Monday , June 18 2018

Novel Two Degree of Freedom Model Matching Controller for
Desired Tracking and Disturbance Rejection

National Institute of Technology-Calicut,
P O NITC, Calicut-673601, Kerala, India.,,

ABSTRACT: A control scheme is proposed in the present paper that introduces Two Degree of Freedom (2-DOF) controller to eliminate the effect of disturbances while tracking the desired trajectory, for Two-Input Two-output (TITO) systems, by implementing an original method that infuses three techniques such as the model order reduction, optimization and the approximate model matching techniques. From authors’ knowledge, first time in literature, the objective of this kind of a proposed method is to accomplish a single low order 2-DOF controller, which can handle desired tracking and disturbance rejection simultaneously, using AGTM/AGMP matching method combined with optimization technique. The desired specifications for achieving the set-point tracking may be encompassed inside what resembles a transfer function matrix. This method is directed at ensuring that the closed loop system is stabilized by implementing a 2-DOF controller while also guaranteeing that it is capable of exhibiting the specified performance standards. This method is cost-effective, computationally simple, easy to implement and can be used for the design without any restriction in the structure/order of the model closed loop transfer function or 2-DOF controller. The efficacy of the proposed methodology is realized when it is performed on coupled tank process.

KEYWORDS: AGTM/AGMP matching method; 2-DOF controller; model matching; model order reduction; TITO system.


Novel Two Degree of Freedom Model Matching Controller for Desired Tracking and Disturbance Rejection, Studies in Informatics and Control, ISSN 1220-1766, vol. 26(1), pp. 105-114, 2017.


  1. Antonio Visioli. (2004). A new design for a PID plus feedforward controller, Journal of Process Control, 14, 457-463.
  2. Arjin Nurnsomrarr, Tianchai Suksri & Maitree Thumma. (2007). Design of 2-DOF PI Controller with Decoupling for Coupled-Tank Process, In Proceedings of the International Conference on Control Automation and Systems, COEX, Seoul, Korea, 17-20.
  3. B. C. Kuo. (1995). Automatic Control Systems, Prentice Hall, Englewood Cliffs, NJ.
  4. C. A. Desoer & C. L. Gustafson. (1984). Algebraic Theory of Linear Multivariable Feedback Systems. IEEE Transaction on Automatic Control, 29, 909-917.
  5. Chih-Min Lin & Jiann-Min Wu. (1996). Two-degree-of-freedom Optimal Flight Control System Design. In IEEE Proceedings of the 35th Conference on Decision and Control, Japan, December.
  6. C. M. Liaw. (1992). Design of a Two-Degree-of-Freedom Controller for Motor Drives, IEEE Transaction on Automatic Control, 37 (8), 1215-1220.
  7. Cristina Şerban & Doina Carp, (2016). Optimization of Container Stowage in a Yard Block Using a Genetic Algorithm, Studies in Informatics and Control, 25 (1), 123-130.
  8. D. E. Rivera & M. Morari. (1987). Control relevant model reduction problem for SISO using H and μ controller synthesis, International Journal of Control, 48 (2), 505-527.
  1. Don Isarakorn, (2012). DC Motor Control using CDM based Two-Degree-of-Freedom Controller for Desired Tracking and Disturbance Rejection Characteristics, In Proceedings of the 12th International Conference on Control Automation and Systems, ICC, 1167 – 1172.
  2. G. A. Baker, (1975). Essentials of Pade Approximation, Academic Press,
    New York.
  3. I. M. Horowitz. (1963). Synthesis of Feedback Systems, Academic Press.
  4. J. G. Truxal, (1955). Automatic feedback control system synthesis, Mc Graw Hill, New York.
  5. J. Pal, B. Sarvesh & M. K. Ghosh. (1995). An algebraic method for controller design, Control Theory & Advanced Technology (Japan), 10 (4), 2125-2131.
  6. J. Pal. (1993). Control system design using approximate model matching, System Science(Poland), 19 (3), 5-23.
  7. Khira Dchich, Abderrahmen Zaafouri & Abdelkader Chaari. (2015). Combined Riccati-Genetic Algorithms Proposed for Non-Convex Optimization Problem Resolution – A Robust Control Model for PMSM, Studies in Informatics and Control, 24 (3), 317-328.
  8. Krishnakumar K. & Goldberg D.E. (1992). Control system optimization using Genetic algorithms, Journal of Guidance Control and Dynamics, 15 (3), 735-740.
  9. Miluse Viteckova & Antonin Vitecek. (2008). Two-Degree of freedom controller tuning for integral plus time delay plants, ICIC Express Letters, 2 (3), 225-229.
  10. Mituhiko Araki & Hidefumi Taguchi. (2003). Two-Degree-of-Freedom PID Controllers. International Journal of Control Automation and Systems, 1 (4), 401-411.
  11. Pal. J. (1986). An algorithm method for the simplification of linear dynamic scalar systems, International Journal of Control, 43 (1), 257-269.
  12. Paul Pocatilu & Ion Ivan. (2013). A Genetic Algorithm-based System for Automatic Control of Test Data Generation, Studies in Informatics and Control, 22 (2), 219-226.
  13. P. Febina Beevi, T. K. Sunil Kumar & Jeevamma Jacob. (2016). GA tuned Two Degree of Freedom PID Controller for Time Delay Systems, In Proceedings of International Conference on Innovative Systems, ICIS.
  14. P. Febina Beevi, T. K. Sunil Kumar & Jeevamma Jacob. (2015). Novel Design Method for Two Degree of Freedom Controllers, International Review of Automatic Control, 8 (4), 281-288.
  15. P. Febina Beevi, T. K. Sunil Kumar & Jeevamma Jacob. (2016). Two Degree of Freedom Controller Design By AGTM\AGMP Matching Method for Time Delay Systems, Procedia Technology, Elsevier, 25, 20 – 27.
  16. Peter Dorato, Chaouki Abdallah & Vito Cerone, (1995). Linear-Quadratic Control: An Introduction, Prentice Hall, New Jersey.
  17. S. Banerjee, T. K. Sunil Kumar, J. Pal & D. Prasad. (2006). A novel method for controller design for simultaneous stabilization and performance improvement of an electromagnetic levitation system, Asian Journal of Control, 8 (1), 50-55.
  18. Weidong Zhang, Wei Wang, Xing He & Xioming Xu. (2003). Analytical Design of New Two-Degree-of-Freedom Controller for Integrating processes. In Proceedings of the 42nd IEEE Conference on Decision and Control (pp. 2496 – 3619).
  19. William A. Wolovich. (1994). Automatic Control System: Basic analysis & design, Saunders College Publishing, Harcount Brace College Publishers, New York.
  20. Zhang Wei, Sun Bo, Zhang Xi & Zhang Weidong. (2013). Two-degree-of-freedom Controller Design for MIMO Systems with Multiple Time Delays Based on Inversing Decoupling, In Proceedings of the 32nd Chinese Control Conference, Xi’an, China, 26-28.