Sateesh Kumar VAVILALA, Vinopraba THIRUMAVALAVAN, Radhakrishnan THOTA, Sivakumaran NATARAJAN

Design of the fractional order internal model controller using the swarm intelligence techniques for the coupled tank system

The coupled tank system (comprising two tanks) is used in the chemical industries, water treatment plants etc. Level control of the coupled tank system is a common problem in the process control industry. This work proposes a fractional order internal model controller (FOIMC) with a higher order fractional filter for the level control of the coupled tank system. A first order plus delay time (FOPDT) model of the system is used in the controller design. FOIMC has advantages like robustness to changes in the system gain and extended stability margins. The proposed higher order fractional filter makes the controller physically realizable and quickly roll off the magnitude Bode plot, neglecting the high frequency noise. The particle swarm optimisation (PSO) algorithm is a swarm intelligence based algorithm used for the optimisation problems. The parameters of the FOIMC are optimized with the PSO algorithm by minimizing an objective function constructed using time domain specifications. The novel objective function includes weighted peak overshoot, settling time, and integral square error. A MATLAB (MathWorks, Inc., Natick, MA, USA) based tool, fractional order modelling and control (FOMCON) is used to simulate the fractional order controller. Performance of the proposed FOIMC is compared with two state of the art. Robustness to change in the operating point (tank height) is verified. The proposed FOIMC and the state of the art controllers are implemented on the laboratory setup, and the experimental results are compared

