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Four-Stage Continuous-Time Feedback Controller Design

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Part of the book series: Mechanical Engineering Series ((MES))

Abstract

In this chapter, the results of three-stage continuous-time feedback controller design from Chap. 4 are extended to the four-stage feedback controller design. This facilitates independent control of four subsets of system state variables representing four artificial or natural subsystems of a system under consideration. The newly derived technique requires only solutions of reduced-order subsystem level algebraic equations for the design of appropriate local feedback controllers using only the corresponding subsystem state feedback (partial feedback). 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, and observer-based controllers, may be used to control different subsystems. This feature has not been available for any other known linear feedback controller design technique.

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References

  • Amjadifard R, Beheshti M, Yazdanpaanah M (2011) Robust stabilization for a singularly perturbed systems. Trans ASME J Dyn Syst Meas Control 133:051004-1–051004-6

    Article  Google Scholar 

  • Chen T (2012) Linear system theory and design. Oxford University Press, Oxford, UK

    Google Scholar 

  • 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 124:467–472

    Article  Google Scholar 

  • Demetriou M, Kazantzis N (2005) Natural observer design for singularly perturbed vector second-order systems. Trans ASME J Dyn Syst Meas Control 127:648–655

    Article  Google Scholar 

  • Dimitriev M, Kurina G (2006) Singular perturbations in control systems. Autom Remote Control 67:1–43

    Article  MathSciNet  Google Scholar 

  • 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 123:132–139

    Article  Google Scholar 

  • Kokotovic P, Khalil H, O’Reilly J (1999) Singular perturbation methods in control: analysis and design. Academic Press, Orlando

    Book  Google Scholar 

  • Kuehn C (2015) Multiple time scale dynamics. Springer, Cham

    Book  Google Scholar 

  • Munje R, Patre B, Tiwari A (2014) Periodic output feedback for spatial control of AHWR: a three-time-scale approach. IEEE Trans Nucl Sci 61:2373–2382

    Article  Google Scholar 

  • Munje R, Parkhe J, Patre B (2015a) Control of xenon oscillations in advanced heavy water reactor via two-stage decomposition. Ann Nucl Energy 77:326–334

    Article  Google Scholar 

  • 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 744–749

    Google Scholar 

  • Naidu DS, Calise A (2001) Singular perturbations and time scales in guidance and control of aerospace systems: survey. AIAA J Guid Control Dyn 24:1057–1078

    Article  Google Scholar 

  • Pukrushpan J, Stefanopoulou A, Peng H (2004a) Control of fuel cell power systems: principles, modeling and analysis and feedback design. Springer, London

    Book  Google Scholar 

  • Shapira I, Ben-Asher J (2004) Singular perturbation analysis of optimal glide. AIAA J Guid Control Dyn 27:915–918

    Article  Google Scholar 

  • 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 58:3305–3316

    Article  Google Scholar 

  • 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 58:1264–1276

    Article  Google Scholar 

  • Sinha A (2007) Linear systems: optimal and robust control. Francis & Taylor, Boca Raton

    Book  Google Scholar 

  • Wang Z, Ghorbel F (2006) Control of closed kinematic chains using a singularly perturbed dynamics model. Trans ASME J Dyn Syst Meas Control 128:142–151

    Article  Google Scholar 

  • Zenith F, Skogestad S (2009) Control of mass and energy dynamics of polybenzimidazole membrane fuel cells. J Process Control 19:15–432

    Article  Google Scholar 

Download references

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Radisavljević-Gajić, V., Milanović, M., Rose, P. (2019). Four-Stage Continuous-Time Feedback Controller Design. In: Multi-Stage and Multi-Time Scale Feedback Control of Linear Systems with Applications to Fuel Cells. Mechanical Engineering Series. Springer, Cham. https://doi.org/10.1007/978-3-030-10389-7_6

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