Open Access Open Access  Restricted Access Subscription or Fee Access

Novel Design Method for Two Degree of Freedom Controllers

P. Febina Beevi(1*), T. K. Sunil Kumar(2), Jeevamma Jacob(3)

(1) National Institute of Technology, India
(2) Department of Electrical Engineering, National Institute of Technology, India
(3) Department of Electrical Engineering, National Institute of Technology, India
(*) Corresponding author


DOI: https://doi.org/10.15866/ireaco.v8i4.6330

Abstract


This paper proposes the design of a general Two Degree of Freedom (2-DOF) controller and a 2-DOF PID controller using a novel method which combines model order reduction, model matching concepts as well as optimization techniques. The desired spectrum is embodied in the form of a transfer function which can be constructed from a set of time domain specifications such as rise time, settling time, peak over shoot, etc. Another approach to create the model transfer function could be to use the Linear Quadratic Gaussian (LQG) theory for a given set of weighting matrices. The proposed method not only ensures stability of the closed loop system with 2-DOF controller but also guarantees the required performance criteria. The developed method does not pose any restriction on either the order of the model or on the structure/order of the controller transfer function. Moreover this method is computationally simple and easy to implement. Since it is an algebraic method, the problem of finding the parameters of 2-DOF controller is formulated as that of finding the solution of linear non-homogeneous equations. The proposed method yields an output feedback controller instead of an optimal state feedback one. Simulation results demonstrate the effectiveness of the proposed method.
Copyright © 2015 Praise Worthy Prize - All rights reserved.

Keywords


AGTM/AGMP Matching Method; Feedforward Type; Model Matching; Model Order Reduction; 2-DOF Controller; 2-DOF PID Controller

Full Text:

PDF


References


William A. Wolovich, Automatic Control System: Basic analysis & design, (Saunders College Publishing, Harcount Brace College Publishers, New York,1994).

I.M.Horowitz, Synthesis of Feedback Systems, (Academic Press, 1963).
http://dx.doi.org/10.1016/b978-1-4832-3282-9.50014-4

B.C.Kuo, Automatic Control Systems, (Prentice Hall, Englewood Cliffs, NJ, 1995).
http://dx.doi.org/10.1002/aic.690411022

C.A.Desoer and C.L.Gustafson, Algebraic Theory of Linear Multivariable Feedback Systems, IEEE Transaction on Automatic Control, vol 29, pp. 909-917, 1984.
http://dx.doi.org/10.1109/tac.1984.1103410

Don Isarakorn, DC Motor Control using CDM based Two-Degree-of-Freedom Controller for Desired Tracking and Disturbance Rejection Characteristics, 12th International Conference on Control, Automation and Systems, ICC, Jeju Island, Korea, pp. 1167 – 1172, Oct. 2012.

C.M. Liaw, Design of a Two-Degree-of-Freedom Controller for Motor Drives, IEEE Transaction on Automatic Control, vol 37, no.8, pp. 1215-1220, August 1992.
http://dx.doi.org/10.1109/9.151110

Chih-Min Lin and Jiann-Min Wu, Two-degree-of-freedom Optimal Flight Control System Design, IEEE Proceedings of the 35th Conference on Decision and Control, Japan, December 1996.
http://dx.doi.org/10.1109/cdc.1996.572682

Weidong Zhang,Wei Wang,Xing He And Xioming Xu, Analytical Design of New Two-Degree-of-Freedom Controller for Integrating processes, Proceedings of the 42nd IEEE Conference on Decision and Control, Hawaii USA, pp. 2496 – 3619, December 2003.
http://dx.doi.org/10.1109/cdc.2003.1272995

Antonio Visioli, A new design for a PID plus feedforward controller, Journal of Process Control 14, pp. 457-463, 2004.
http://dx.doi.org/10.1016/j.jprocont.2003.09.003

Miluse Viteckova and Antonin Vitecek, Two-Degree of freedom controller tuning for integral plus time delay plants, ICIC Express Letters, vol. 2, no. 3, pp. 225-229, 2008.

Mituhiko Araki and Hidefumi Taguchi, Two-Degree-of-Freedom PID Controllers, International Journal of Control, Automation, and Systems, vol. 1, no. 4, December 2003.
http://dx.doi.org/10.9746/sicetr1965.38.441

Wuhua Hu, Gaoxi Xiao, and Wen-Jian Cai, PID Controller Design Based on Two-Degrees-of-Freedom Direct Synthesis, IEEE Chinese Control and Decision Conference, 2011.
http://dx.doi.org/10.1109/ccdc.2011.5968258

D.E.Rivera. and M.Morari, Control relevant model reduction problem for SISO using H∞ and µ controller synthesis, International Journal of Control, vol. 48, no. 2, pp. 505-527,1987.
http://dx.doi.org/10.1080/00207178708933913

J.G.Truxal, Automatic feedback control system synthesis, (New York, Mc Graw Hill, 1955).