PDF

___

1] Sathish Kumar K, Kirubakaran V, Radhakrishnan TK. Real time modeling and control of three tank hybrid system. Chemical Product and Process Modelling 2017; 13 (1): 1-10. doi: 10.1515/cppm-2017-0016
[2] Damrudhar, Tanti DK. Comparative performance analysis for two tanks liquid level control system with various controllers using MATLAB. International Journal of Latest Trends in Engineering and Technology 2016; 7 (2): 345-352. doi: 10.21172/1.72.555
[3] Lakshmanprabu SK, Banu US. Adaptive multiloop IMC based PID controller tuning using bat optimisation algorithm for two interacting conical tank process. International Journal of Advanced Intelligence Paradigm 2019; 13 (3): 263-287. doi: 10.1504/IJAIP.2019.101979
[4] Verma B, Padhy PK. Indirect IMC-PID controller design. IET Control Theory Applications 2019; 13 (2): 297-305. doi: 10.1049/iet-cta.2018.5454
[5] Podlubny I, Dorack L, Kostial I. On fractional derivatives, fractional order dynamic systems and P IλDμ . In: IEEE 1997 Decision and Control Conference, San Deogo, USA; 1997; pp. 4985-4990. doi: 10.1109/CDC.1997.649841
[6] Vinopraba T, Sivakumaran N, Narayanan S, Radhakrishnan TK. Design of internal model control based fractional order PID controller. Journal of Control Theory Applications 2012; 10: 297-302. doi: 10.1007/s11768-012-1044-4
[7] Pachuari N, Yadav J, Rani A, Singh V. Modified fractional order IMC design based on drug scheduling for cancer treatment. Computers in Biology and Medicine 2019; 109: 121-137. doi: 10.1016/j.compbiomed.2019.04.013
[8] Maamar B, Rachid M. IMC PID fractional order filter controllers design for integer order systems. ISA Transactions 2014; 53 (5): 1620-1628. doi: 10.1016/j.isatra.2014.05.007
[9] Baruah G, Majhi S, Mahanta C. Design of FOPI controller for time delay systems and its experimental validation. International Journal of Automation and Computing 2019; 16 (3): 310-328. doi: 10.1007/s11633-018-1165-4
[10] Rayalla R, Ambati SR, Gara UB. An improved fractional filter fractional IMC-PID controller design and analysis for enhanced performance of non-integer order plus time delay processes. European Journal of Electrical Engineering 2019; 21 (2): 139-147. doi: 10.18280/ejee.210203
[11] Nasir AW, Singh AK. IMC based fractional order controller for non-minimum phase system. In: 2015 Indian Control Conference, New Delhi, India 2015; 25 (6): pp. 1-6. doi: 10.1109/INDICON.2015.7443593
[12] Idamakanti K, Nasir AW, Singh AK. IMC based controller design for automatic generation control of multi-area power system via simplified decoupling. International Journal of Control, Automation and Systems 2018; 16 (3): 994-1010. doi: 10.1007/s12555-017-0362-1
[13] Sonker B, Kumar D, Samuel P. Dual loop IMC structure for load frequency control issue of multi-area multi- sources power systems. International Journal of Electrical Power & Energy Systems 2019; 112: 476-494. doi: 10.1016/j.ijepes.2019.04.042
[14] Chu M, Xu C, Chu J. Graphical IMC-PID tuning based on maximum sensitivity for fractional-order uncertain systems. In: 2018 IEEE International Conference on Automation, Electronics and Electrical Engineering 2018; pp. 257-261. doi: 10.1109/AUTEEE.2018.8720809
[15] Li D, He X, Song T, Jin Q. Fractional order IMC controller design for two-input-two-output fractional order system. International Journal of Control, Automation and Systems 2019; 17(4): 936-947. doi: 10.1007/s12555-018-0129-3
[16] Muresan CI, Birs IR, Prodan O, Nascu I, Keyser RD. Approximation methods for FO-IMC controllers for time delay systems. In: International Conference on Electrical Engineering and Green Energy; 2019; pp. 1-6. doi: 10.1051/e3sconf/201911501003
[17] Monje C, Chen YQ, Vinagre, Xue, Felieu V. Fractional-order systems and controls: Fundamentals and applications. London, UK: Springer-Verlag, 2010
18] Teplijakov A, Petlenkov E, Belikov J. FOMCON: A MATLAB toolbox for fractional order system identification and control. International Journal of Microelectronics and Computer Science; 2011; 2 (2): 51-62.
[19] Kennedy J, Eberhart R. Particle swarm optimisation. In: International Conference on Neural Networks; Perth, Australia; 1995. pp. 1942-1948.
[20] Maiti D, Biswas S, Konar A. Design of a fractional order PID controller using particle swarm optimisation technique. In: 2nd National Conference on Recent Trends in Information Systems; Coimbatore, India; 2008. arXiv:0810.3776
[21] Xu L, Song B, Cao M, Xiao Y. A new approach to optimal design of digital fractional order PID controller. NeuroComputing 2019; 363: 66-77. doi: 10.1016/j.neucom.2019.06.059
[22] Das S, Pan I, Das S, Gupta A. A novel fractional order fuzzy PID controller and its optimal time domain tuning based on integral performance indices. Engineering Applications of Artificial Intelligence 2012; 25 (2): 430-442. doi: 10.1016/j.engappai.2011.10.004
[23] Zafer B, Oguzhan K. Fractional PID controllers tuned by evolutionary algorithms for robot trajectory control. Turkish Journal of Electrical Engineering & Computer Sciences 2012; 20 (1): 1123-1136. doi: 10.3906/elk-1102- 1011
[24] Mahdi S, Babak M, Gevork BG, Soodabeh S. Optimal fractional-order PID controller of inverter-based power plants for power systems LFO damping, Turkish Journal of Electrical Engineering & Computer Sciences 2020; 28: 485-499. doi: 10.3906/elk-1907-31
[25] Tavazoei MS. Notes on integral performance indices in fractional order control systems. Journal of Process Control 2010; 20 (3): 285-291. doi: 10.1016/j.jprocont.2009.09.005
[26] Castillo-Garcia FJ, Feliu-Batlle V., Rivas-Perez R. Time domain tuning of fractional order controllers combined with smith predictor for automation of water distribution in irrigation main channel pools. Asian Journal of Control 2013; 15 (3): 819-833. doi: 10.1002/asjc.558
[27] Rajesh R. Optimal tuning of FOPID controller based on PSO algorithm with reference model for a conical tank system. Springer Nature Applied Sciences 2019; 1. doi: 10.1007/s42452-019-0754-3
[28] Arya PP, Chakraborthy S. IMC based fractional order controller design for specific non-minimum phase systems. In: IFAC Conference on Advances in Proportional-Integral-Derivative Control; Ghent, Belgium 2018; 51 (4): 4496-4509. doi: 10.1016/j.ifacol.2018.06.123
[29] Komathi C, Umamaheswari MG. Design of GWO algorithm based FOPI controller for power factor cor- rection in SMPS applications. IEEE Transactions On Power Electronics 2019; 35 (2): 2100-2118. doi: 10.1109/TPEL.2019.2920971
[30] Rayalla R, Ambati SR, Gara BUB. Analytical design of fractional IMC filter PID control strategy for perfor- mance enhancement of cascade control systems. International Journal of Systems Science 2020: 1699-1713. doi: 10.1080/00207721.2020.1773571
[31] Morrari M, Zafiriou E. Robust process control. Englewood Cliffs, NJ, USA: Prentice Hall, 1989.
[32] Alfaro VM, Vilanova R., PID control in the third millennium 2012. London, UK: Springer,2012, pp. 349-380