Introduction to the Discrete LSDP Controller and the Performance by Exploiting the Gap Metric Theory

Ali Ameur Haj Salah(1*), Tarek Garna(2), Hassani Messaoud(3)

(1) Laboratory of Automatic Control, Signal and Image Processing (ATSI), National Engineering School of Monastir (ENIM), 5000, Monastir, Tunisia
(2) Laboratory of Automatic Control, Signal and Image Processing (ATSI), National Engineering School of Monastir (ENIM), 5000, Monastir, Tunisia
(3) Laboratory of Automatic Control, Signal and Image Processing (ATSI), National Engineering School of Monastir (ENIM), 5000, Monastir, Tunisia
(*) Corresponding author


DOI's assignment:
the author of the article can submit here a request for assignment of a DOI number to this resource!
Cost of the service: euros 10,00 (for a DOI)

Abstract


This paper describes the introduction to the discrete LSDP (Loop Shaping Design Procedure) controller in order to develop a robust controller which guarantees the stability for the family of uncertain systems. To determine the validity domain of the discrete LSDP (DLSDP) we propose to use the gap metric theory for studying robustness properties as a function of the stability margin provided by the DLSDP controller with respect to parameter uncertainties. The latter are modeled by using the left normalized coprime factors (NCFs) representation. The effectiveness of the DLSDP controller is validated on a second-order electrical linear system.
Copyright © 2013 Praise Worthy Prize - All rights reserved.

Keywords


Discrete Loop Shaping; DLSDP Controller; Robust Control; Gap Metric

Full Text:

PDF


References


SL. Ballois, and G. Duc, H∞ control of a satellite axis: Loop shaping, controller reduction, and μ-analysis, contr. Eng. Practice, Vol. 4 (Issue 7):1001-1007, 1996.

S. M. Djouadi, and L. Yanyan, On the computation of the gap metric for LTV systems, Systems & Control Letters, Vol. 56 (Issue 11-12):753-758, 2007.

J. C. Doyle, Advances in Multivariable Control, Lecture Notes at ONR/Honeywell Workshop, Minneapolis, Oct. 8-10, 1984.

J. C. Doyle, Synthesis of robust controllers and filters, Proc. IEEE Conf. on Decision and Control, pp. 109-114, San Antonio, Texas, 1983.

J. Feng, A study of optimality in the H∞ loop-shaping design method, Ph.D. dissertation, Department of Engineering, University of Cambridge, 1995.

K. Glover, and AP. Dowling, Control of combustion oscillations via H∞ loop shaping, μ-analysis and integral quadratic constraints, Automatica, Vol. 39 (Issue 2): 219-31, 2003.

M. Green, D.J.N. Limebeer, Linear Robust Control (Prentice-Hall, 1995).

T.T. Georgiou, and M. Smith, Optimal Robustness in the Gap Metric, IEEE Transactions on Automatic Control, Vol. 35 (Issue 6):673-686, 1990.

O. Galan, J. A. Romagnoli, A. Palazoglu, and Y. Arkun, Gap metric concept and implications for multilinear model-based controller design, Industrial Engineering Chemical Research, Vol. 42 (Issue 10): 2189-2197, 2003.

M. Green, K. Glover, D. Limebeer, and J.C. Doyle, A J-spectral factorization approach to H∞ control, SIAM J. of Control and Opt., Vol. 28 (Issue 6):1350-1371, 1990.

J. Jayender, RV. Patel, S. Nikumb, M. Ostojic, H∞ loop shaping controller for shape memory alloy (SMA) actuators, In: Proceedings of the 44th IEEE Conference on Decision and Control and European Control Conference, Seville, pp. 653-658, Spain, Dec 12-15, 2005.

S. Kaitwanidvilai, and M. Parnichkun, Genetic algorithm-based fixed-structure robust H∞ loop shaping control of a pneumatic servo system, J. Robot Mechatron, Vol. 16 (Issue 4): 362-73, 2004.

D. McFarlane, and K. Glover, A Loop Shaping Design Procedure Using H∞ Synthesis, IEEE Transactions on Automatic Control, Vol. 37 (Issue 6):759-769, 1992.

D. McFarlane, and K. Glover, Robust Controller Design Using Normalized Coprime Factor Plant Descriptions, Vol. 138 of Lecture Notes in Control and Information Sciences, Springer-Verlag, Berlin. 1990.

S. Mammar, and G. Duc, A loop shaping Hinfini design: Application to the robust stabilization of a helicopter, Control Engineering Practice, Vol. 1, (Issue 2):349-356, 1993.

E. Prempain, and I. Postlethwaite, Static H∞ loop shaping control of fly-by-wire helicopter, Automatica, Vol. 41, (Issue 9):1517–1528, 2005.

A. Tahar, M. N. Abdelkrim, Multimodel H∞ Loop Shaping Control of Uncertain Weakly Coupled Systems, (2011) International Review of Automatic Control (IREACO), 4 (3), pp. 351-361.

K. Zhou, J. C. Doyle, K. Glover, Robust and Optimal Control (Prentice-Hall, 1996).

Vachirasricirikul, S., Ngamroo, I., Heuristic optimization based-fixed structure robust H∞ loop shaping controller design with automatic weights selection of controllable distributed generations for Microgrid stabilization, (2012) International Review of Electrical Engineering (IREE), 7 (2), pp. 4146-4154.

Rajaa Vikhram, G.Y., Latha, S., Robust shunt FACTS controller design for power system damping improvement, (2013) International Review of Electrical Engineering (IREE), 8 (2), pp. 792-801.

L. Saidi, S. Benacer, M. Boulemden, A New Sensitivity Function Loop Shaping Design Based on Extended Observers, (2011) International Review of Automatic Control (IREACO), 4 (5), pp. 594-601.

Dchich, K., Zaafouri, A., Chbeb, A., Jemli, M., Position sensorless robust control of PMSM using the Extended Kalman Filter algorithm, (2013) International Review on Modelling and Simulations (IREMOS), 6 (2), pp. 380-386.


Refbacks

  • There are currently no refbacks.



Please send any question about this web site to info@praiseworthyprize.com
Copyright © 2005-2020 Praise Worthy Prize