Skip to main content

State Feedback Control Design for Stefan System

  • Chapter
  • First Online:
Materials Phase Change PDE Control & Estimation

Part of the book series: Systems & Control: Foundations & Applications ((SCFA))

  • 605 Accesses

Abstract

This chapter presents the design procedure of the control algorithm for the one-phase Stefan system. Due to the recent advancement in computing, a sophisticated PDE control algorithm with complex computations can be practically implemented. With the phase changes appearing in a variety of scientific phenomena and industrial processes, such a control algorithm has numerous practical applications in science and engineering (we introduce some examples in Part II).

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 99.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 129.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 129.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. H. Anfinsen, O.M. Aamo, Adaptive Control of Hyperbolic PDEs (Springer, New York, 2019)

    Book  MATH  Google Scholar 

  2. A. Armaou, P.D. Christofides, Robust control of parabolic PDE systems with time-dependent spatial domains. Automatica 37, 61–69 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  3. A. Baccoli, A. Pisano, Y. Orlov, Boundary control of coupled reaction-advection-diffusion systems with spatially-varying coefficients. Automatica 54, 80–90 (2015)

    Article  MATH  Google Scholar 

  4. N. Bekiaris-Liberis, M. Krstic, Compensation of state-dependent input delay for nonlinear systems. IEEE Trans. Autom. Control 58(2), 275–289 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  5. N. Bekiaris-Liberis, M. Krstic, Compensation of wave actuator dynamics for nonlinear systems. IEEE Trans. Autom. Control 59(6), 1555–1570 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  6. N. Bekiaris-Liberis, M. Krstic, Nonlinear Control Under Nonconstant Delays, vol. 25 (SIAM, Philadelphia, 2014)

    MATH  Google Scholar 

  7. N. Boonkumkrong, S. Kuntanapreeda, Backstepping boundary control: an application to rod temperature control with Neumann boundary condition. Proc. Inst. Mech. Eng. I J. Syst. Control Eng. 228(5), 295–302 (2014)

    Google Scholar 

  8. D.M. Boskovic, M. Krstic, W. Liu, Boundary control of an unstable heat equation via measurement of domain-averaged temperature. IEEE Trans. Autom. Control 46(12), 2022–2028 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  9. X. Cai, M. Krstic, Nonlinear control under wave actuator dynamics with time- and state-dependent moving boundary. Int. J. Rob. Nonlinear Control 25(2), 222–251 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  10. P.D. Christofides, Robust control of parabolic PDE systems. Chem. Eng. Sci. 53, 2949–2965 (1998)

    Article  Google Scholar 

  11. F. Conrad, D. Hilhorst, T.I. Seidman, Well-posedness of a moving boundary problem arising in a dissolution-growth process. Nonlinear Anal. 31, 795–803 (2007)

    MATH  Google Scholar 

  12. N. Daraoui, P. Dufour, H. Hammouri, A. Hottot, Model predictive control during the primary drying stage of lyophilisation. Control Eng. Pract. 18, 483–494 (2010)

    Article  Google Scholar 

  13. J. Deutscher, Backstepping design of robust output feedback regulators for boundary controlled parabolic PDEs. IEEE Trans. Autom. Control 61(8), 2288–2294 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  14. M. Diagne, N. Bekiaris-Liberis, A. Otto, M. Krstic, Control of transport PDE/nonlinear ODE cascades with state-dependent propagation speed. IEEE Trans. Autom. Control 62(12), 6278–6293 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  15. P. Frihauf, M. Krstic, Leader-enabled deployment onto planar curves: a PDE-based approach. IEEE Trans. Autom. Control 56(8), 1791–1806 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  16. A. Hasan, O.M. Aamo, M. Krstic, Boundary observer design for hyperbolic PDE-ODE cascade systems. Automatica 68, 75–86 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  17. T. Hu, Z. Lin, Control Systems with Actuator Saturation: Analysis and Design (Springer, New York, 2001)

    Book  MATH  Google Scholar 

  18. M. Izadi, S. Dubljevic, Backstepping output feedback control of moving boundary parabolic PDEs. Eur. J. Control 21, 27 – 35 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  19. H.K. Khalil, J.W. Grizzle, Nonlinear Systems, vol. 3 (Prentice Hall, Upper Saddle River, NJ, 2002)

    Google Scholar 

  20. M. Krstic, Compensating actuator and sensor dynamics governed by diffusion PDEs. Syst. Control Lett. 58, 372–377 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  21. M. Krstic, Delay Compensation for Nonlinear, Adaptive, and PDE Systems (Birkhauser, Boston, 2009)

    Book  MATH  Google Scholar 

  22. M. Krstic, Input delay compensation for forward complete and strict-feedforward nonlinear systems. IEEE Trans. Autom. Control 55(2), 287–303 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  23. M. Krstic, A. Smyshlyaev, Adaptive boundary control for unstable parabolic PDEs–Part I: Lyapunov design. IEEE Trans. Autom. Control 53(7), 1575–1591 (2008)

    Article  MATH  Google Scholar 

  24. M. Krstic, A. Smyshlyaev, Backstepping boundary control for first-order hyperbolic PDEs and application to systems with actuator and sensor delays. Syst. Control Lett. 57, 750–758 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  25. M. Krstic, A. Smyshlyaev, Boundary Control of PDEs: A Course on Backstepping Designs (SIAM, Singapore, 2008)

    Book  MATH  Google Scholar 

  26. M. Krstic, I. Kanellakopoulos, P.V. Kokotovic, Nonlinear and Adaptive Control Design (Wiley, New York, 1995)

    MATH  Google Scholar 

  27. F. Kuznik, J. Virgone, J. Noel, Optimization of a phase change material wallboard for building use. Appl. Therm. Eng. 28(11), 1291–1298 (2008)