Krishnakumar K. and Goldberg D.E., Control system optimization using Genetic algorithms, Journal of Guidance, Control and Dynamics, vol. 15, no. 3, pp.735-740,May-June 1992.
http://dx.doi.org/10.2514/3.20898

Ali Taki El-Deen, Ahmed Abdel Hakim Mahmoud and Ahmed R. El-Sawi, Optimal PID Tuning for DC Motor Speed Controller Based on Genetic Algorithm, International Review of Automatic Control, vol. 8, no. 1, pp.80-85, 2015.
http://dx.doi.org/10.15866/ireaco.v8i1.4839

G.A.Baker, Essentials of Pade Approximation, (Academic Press, New York, 1975).

Pal.J, An algorithm method for the simplification of linear dynamic scalar systems, International Journal of Control, vol. 43, no. 1, pp. 257-269, 1986.
http://dx.doi.org/10.1080/00207178608933462

S.Banerjee, T.K. Sunil Kumar, J.Pal and D, Prasad, A novel method for controller design for simultaneous stabilization and performance improvement of an electromagnetic levitation system, Asian Journal of Control, vol. 8, no. 1, pp. 50-55, 2006.
http://dx.doi.org/10.1111/j.1934-6093.2007.tb00394.x

J.Pal, Control system design using approximate model matching, System Science(Poland), vol. 19, no. 3, pp. 5-23,1993.

J.Pal, B.Sarvesh and M.K.Ghosh, An algebraic method for controller design, Conrol Theory & Advanced Technology (Japan), vol. 10, no. 4, part 5, pp.2125-2131, Dec.1995.

Jasmine Selvakumari Jeya, I., Suganthi, J., Watermarking relational databases using genetic algorithm with ring crossover technique, (2014) International Review on Computers and Software (IRECOS), 9 (3), pp. 456-467.

Alshraideh, M., Tahat, L., Multiple-population genetic algorithm for solving min-max optimization problems, (2015) International Review on Computers and Software (IRECOS), 10 (1), pp. 9-19.
http://dx.doi.org/10.15866/irecos.v10i1.4612

Deepa, A.J., Kavitha, V., Neurofuzzy and genetic network programming based intrusion detection system, (2014) International Review on Computers and Software (IRECOS), 9 (2), pp. 295-301.

Rajamani, V., Babu, P., Genetic algorithm based Bi level histogram modification framework for image contrast enhancement, (2014) International Review on Computers and Software (IRECOS), 9 (6), pp. 920-927.

Boschett, G., Mariscotti, A., Optimizing the energy efficiency of electric transportation systems operation using a genetic algorithm, (2014) International Review of Electrical Engineering (IREE), 9 (4), pp. 783-791.
http://dx.doi.org/10.15866/iree.v9i4.1532

Zongo, O.A., Oonsivilai, A., Comparison between harmony search algorithm, Genetic algorithm and Particle Swarm Optimization in economic power dispatch, (2015) International Review of Electrical Engineering (IREE), 10 (2), pp. 286-292.
http://dx.doi.org/10.15866/iree.v10i2.5361

Gosálbez, I.G., Lehtonen, M., Stochastic genetic algorithm and its application as a demand control tool for houses with thermal energy storage systems, (2015) International Review on Modelling and Simulations (IREMOS), 8 (3), pp. 284-292.
http://dx.doi.org/10.15866/iremos.v8i3.6045

Essalmi, A., Mahmoudi, H., Bennassar, A., Akherraz, M., Abbou, A., Genetic algorithm vector control of permanent magnet synchronous motor based on neuro space vector modulation, (2014) International Review on Modelling and Simulations (IREMOS), 7 (3), pp. 436-443.

Omar, H., Zaky, E., Ibrahim, G., Elsawy, A., An Algorithm Based Levenberg Marquardt Method with Genetic Algorithm for Solving Continuation Problems, (2013) International Journal on Numerical and Analytical Methods in Engineering (IRENA), 1 (1), pp. 20-30.

Kébé, A., Remy, G., Diallo, D., Sizing and Control Strategy of a Micro-Grid for an Isolated Site: a Case Study in Senegal, (2014) International Journal on Energy Conversion (IRECON), 2 (6), pp. 172-178.

Abdelhakem-Koridak, L., Rahli, M., Benayed, F., Genetic Optimization for Combined Heat and Power Dispatch, (2014) International Journal on Engineering Applications (IREA), 2 (5), pp. 163-168.


Refbacks

  • There are currently no refbacks.



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