Paper:

# An Application of the Modified PID Control System for Heat Flow Experiment

## Takaaki Hagiwara, Kou Yamada, Iwanori Murakami,

Yoshinori Ando, Shun Matsuura, and Satoshi Aoyama

Department of Mechanical System Engineering, Gunma University, 1-5-1 Tenjincho, Kiryu, Gunma 376-8515, Japan

The Proportional-Integral-Derivative (PID) controller structure is the most widely used in industrial applications thanks to its structural simplicity and applicability in solving practical control problems. It is not, however, almighty. Yamada and Hagiwara proposed design modified PID controllers to make control for any plant stable and make admissible sets of P, I, and D parameters mutually independent. Applying modified PID control to practical plants requires that the influence of disturbance in the plant be considered. In many cases, this disturbance is unknown, making it difficulty to attenuate. Although designs have been proposed for modified PID control to attenuate unknown disturbances, little has been done in examining the attenuation of unknown disturbances. We demonstrate the effectiveness of modified PID control in attenuating unknown disturbances for temperature control in heat flow experiments.

*Int. J. Automation Technol.*, Vol.4, No.5, pp. 469-476, 2010.

- [1] N. Suda, “PID contro,” Asakura Shoten, 1992 (in Japanese).
- [2] K. Astrom and T. Hagglund, “PID controllers: Theory design, and tuning,” Instrument Society of America, North Carolina, 1995.
- [3] A. Datta, M. Z. Ho, and S. P. Bhattacharyya, “Structure and Synthesis of PID Controllers,” Springer-Velag, London, 2000.
- [4] J. G. Zieglae and N. B. Nicholes, “Optimum settings for automatic controllers,” Trans. ASME, 64, pp. 759-768, 1942.
- [5] P. Hazebroek and B. L. van der Warden, “The Optimal Adjustment of Regulators,” Trans. ASME, 72, pp. 317-332, 1950.
- [6] P. Hazebroek and B. L. van der Warden, “Theoretical Considerations on the Optimal Adjustment of Regurators,” Trans. ASME, 72, pp. 309-315, 1950.
- [7] W. A. Wolf, “Controller Setting for Optimum Control,” Trans. ASME, 73, pp. 413-418, 1951.
- [8] K. L. Chien, J. A. Hrones, and J. B. Reswick, “On the Automatic Control of Generalized Passive Systems,” Trans. ASME, 74, pp. 175-185, 1952.
- [9] G. H. Cohen and G. A. Coon, “Theoretical Consideration of Retaeded Control,” Trans. ASME, 75, pp. 857-834, 1953.
- [10] A. M. Lopez, J. A. Miller, C. L. Smith, and P. W. Murrill, “Tuning Controllers with Error-Integral Criteria,” Instrumentation Technology, 14, pp. 52-62, 1967.
- [11] J. A. Miller, A. M. Lopez, C. L. Smith, and P. W. Murrill, “A Comparison of Controller Tuning Techniques,” Controll Engineering, 14, pp. 72-75, 1967.
- [12] T. Kitamori, “A method of control system design based upon partial knowledge about controlled process,” Transactions of the Society of Instrument and Control Engineers, 15-4, pp. 549-555, 1979 (in Japanese).
- [13] T. Kitamori, “Design method for PID control systems,” Journal of the Society of the Instrument and Congtrol Engineers, 19-4, pp. 382-391, 1980 (in Japanese).
- [14] P. Cominos and N. Munro, “PID Controllers: Recent Tuning Methods and Design to Specification,” IEE Proceedings, 149, pp. 46-53, 2002.
- [15] F. Zheng, Q. G. Wang, and T. H. Lee, “On the Design of Multivariable PID Controllers via LMI Approach,” Automatica, 38-3, pp. 517-526, 2002.
- [16] C. Lin, Q. G.Wang, and T. H. Lee, “An Improvement on Multivariable PID Controller Design via Iterative LMI Approach,” Automatica, 40-3, pp. 519-525, 2004.
- [17] N. Viorel, M. Constantin, A. Dorel, and C. Emil, “Aspects of Pole Placement Technique in Symmetrical Optimum Method for PID Controller Design,” Preprints of the 16th IFAC World Congress DVD-ROM, 2005.
- [18] K. Tamura and K. Shimizu, “Eigenvalue Assignment Method by PID Control for MIMO System,” Transactions of The Institute of Systems, Control and Information Engineers, 19-5, pp. 193-202, 2006 (in Japanese).
- [19] J. Yang, “Parameter Plane Control Design for a Two-tank Chemical Reactor Systems,” Journal of the Franklin Institute, 331B-1, pp. 61-76, 1994.
- [20] M. T. Ho, A. Datta, and S. P. Bhattacharyya, “A linear programming characterization of all stabilizing PID controllers,” Proceedings of the American Control Conference 1997, pp. 3922-3928, 1997.
- [21] K. Yamada and T. Moki, “A design method for PI control for minimum phase systems,” Intelligent Engineering Systems Through Artificial Neural Networks, Vol.13, pp. 571-576, 2003.
- [22] K. Yamada, “Modified PID controllers for minimum phase systems and their practical application,” Proceedings of The 2005 Electrical Engineering/Electronics, Computer, Telecommunication, and Information Technology (ECTI) International Conference, Vol.II of II, pp. 457-460, 2005.
- [23] K. Yamada, N. Matsushima, and T. Hagiwara, “A design method for modified PID controllers for stable plants,” Proceedings of the 2006 Electrical Engineering/Electronics, Computer, Telecommunication, and Information Technology (ECTI) International Conference, Vol.I of II, pp. 123-126, Ubon Ratchathani, Thailand, 2006.
- [24] K. Yamada, N. Matsushima, and T. Hagiwara, “A design method for modified PID controllers for stable plants,” ECTI Transactions on Electrical Eng., Electronics, and Communications, Vols.5-1, pp. 31-40, 2007.
- [25] K. Yamada and T. Hagiwara, “A design method of modified PID controller for unstable plants,” Intelligent Engineering System Through Artificial Neural Networks, Vol.16, pp. 753-758, 2006.
- [26] K. Yamada, T. Hagiwara, and Y. Shimizu, “A design method of robust stabilizing modified PID controllers,” Theoretical and Applied Mechanics, Vol.56, pp. 123-134, 2007.
- [27] K. Yamada, I. Murakami, Y. Ando, T. Hagiwara, Y. Imai, and M. Kobayashi, “The parametrization of all disturbance observers,” ICIC Express Letters, An International Journal of Research and Surveys, Vol.2, No.4, pp. 421-426, 2008.
- [28] M. Vidyasagar, “Control System Synthesis –A factorization approach–,” MIT Press, 1985.
- [29] K. Yamada and W. Kinoshita, “New state space design method of stable filtered inverse systems and their application,” Transactions of the Institute of Systems, Control and Information Engineers, Vol.16, No.2, pp. 85-93, 2003.
- [30] T. Hagiwara, K. Yamada, I. Murakami, Y. Ando, and S. Matsuura, “A design method for modified PID control systems to attenuate unknown output disturbances,” (submitted).