Abstract
In this chapter, we first present a general algorithm for a two-stage feedback controller design for linear continuous-time, time-invariant, dynamic systems following the results of Radisavljevic-Gajic and Rose (2014), Sect. 2.1. The proposed design significantly reduces the computational requirements and provides flexibility of designing different types of controllers for different dynamic parts of the system – subsystems that form the given system.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Ali J, Hoang N, Hissain M, Dochain D (2015) Review and classification of recent observers applied in chemical process systems. Comput Chem Eng 76:27–41
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
Bingulac S, Van Landingham H (1993) Algorithms for computer aided design of multivariable control systems. Marcel Dekker, New York
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
Cipiti F, Pino L, Vita A, Lagana M, Rucupero V (2013) Experimental investigation on a methane fuel processor for polymer electrolyte fuel cells. Int J Hydrogen Energy 38:2387–2397
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
Dong X, El-Gorashi T, Elmirghani J (2012) Use of renewable energy in an IP over WDM network with data centers. IET Optoelectron 6:155–164
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.727
Golub G, Van Loan C (2012) Matrix computations. Academic Press
Gou B, Na W, Diong B (2010) Fuel cells: modeling, control, and applications. CRC Press Taylor & Francis Group, Boca Raton
Hoffmann P, Dorgan B (2012) Tomorrow’s energy: hydrogen, ‘fuel cells, and prospects for a cleaner planet. MIT Press, Cambridge, MA
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
Khalil H (2002) Nonlinear systems. Prentice Hall, Upper Saddle River
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
Laghrouche S, Harmouche M, Ahmed F, Chitour Y (2015) Control of PEMFC air-feed system using Lyapunov-based robust and adaptive higher order sliding mode control. IEEE Trans Control Syst Technol 23:1594–1601
Laurim D, Salcedo J, Garcia-Nieto S, Martinez M (2010) Model predictive control relevant identification: multiple input multiple output against multiple input single output. IET Control Theory Appl 4:1756–1766
Matraji I, Laghtouche S, Jemei S, Wack M (2013) Robust control of the PEM fuel cell air-feed system via sub-optimal second order sliding model. Appl Energy 104:945–957
Matraji I, Ahmed F, Laghrouche S, Wack M (2015) Comparison of robust and adaptive second order sliding mode control in PEMFC air-feed systems. Int J Hydrogen Energy 40:9491–9504
Medanic J (1982) Geometric properties and invariant manifolds of the Riccati equation. IEEE Trans Autom Control 27:670–677
Na K, Gou B (2008) Feedback linearization based nonlinear control for PEM fuel cells. IEEE Trans Energy Convers 23:179–190
Na K, Gou B, Diong B (2007) Nonlinear control of PEM fuel cells by exact linearization. IEEE Trans Ind Appl 43:1426–1433
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
Ogata K (1995) Discrete-time control systems. Prentice Hall, Englewood Cliffs
Phillips R (1980a) Reduced order modeling and control of two-time scale discrete systems. Int J Control 31:65–780
Phillips R (1980b) Two-stage design of linear feedback controls. IEEE Trans Autom Control 25:1220–1223
Phillips R (1983) The equivalence of time-scale decomposition techniques used in the analysis and design of linear systems. Int J Control 37:1239–1257
Pilloni A, Pisano A, Usai E (2015) Observer based air excess ratio control of a PEM fuel cell system via high order sliding mode. IEEE Trans Ind Electron 6:1–10
Pukrushpan J, Stefanopoulou A, Peng H (2004a) Control of fuel cell power systems: principles, modeling and analysis and feedback design. Springer, London
Pukrushpan J, Peng H, Stefanopoulou A (2004b) Control oriented modeling and analysis for automotive fuel cell systems. Trans ASME J Dyn Syst Meas Control 126:14–25
Pukrushpan J, Stefanopoulou A, Varigonda S, Eborn J, Haugstteter C (2006) Control-oriented model of fuel processor for hydrogen generation in fuel cell applications. Control Eng Pract 14:277–293
Radisavljevic V (2011) On controllability and system constraints of a linear models of proton exchange membrane and solid oxide fuel cells. J Power Sources 196:8549–8552
Radisavljevic-Gajic V (2015c) Full- and reduced-order linear observer implementations in MATLAB/Simulink. IEEE Control Syst Mag 35:91–101
Radisavljevic-Gajic V, Rose P (2014) A new two stage design of feedback controllers for a hydrogen gas reformer. Int J Hydrogen Energy 39:11738–11748
Radisavljevic-Gajic V, Rose P, Clayton G (2015) Two-stage design of linear feedback controllers for proton exchange membrane fuel cells. In: ASME dynamic systems and control conference, Columbus, doi: https://doi.org/10.1115/DSCC2015-9973
Serra M, Aguado J, Ansede X, Riera J (2005) Controllability analysis of decentralized linear controllers for polymeric fuel cells. J Power Sources 151:93–102
Shapira I, Ben-Asher J (2004) Singular perturbation analysis of optimal glide. AIAA J Guid Control Dyn 27:915–918
Simoncini S (2016) Computational methods for linear matrix equations. SIAM Rev 58:377–441
Sinha A (2007) Linear systems: optimal and robust control. Francis & Taylor, Boca Raton
Stewart G (1973) Matrix computations. Academic Press
Tong S, Qian D, Fang J, Li H (2013) Integrated modeling and variable fuzzy control of a hydrogen-air fuel cell system. Int J Electrochem Sci 8:3636–3652
Tsourapas V, Stefanopoulou A, Sun J (2007) Model-based control of an integrated fuel cell and fuel processor with exhaust heat regulation. IEEE Trans Control Syst Technol 15:233–244
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
Wang F-C, Guo Y-F (2015) Robustness analysis of PEMFC systems on the production line. Int J Hydrogen Energy 40:1959–1966
Wang Y-X, Kim Y-B (2014) Real-time control of air excess ratio of a PEM fuel cell system. IEEE/ASME Trans Mechatron 19:852–861
Zhou K, Doyle J (1998) Essential of robust control. Prentice Hall, Upper Saddle River
Zhu J, Zhang D, King K (2001) Reforming of CH4 by partial oxidation: thermodynamic and kinetic analysis. Fuel 80:899–905
Nehrir M, Wang C (2009) Modeling and control of fuel cells: distributed generation applications. Wiley, Hoboken
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). Continuous-Time Two-Stage 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_2
Download citation
DOI: https://doi.org/10.1007/978-3-030-10389-7_2
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)