Technical Brief

Three-Stage Feedback Controller Design With Applications to Three Time-Scale Linear Control Systems

[+] Author and Article Information
Verica Radisavljevic-Gajic

Department of Mechanical Engineering,
Villanova University,
800 East Lancaster Avenue,
Villanova, PA 19085
e-mail: verica.gajic@villanova.edu

Milos Milanovic

Department of Mechanical Engineering,
Villanova University,
800 East Lancaster Avenue,
Villanova, PA 19085
e-mail: mmilano5@villanova.edu

Garrett Clayton

Department of Mechanical Engineering,
Villanova University,
800 East Lancaster Avenue,
Villanova, PA 19085
e-mail: garett.clayton@villanova.edu

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received May 17, 2016; final manuscript received March 10, 2017; published online June 28, 2017. Assoc. Editor: Soo Jeon.

J. Dyn. Sys., Meas., Control 139(10), 104502 (Jun 28, 2017) (10 pages) Paper No: DS-16-1252; doi: 10.1115/1.4036408 History: Received May 17, 2016; Revised March 10, 2017

This paper presents a new technique for design of full-state feedback controllers for linear dynamic systems in three stages. The new technique is based on appropriate partitioning of the linear dynamic system into linear dynamic subsystems. Every controller design stage is done at the subsystem level using only information about the subsystem (reduced-order) matrices. Due to independent design in each stage, different subsystem controllers can be designed to control different subsystems. Partial subsystem level optimality and partial eigenvalue subsystem assignment can be achieved. Using different feedback controllers to control different subsystems of a system has not been present in any other known linear full-state feedback controller design technique. The new technique requires only solutions of reduced-order subsystem level algebraic equations. No additional assumptions were imposed except what is common in linear feedback control theory (the system is controllable (stabilizable)) and theory of three time-scale linear systems (the fastest subsystem state matrix is invertible)). The local full-state feedback controllers are combined to form a global full-state controller for the system under consideration. The presented results are specialized to the three time-scale linear control systems that have natural decomposition into slow, fast, and very fast subsystems, for which numerical ill conditioning is removed and solutions of the design algebraic equations are easily obtained. The proposed three-stage three time-scale feedback controller technique is demonstrated on the eighth-order model of a fuel cell model.

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Radisavljevic-Gajic, V. , and Rose, R. , 2014, “ A New Two-Stage Design of Feedback Controllers for a Hydrogen Gas Reformer,” Int. J. Hydrogen Energy, 39(22), pp. 11738–11748. [CrossRef]
Radisavljevic-Gajic, V. , 2014, “ A Simplified Two-Stage Design of Linear Discrete-Time Feedback Controllers,” ASME J. Dyn. Syst. Meas. Control, 137(1), p. 014506. [CrossRef]
Radisavljevic-Gajic, V. , 2015, “ Two-Stage Feedback Design for a Class of Linear Discrete-Time Systems With Slow and Fast Variables Modes,” ASME J. Dyn. Syst. Meas. Control, 137(8), p. 084502. [CrossRef]
Chen, T.-C. , 2009, Linear System Theory and Design, Oxford University Press, New York.
Sinha, A. , 2007, Linear Systems: Optimal and Robust Control, CRC Press, Boca Raton, FL, Chap. 3–4.
Zhou, K. , and Doyle, J. , 1998, Essential of Robust Control, Prentice Hall, Upper Saddle River, NJ.
Radisavljevic, V. , 2006, “ Simple Practical Classical-H2 Robust Controller,” AIAA J. Guid. Control Dyn., 29(6), pp. 1417–1420. [CrossRef]
Veillete, R. , 1995, “ Reliable Linear-Quadratic State-Feedback Control,” Automatica, 31(1), pp. 137–143. [CrossRef]
Radisavljevic-Gajic, V. , 2015, “ Full- and Reduced-Order Linear Observer Implementations in MATLAB/Simulink,” IEEE Control Syst., 35(5), pp. 91–101. [CrossRef]
Kokotovic, P. , Khalil, H. , and O'Reilly, J. , 1999, “ Linear Feedback Control,” Singular Perturbation Methods in Control: Analysis and Design, SIAM, Philadelphia, PA, pp. 93–156. [CrossRef]
Naidu, D. , and Calise, A. , 2001, “ Singular Perturbations and Time Scales in Guidance and Control of Aerospace Systems: A Survey,” AIAA J. Guid. Control Dyn., 24(6), pp. 1057–1078. [CrossRef]
Kuehn, C. , 2015, Multiple Time Scale Dynamics, Springer, New York. [CrossRef]
Hsiao, F. H. , Hwang, J. D. , and Pan, S. T. , 2001, “ Stabilization of Discrete Singularly Perturbed Systems Under Composite Observer-Based Control,” ASME J. Dyn. Syst. Meas. Control, 123(1), pp. 132–139. [CrossRef]
Kim, B.-S. , Kim, Y.-Y. , and Lim, M.-T. , 2004, “ LQG Control for Nonstandard Singularly Perturbed Discrete-Time Systems,” ASME J. Dyn. Syst. Meas. Control, 126(4), pp. 860–864. [CrossRef]
Amjadifard, R. , Beheshti, M. , and Yazdanpaanah, M. , 2011, “ Robust Stabilization for a Class of Singularly Perturbed Systems,” ASME J. Dyn. Syst. Meas. Control, 133(5), p. 051004. [CrossRef]
Medanic, J. , 1982, “ Geometric Properties and Invariant Manifolds of the Riccati Equation,” IEEE Trans. Autom. Control, 27(3), pp. 670–677. [CrossRef]
Shimjith, S. R. , Tiwari, A. P. , and Bandyopadhyay, B. , 2011, “ A Three-Time-Scale Approach for Design of Linear State Regulators for Spatial Control of Advanced Heavy Water Reactor,” IEEE Trans. Nucl. Sci., 58(3), pp. 1264–1276. [CrossRef]
Munje, R. K. , Parkhe, J. G. , and Patre, B. M. , 2015, “ Control of Xenon Oscillations in Advanced Heavy Water Reactor Via Two-Stage Decomposition,” Ann. Nucl. Energy, 77, pp. 326–334. [CrossRef]
Pukrushpan, J. , Stefanopoulou, A. , and Peng, H. , 2004, Control of Fuel Cell Power Systems: Principles, Modeling, Analysis, and Feedback Design, Springer, New York. [CrossRef]
Pukrushpan, J. , Peng, H. , and Stefanopoulou, A. , 2004, “ Control Oriented Modeling and Analysis for Automotive Fuel Cell Systems,” ASME J. Dyn. Syst. Meas. Control, 126(1), pp. 14–25. [CrossRef]
Graham, R. , Knuth, D. , and Patashnik, O. , 1989, Concrete Mathematics, Addison-Wesley, Boston, MA.
Golub, G. , and Van Loan, C. , 2012, Matrix Computations, Academic Press, Cambridge, MA.
Bartels, R. , and Stewart, G. , 1972, “ Solution of the Matrix Equation AX + XB + C = 0,” Commun. ACM, 15(9), pp. 820–826. [CrossRef]





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