    Article  Google Scholar 

  28. A. Maidi, J.-P. Corriou, Boundary geometric control of a linear Stefan problem. J. Process Control 24, 939–946 (2014)

    Article  MATH  Google Scholar 

  29. S.J. Moura, F.B. Argomedo, R. Klein, A. Mirtabatabaei, M. Krstic, Battery state estimation for a single particle model with electrolyte dynamics. IEEE Trans. Control Syst. Technol. 25(2), 453–468 (2016)

    Article  Google Scholar 

  30. S.J. Moura, N.A. Chaturvedi, M. Krstic, Adaptive partial differential equation observer for battery state-of-charge/state-of-health estimation via an electrochemical model. J. Dyn. Syst. Meas. Control 136(1), 011015-1–011015-11 (2014)

    Google Scholar 

  31. T.R. Oliveira, M. Krstic, D. Tsubakino, Extremum seeking for static maps with delays. IEEE Trans. Autom. Control 62(4), 1911–1926 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  32. N. Petit, Control problems for one-dimensional fluids and reactive fluids with moving interfaces, in Advances in the Theory of Control, Signals and Systems with Physical Modeling. Lecture Notes in Control and Information Sciences, vol. 407 (EPF, Lausanne, 2010), pp. 323–337

    Google Scholar 

  33. B. Petrus, J. Bentsman, B.G. Thomas, Application of enthalpy-based feedback control methodology to the two-sided Stefan problem, in American Control Conference (ACC) (IEEE, Portland, 2014), pp. 1015–1020

    Google Scholar 

  34. B. Petrus, J. Bentsman, B.G. Thomas, Feedback control of the two-phase Stefan problem, with an application to the continuous casting of steel, in Conference on Decision and Control (CDC) (IEEE, Atlanta, 2010), pp. 1731–1736

    Google Scholar 

  35. B. Petrus, J. Bentsman, B.G. Thomas, Enthalpy-based feedback control algorithms for the Stefan problem, in Conference on Decision and Control (CDC) (IEEE, Maui, 2012), pp. 7037–7042

    Google Scholar 

  36. J. Qi, R. Vazquez, M. Krstic, Multi-agent deployment in 3-D via PDE control. IEEE Trans. Autom. Control 60(4), 891–906 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  37. C. Sagert, F. Di Meglio, M. Krstic, P. Rouchon, Backstepping and flatness approaches for stabilization of the stick-slip phenomenon for drilling. IFAC Proc. Vol. 46(2), 779–784 (2013)

    Article  Google Scholar 

  38. A. Smyshlyaev, M. Krstic, Closed-form boundary state feedbacks for a class of 1-D partial integro-differential equations. IEEE Trans. Autom. Control 49(12), 2185–2202 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  39. A. Smyshlyaev, M. Krstic, On control design for PDEs with space-dependent diffusivity or time-dependent reactivity. Automatica 41(9), 1601–1608 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  40. A. Smyshlyaev, M. Krstic, Adaptive boundary control for unstable parabolic PDEs–Part II: estimation-based designs. Automatica 43(9), 1543–1556 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  41. A. Smyshlyaev, M. Krstic, Adaptive boundary control for unstable parabolic PDEs–Part III: output feedback examples with swapping identifiers, Automatica 43(9), 1557–1564 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  42. G.A. Susto, M. Krstic, Control of PDE–ODE cascades with Neumann interconnections. J. Franklin Inst. 347, 284–314 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  43. S. Tang, C. Xie, State and output feedback boundary control for a coupled PDE–ODE system. Syst. Control Lett. 60, 540–545 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  44. R. Vazquez, M. Krstic, Control of Turbulent and Magnetohydrodynamic Channel Flows: Boundary Stabilization and State Estimation (Birkhauser, Boston, 2008)

    MATH  Google Scholar 

  45. R. Vazquez, M. Krstic, Boundary control of coupled reaction-advection-diffusion systems with spatially-varying coefficients. IEEE Trans. Autom. Control 62(4), 2026–2033 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  46. R. Vazquez, M. Krstic, Boundary control and estimation of reaction-diffusion equations on the sphere under revolution symmetry conditions. Int. J. Control 92(1), 2–11 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  47. J. Wang, M. Krstic, Delay-compensated control of sandwiched ODE-PDE-ODE hyperbolic systems for oil drilling and disaster relief. Preprint available at https://arxiv.org/abs/1910.05948 (2019)

  48. J. Wang, S. Koga, Y. Pi, M. Krstic, Axial vibration suppression in a partial differential equation model of ascending mining cable elevator. J. Dyn. Syst. Meas. Control 140(11), 111003 (2018)

    Google Scholar 

  49. J. Wang, Y. Pi, M. Krstic, Balancing and suppression of oscillations of tension and cage in dual-cable mining elevators. Automatica 98, 223–238 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  50. J. Wang, S.X. Tang, Y. Pi, M. Krstic, Exponential regulation of the anti-collocatedly disturbed cage in a wave PDE-modeled ascending cable elevator. Automatica 95, 122–136 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  51. J. Wang, S.X. Tang, M. Krstic, Adaptive output-feedback control of torsional vibration in off-shore rotary oil drilling systems. Automatica 111, 108640 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  52. H. Yu, M. Krstic, Traffic congestion control for Aw-Rascle-Zhang model. Automatica 100, 38–51 (2019)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Koga, S., Krstic, M. (2020). State Feedback Control Design for Stefan System. In: Materials Phase Change PDE Control & Estimation. Systems & Control: Foundations & Applications. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-58490-0_2

Download citation

Publish with us

Policies and ethics