Modeling and Performance Evaluation of P, PI, PD and PID Temperature Controller for Water Bath

  • J. S. Madugu Department of Pure and Applied Physics, Adamawa State University, Mubi, Adamawa State, Nigeria
  • P. G. Vasira Department of Pure and Applied Physics, Adamawa State University, Mubi, Adamawa State, Nigeria
Keywords: Water bath, PID, compensator, offset, response, heater, steady-state, open-loop.

Abstract

Water bath temperature control is one of the most widely used processes in academic laboratories and industries. It usually contains single or mixture of liquid substances whose temperature is the subject of control. In this paper, a performance evaluation of P, PI, PD, and PID algorithms for the system was investigated. A mathematical model of the first order system was derived using the lumped parameter model. The time constant of the water bath was obtained theoretically and found to be 356s and time lag of 5s. The gain of the heater of 1500 W was computed and found to be 0.047 oC/K. An open loop reaction curve of the system was then obtained by measuring the temperature response to step input against time and plotting same using MATLAB. The P, PI, PD and PID control strategies were subsequently designed to control the temperature of the water bath. The compensators were manually tuned to P = 3000; P = 21.5599, I = 0.0034539; P = 22.7179, D = 0.0067356; and P = 25.4904, I = 0.0034802, D = 10.5302 respectively. These gains were used to manipulate the temperature set points for the water bath. The performance of the MATLAB simulated results were evaluated and compared against each other. The results show that P control requires high step input (3000 W) though the offset could be reduced. The PI control on the other hand exhibits fast response and reduced steady state error. PD control for the plant was found to be highly unstable for all the tuned values of the gains which makes it unfit for the first order system. The PID compensator provided compromise between the P and PI. It exhibited a rise time of 541s, settling time of 794s and an overshoot 1.10%.

References

[1] M. F. Basar and N. Hasim. A Water Bath Control System in a Virtual Laboratory Environment. Journal of Computer Science and Engineering, Volume 9, Issue 1, September 2011.
[2] N. Hasim, M. F. Basar, M. S. Aras. “Design and Development of a Water Bath Control System: A Virtual Laboratory Environment”, IEEE Students Conference on Research and Development (SCOReD, 2011).
[3] M. Khalid and S. Omatu. A neural network controller for a temperature control system, IEEE Control Systems, Vol. 12, pp.58−64, June 1992.
[4] P. M. Mary, N. S. Marimuthu and A. Singh. Design of Intelligent Self-Tuning Temperature Controller for Water Bath Process, International Journal of Imaging Science and Engineering, pp. 121−124, Vol. 1, No. 4, October 2007.
[5] B. Claudia, F. Cesare and R. Riccado.” International Summer School on Fuzzy Logic Control: Advance in Methodology”, Singapore World Scientific, 1998.
[6] K. Shimojima, T. Fukuda and Y. Hasegawa, self-tuning fuzzy modeling with adaptive membership function rules and hierarchical structure based on genetic algorithm, Fuzzy Sets Syst., Vol. 71 pp. 295−309, 1995.
[7] J. G. Dawson, Z. Gao and T. A. Trautzsch. “A Stable Self-Tuning Fuzzy Logic Control System for Industrial Temperature Regulation”.
[8] A. Lindsay, D. Liu, S. Murray and D. Lowe. “Remote Laboratories in Engineering Education Trends in Students’ Perceptions”, Proceedings of the 2007 AaeE Conference, Melbourne.
[9] S. D. Markande, P. M. Joshi, S. K. Katti. Microcontroller Based Temperature Controller Implementation of Fuzzy Logic, IE (I) Journal−CP, Vol. 85, May 2004.
[10] E. H. Goud, A. Harshika, G. Akhil, D. Charishma, K. Bhupathi and I. K. Swamy. Real Time Based Temperature Control Using Arduino. International Journal of Innovations in Engineering and Technology, Volume 8 Issue 2, April, 2017, pp. 209−215.
[11] O. P. Verma, R. Singla and R. Kumar. Intelligent Temperature Controller for Water-Bath System; World Academy of Science, Engineering and Technology. International Journal of Electrical and Computer Engineering, Vol. 6, No. 9, 2012.
[12] P. Madheswari and L. Rose. Temperature Control using Artificial Intelligence in Water Bath System. International Journal on Advanced Electrical and Computer Engineering, Volume-1, Issue-1, 2014.
[13] T. Kativa, B. N. Parvathi, M. Lavanya and M. Arivalagan. Temperature Control Water Bath System using PID Controller, International Journal of Applied Engineering Research, Vol. 10, N0. 4, 2015, pp.3443−3446.
[14] Katsuhiko Ogata (2012). Modern Control Engineering, PHI Learning Private Limited, 5th Edition, New Delhi.
[15] Farhan, A. S. and Albaradi A. R. PID Controllers and Algorithms: Selection and Design Techniques Applied in Mathematical Syaytems Design−Part II. International Journal of Engineering Sciences, 2(5) May, 2013, pp. 191−203.
[16] J. Tavoosi, M. Alaei, B. Jahani and M. A. Daneshwar. A Novel Intelligent Control System Design for Water Bath Temperature Control, Australian Journal of Basic and Applied Sciences, 5(12): 1879−1885.
[17] L. Xinping and Z. Xiaodong. Multi-variable Fuzzy Controller for Water Tank Temperature Control System, International Journal of Digital Content Technology and its Application (JDTA), Volume 6, Number 13, July 2012. doi:10.4156/jdeta.vol6./Issue13:10
[18] Y. V. Parkale. Comparism of ANN Controller and PID Controller for Industrial Water Bath Temperature Control System using MATLAB Environment. International Journal of Computer Applications (0975−8887), Volume 33, No. 2, September 2012.
[19] R. J. Richards. Solving Problems in Control, Longman Scientific and Technical Group Ltd, John Wiley and Sons Inc., New York, 1993.
[20] M. Ramzi, H. Youlal, and M. Haloua. Continuous Time Identification and decentralized PID Controller of an Aerothermic Process, Instrumentation Journal of Smart Sensing and Intelligent Systems, Vol. 5, No. 2. June 2012.
Published
2018-10-15
Section
Articles