), 40–48 (1988)

    Article  Google Scholar 

  55. Lucibello, P., Bellezza, F.: Nonlinear adaptive control of a two link flexible robot arm. In: IEEE Conference on Decision and Control, pp. 2545–2550 (1990)

  56. Yang, Y., Huang, K.: Adaptive lattice estimation and control of a manipulator with one flexible forearm. Int. Electr. Eng. Proc. 139(3), 237–244 (1992)

    MATH  Google Scholar 

  57. Koivo, A.J., Lee, K.S.: Self-tuning control of a two-link manipulator with a flexible forearm. Int. J. Robot. Res. 11(4), 383–395 (1992)

    Article  Google Scholar 

  58. Zhongyi, C., Jing C.: Vibration control of maneuvering spacecraft with flexible manipulator using adaptive disturbance rejection filter and command shaping technology. In: 2012 Sixth International Conference on Internet Computing for Science and Engineering (ICICSE), 21–23 Apr. 2012, pp. 97–101 (2012). doi:10.1109/ICICSE.2012.13

  59. Tokhi, M.O., Kourtis, S., Poerwanto, H., Azad, A.K.M.: Control of flexible manipulator systems using filtered command inputs. Mach. Vib. 4, 68–89 (1995)

    Google Scholar 

  60. Tokhi, M.O, Azad, A.K.M.: Control of flexible manipulator systems. Proc. IMechE-I J. Syst. Control Eng. 210(I2), 113–130 (1996)

    Article  Google Scholar 

  61. Carmelo di, C., Arcangelo, M.: Exact modeling for control of flexible manipulators. J. Vib. Control 18(10), 1526–1551 (2012)

    Article  MathSciNet  Google Scholar 

  62. Goldberg, D.: Genetic Algorithm in Search, Optimisation and Machine Learning. Addison-Wesley, Massacheusetts (1989)

    Google Scholar 

  63. Holland, J.H.: Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control and Artificial Intelligence. MIT Press, Cambridge, Masssachusetts (1992)

    Google Scholar 

  64. Ogata, K.: Modern Control Engineering, 4th edn. Prentice-Hall Inc (2002)

  65. Tan, K.K., Huang, S., Ferdous, R.: Robust self-tuning PID controller for nonlinear systems. J. Process Control 12(7), 753–761 (2002)

    Article  Google Scholar 

  66. Chen, G., Ying, H.: BIBO stability of nonlinear fuzzy PI control systems. J. Intell. Fuzzy Syst. 5, 245–256 (1997)

    Google Scholar 

  67. Malki, H., Li, H., Chen, G.: New design and stability analysis of a fuzzy proportional-derivative control system. IEEE Trans. Fuzzy Syst. 2, 245–254 (1995)

    Article  Google Scholar 

  68. Misir, D., Malki, H., Chen, G.: Design and analysis of a fuzzy proportional-integral-derivative controller. Int. J. Fuzzy Sets Syst. 79, 297–314 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  69. Sooraksa, P., Chen, G.: Fuzzy (PID)2 control for flexible robot arms. In: Proc. IEEE Int. Conf. on Control Appl., 15–18 Sept., pp. 536–541. Deerborn, MI (1996)

  70. Ortega, R., Loria, A., Kelly, R.: A semiglobally stable output feedback PID regulator for robot manipulators. IEEE Trans. Autom. Control 40(8), 1432–1436 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  71. Alvarez, J., Cervantes, I., Kelly, R.: PID regulation of robot manipulators: stability and performance. Syst. Control Lett. 41(2), 73–83 (2000)

    Article  MATH  Google Scholar 

  72. Arimoto, S.: Control Theory of Non-Linear Mechanical Systems: a Passivity-Based and Circuit-Theoretic Approach. Oxford Univ. Press, London, UK (1996)

  73. Meza, J.L., Santibañez, V., Campa, R.: An estimate of the domain of attraction for the PID regulator of manipulators. Int. J. Robot. Autom. 22(3), 187–195 (2007)

    Google Scholar 

  74. Kelly, R., Haber, R., Haber, R.E., Reyes, F.: Lyapunov stable control of robot manipulators: a fuzzy self-tuning procedure. Intell. Autom. Soft Comput. 5(4), 313–326 (1999)

    Article  Google Scholar 

  75. Meza, J.L., Santibanez, V., Soto, R., Llama, M.A.: Fuzzy self-tuning PID semiglobal regulator for robot manipulators. IEEE Trans. Ind. Electron. 59(6), 2709–2717 (2012). doi:10.1109/TIE.2011.2168789

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to S. K. Sharma.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sharma, S.K., Sutton, R. & Tokhi, M.O. Local Model and Controller Network Design for a Single-Link Flexible Manipulator. J Intell Robot Syst 74, 605–623 (2014). https://doi.org/10.1007/s10846-013-9847-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10846-013-9847-1

Keywords

Navigation