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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
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
Chen T (2012) Linear system theory and design. Oxford University Press, Oxford, UK
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
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
Dimitriev M, Kurina G (2006) Singular perturbations in control systems. Autom Remote Control 67:1–43
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
Kokotovic P, Khalil H, O’Reilly J (1999) Singular perturbation methods in control: analysis and design. Academic Press, Orlando
Kuehn C (2015) Multiple time scale dynamics. Springer, Cham
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
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
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
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
Pukrushpan J, Stefanopoulou A, Peng H (2004a) Control of fuel cell power systems: principles, modeling and analysis and feedback design. Springer, London
Shapira I, Ben-Asher J (2004) Singular perturbation analysis of optimal glide. AIAA J Guid Control Dyn 27:915–918
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
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
Sinha A (2007) Linear systems: optimal and robust control. Francis & Taylor, Boca Raton
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
Zenith F, Skogestad S (2009) Control of mass and energy dynamics of polybenzimidazole membrane fuel cells. J Process Control 19:15–432
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this chapter
Cite this chapter
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
Download citation
DOI: https://doi.org/10.1007/978-3-030-10389-7_6
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-10388-0
Online ISBN: 978-3-030-10389-7
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)