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Three-Stage Continuous-Time Feedback Controller Design

  • Verica Radisavljević-Gajić
  • Miloš Milanović
  • Patrick Rose
Chapter
Part of the Mechanical Engineering Series book series (MES)

Abstract

In this chapter, the results of two-stage continuous-time feedback controller design from Chap.  2 are extended to the three-stage feedback controller design. This facilitates control of three subsets of system state variables representing three artificial or natural subsystems of a system under consideration. The presentation follows the recent papers of Radisavljevic-Gajic and Milanovic (2016) and Radisavljevic-Gajic et al. (2017). The new technique introduces simplicity and requires only solutions of reduced-order subsystem level algebraic equations for the design of appropriate local controllers. The local feedback controllers are combined to form a global controller for the system under consideration. The technique presented facilitates designs of independent full-state feedback controllers at the subsystem levels. Different types of local controllers, for example, eigenvalue assignment, robust, optimal in some sense (L1, H2, H,…), observer-driven, Kalman filter-driven controllers, may be used to control different subsystems. This feature has not been available for any other known linear feedback controller design technique.

References

  1. Amjadifard R, Beheshti M, Yazdanpaanah M (2011) Robust stabilization for a singularly perturbed systems. Trans ASME J Dyn Syst Meas Control 133:051004-1–051004-6CrossRefGoogle Scholar
  2. Chen T (2012) Linear system theory and design. Oxford University Press, Oxford, UKGoogle Scholar
  3. Chen C-F, Pan S-T, Hsieh J-G (2002) Stability analysis of a class of uncertain discrete singularly perturbed systems with multiple time delays. Trans ASME J Dyn Syst Meas Control 124:467–472CrossRefGoogle Scholar
  4. Demetriou M, Kazantzis N (2005) Natural observer design for singularly perturbed vector second-order systems. Trans ASME J Dyn Syst Meas Control 127:648–655CrossRefGoogle Scholar
  5. Dimitriev M, Kurina G (2006) Singular perturbations in control systems. Autom Remote Control 67:1–43MathSciNetCrossRefGoogle Scholar
  6. Esteban S, Gordillo F, Aracil J (2013) Three-time scale singular perturbation control and stability analysis for an autonomous helicopter on a platform. Int J Robust Nonlinear Control 23:1360–1392MathSciNetCrossRefGoogle Scholar
  7. Gajic Z, Lim M-T (2001) Optimal control of singularly perturbed linear systems and applications. Marcel Dekker, New YorkCrossRefGoogle Scholar
  8. Gao Y-H, Bai Z-Z (2010) On inexact Newton methods based on doubling iteration scheme for non-symmetric algebraic Riccati equations. Numer Linear Algebra Appl. https://doi.org/10.1002/nla.727MathSciNetCrossRefGoogle Scholar
  9. Golub G, Van Loan C (2012) Matrix computations. Academic PressGoogle Scholar
  10. Graham R, Knuth D, Patashnik O (1989) Concrete mathematics. Addison-Wesley, ReadingzbMATHGoogle Scholar
  11. Hsiao FH, Hwang JD, ST P (2001) Stabilization of discrete singularly perturbed systems under composite observer-based controller. Trans ASME J Dyn Syst Meas Control 123:132–139CrossRefGoogle Scholar
  12. Kokotovic P, Khalil H, O’Reilly J (1999) Singular perturbation methods in control: analysis and design. Academic Press, OrlandoCrossRefGoogle Scholar
  13. Kuehn C (2015) Multiple time scale dynamics. Springer, ChamCrossRefGoogle Scholar
  14. Medanic J (1982) Geometric properties and invariant manifolds of the Riccati equation. IEEE Trans Autom Control 27:670–677MathSciNetCrossRefGoogle Scholar
  15. Munje R, Patre B, Tiwari A (2014) Periodic output feedback for spatial control of AHWR: a three-time-scale approach. IEEE Trans Nucl Sci 61:2373–2382CrossRefGoogle Scholar
  16. Munje R, Parkhe J, Patre B (2015a) Control of xenon oscillations in advanced heavy water reactor via two-stage decomposition. Ann Nucl Energy 77:326–334CrossRefGoogle Scholar
  17. Munje R, Patil Y, Musmade B, Patre B (2015b). Discrete time sliding mode control for three time scale systems. In: Proceedings of the international conference on industrial instrumentation and control, Pune, 28–30 May 2015, pp 744–749Google Scholar
  18. Naidu DS, Calise A (2001) Singular perturbations and time scales in guidance and control of aerospace systems: survey. AIAA J Guid Control Dyn 24:1057–1078CrossRefGoogle Scholar
  19. Pukrushpan J, Stefanopoulou A, Peng H (2004a) Control of fuel cell power systems: principles, modeling and analysis and feedback design. Springer, LondonCrossRefGoogle Scholar
  20. Pukrushpan J, Peng H, Stefanopoulou A (2004b) Control oriented modeling and analysis for automotive fuel cell systems. Trans ASME J Dyn Syst Meas Control 126:14–25CrossRefGoogle Scholar
  21. Radisavljevic V (2011) On controllability and system constraints of a linear models of proton exchange membrane and solid oxide fuel cells. J Power Sources 196:8549–8552CrossRefGoogle Scholar
  22. Radisavljevic-Gajic V, Milanovic M (2016) Three-stage feedback controller design with application to a three-time scale fuel cell system. In: ASME dynamic systems and control conference, MinneapolisGoogle Scholar
  23. Radisavljevic-Gajic V, Milanovic M, Clayton G (2017) Three-stage feedback controller design with applications to three time-scale control systems. ASME J Dyn Syst Meas Control 139:104502-1–104502-10CrossRefGoogle Scholar
  24. Shapira I, Ben-Asher J (2004) Singular perturbation analysis of optimal glide. AIAA J Guid Control Dyn 27:915–918CrossRefGoogle Scholar
  25. Shimjith S, Tiwari A, Bandyopadhyay B (2011a) Design of fast output sampling controller for three-time-scale systems: application to spatial control of advanced heavy water reactor. IEEE Trans Nucl Sci 58:3305–3316CrossRefGoogle Scholar
  26. Shimjith S, Tiwari A, Bandyopadhyay B (2011b) A three-time-scale approach for design of linear state regulators for spatial control of advanced heavy water reactor. IEEE Trans Nucl Sci 58:1264–1276CrossRefGoogle Scholar
  27. Sinha A (2007) Linear systems: optimal and robust control. Francis & Taylor, Boca RatonCrossRefGoogle Scholar
  28. Umbria F, Aracil J, Gordillo F (2014) Three-time-scale singular perturbation stability analysis of three-phase power converters. Asian J Control 16:1361–1372CrossRefGoogle Scholar
  29. Wang Z, Ghorbel F (2006) Control of closed kinematic chains using a singularly perturbed dynamics model. Trans ASME J Dyn Syst Meas Control 128:142–151CrossRefGoogle Scholar
  30. Wedig W (2014) Multi-time scale dynamics of road vehicles. Probab Eng Mech 37:180–184CrossRefGoogle Scholar
  31. Zenith F, Skogestad S (2009) Control of mass and energy dynamics of polybenzimidazole membrane fuel cells. J Process Control 19:15–432CrossRefGoogle Scholar
  32. Zhou K, Doyle J (1998) Essential of robust control. Prentice Hall, Upper Saddle RiverGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Verica Radisavljević-Gajić
    • 1
  • Miloš Milanović
    • 1
  • Patrick Rose
    • 1
  1. 1.Department of Mechanical EngineeringVillanova UniversityVillanovaUSA

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