Advertisement

Adaptive Motion Planning

  • João M. LemosEmail author
  • Rui Neves-Silva
  • José M. Igreja
Chapter
  • 1.1k Downloads
Part of the Advances in Industrial Control book series (AIC)

Abstract

The design of an adaptive servo controller for tracking variable references in a distributed collector solar field is addressed. The structure proposed is made of three main blocks that consist of a motion planner, an incremental controller, and an adaptation mechanism. The motion planner selects the time profile of the manipulated variable (fluid flow) such that the plant state (given by the fluid temperature distribution along the solar field) is driven between successive equilibrium states, as specified. This task is performed using a simplified distributed parameter model, and employs the methods of flat systems and the concept of orbital flatness that is associated with a change of time scale, related to fluid flow. A linear controller stabilizes the actual fluid temperature around this nominal path and compensates for model mismatches and unaccounted disturbances. A control Lyapunov function is then used to modify this control law so as to incorporate adaptation capabilities through the adjustment of a parameter. In this chapter, the motion planning problem is also solved for a moisture control system.

Keywords

Motion Planning Feedback Controller Fluid Temperature Manipulate Variable Motion Planner 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. Bird RB, Stewart WE, Lightfoot EN (2007) em Transport phenomena, 2nd edn. Wiley, WeinheimGoogle Scholar
  2. Fliess M, Lévine J, Martin P, Rouchon P (1995) Flatness and defect of nonlinear systems: introductory theory and examples. Int J Control 61(6):1327–1361CrossRefzbMATHGoogle Scholar
  3. Fliess M, Lévine J, Martin P (1999) A Lie-Bäcklund approach to equivalence and flatness of nonlinear systems. IEEE Trans Autom Control 44:922–937CrossRefzbMATHGoogle Scholar
  4. Fliess M, Lévine J, Martin P, Rouchon P (1995) Design of trajectory stabilizing feedback for driftless flat systems. In: Proceedings of the 3rd ECC, Rome, Italy, pp 1882–1887Google Scholar
  5. Guay M (1999) An algorithm for orbital feedback linearization of single-input control affine systems. Syst Control Lett 38:271–281CrossRefzbMATHMathSciNetGoogle Scholar
  6. Henson M, Seborg D (1997) Nonlinear process control. Prentice Hall, New JerseyGoogle Scholar
  7. Igreja JM, Lemos JM, Rouchon P, Silva RN (2004) Dynamic motion planning of a distributed collector solar field. In: NOLCOS 2004, Stuttgart, GermanyGoogle Scholar
  8. Lewis FL, Syrmos VL (1995) Optimal control. Wiley, New YorkGoogle Scholar
  9. Lynch AF, Rudolph J (2002) Flatness-based boundary control of a class of quasilinear parabolic distributed parameter systems. Int J Control 75(15):1219–1230CrossRefzbMATHMathSciNetGoogle Scholar
  10. Martin Ph, Murray RM, Rouchon P (1997) Flat systems. In: Bastin G, Gevers M (eds) Plenary lectures and mini-courses—European control conferenceGoogle Scholar
  11. Mosca E (1995) Optimal, predictive, and adaptive control. Prentice Hall, New JerseyGoogle Scholar
  12. Mounier H, Rudolph J (1998) Flatness-based control of nonlinear delay systems: a chemical reactor example. Int J Control 71(5):871–890CrossRefzbMATHMathSciNetGoogle Scholar
  13. Respondek W (1998) Orbital feedback linearization of single-input nonlinear control systems. In: Proceedings of the NOLCOS’98, Enschede, The Netherlands, pp 499–504Google Scholar
  14. Respondek W, Pogromsky A, Nijmeier H (2004) Time scaling for observer design with linearizable error dynamics. Automatica 40:277–285CrossRefzbMATHGoogle Scholar
  15. Rothfuss R, Rudolph J, Zeita M (2014) Flatness based control of a nonlinear chemical reactor model. Automatica 32:1433–1439CrossRefGoogle Scholar
  16. Rouchon P (2001) Motion planning, equivalence, infinite dimensional systems. Int J Appl Math Comput Sci 11:165–188zbMATHMathSciNetGoogle Scholar
  17. Rudolph J (2003) Flatness based control of distributed parameter systems. Shaker Verlag, AachenGoogle Scholar
  18. Rudolph J, Mounier H (2000) Trajectory tracking for pi-flat nonlinear delay systems with a motor example. In: Isidori A et al (eds.) Nonlinear control vol 2. Springer, Berlin, pp 339–351Google Scholar
  19. Rudolph J, Winkler J, Woittennek F (2003) Flatness based control of distributed parameter systems: examples and computer exercises from various technological domains. Shaker Verlag, AachenGoogle Scholar
  20. Vollmer U, Raisch J (2003) Control of batch cooling crystallization processes based on orbital flatness. Int J Control 76(16):1635–1643CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • João M. Lemos
    • 1
    Email author
  • Rui Neves-Silva
    • 2
  • José M. Igreja
    • 3
  1. 1.INESC-ID ISTUniversity of LisbonLisboaPortugal
  2. 2.FCTNew University of LisbonCaparicaPortugal
  3. 3.Institute of Engineering of LisbonLisboaPortugal

Personalised recommendations