Home Fractional Order PID Controller Design for Multivariable Systems using TLBO
Article
Licensed
Unlicensed Requires Authentication

Fractional Order PID Controller Design for Multivariable Systems using TLBO

  • Jailsingh Bhookya EMAIL logo and Ravi Kumar Jatoth
Published/Copyright: December 21, 2019
Become an author with De Gruyter Brill

Abstract

The multivariable systems have to control by using multiloop controllers and each closed loop controller has unique characteristics. The successful model structure for design of control system is extremely subject to the accurate choice of the tuning parameters (Kp,Ki,Kd,λ,μ) of the controller. The choice of optimal tuning parameters of Fractional Order PID (FOPID) controller leads to accurate controlling of desired level in multivariable system. Here, for multivariable system, a FOPID controller design based on the advanced optimization technique called Teaching Learning based optimization (TLBO) algorithm is proposed. The goal of paper is (i) The elimination of interaction between the control loops and (ii) Reference tracking along the disturbance in each loop. These objectives are satisfied by using four cost function, namely, integral absolute error (IAE), integral square error (ISE), integral time absolute error (ITAE) and integral time square error (ITSE). Out of these cost functions, ITAE based FOPID controller design using TLBO algorithm provides better performance in terms of fast reference tracking and disturbance elimination in the loop. Moreover, the comparative analysis of convergence characteristics of each objective of the controller by using TLBO is presented. The simulation study confirms that the TLBO algorithm based FOPID controller for multivariable systems (2 × 2) are more robust and exhibits superior response with respect to other algorithm.

References

[1] Ilakkiya A, Divya S, Mannimozhi M. Design of PI controllers for MIMO system with decouplers. Int J Chem Sci. 2016;14:1598–612.Search in Google Scholar

[2] Maghade DK, Patre BM. Decentralized PI/PID controllers based on gain and phase margin specifications for TITO processes. ISA Trans. 2012;51:550–8.10.1016/j.isatra.2012.02.006Search in Google Scholar PubMed

[3] Ateş A, Yeroglu C. Optimal fractional order PID design via Tabu Search based algorithm. ISA Trans. 2016;60:109–18.10.1016/j.isatra.2015.11.015Search in Google Scholar PubMed

[4] Hajare VD, Patre BM, Khandekar AA, Malwatkar GM. Decentralized PID controller design for TITO processes with experimental validation. Int J Dyn Control. 2016;5:583–95.10.1007/s40435-016-0252-zSearch in Google Scholar

[5] Zeng GQ, Xie XQ, Chen MR, Weng J. Adaptive population extremal optimization-based PID neural network for multivariable nonlinear control systems. Swarm Evol Comput. 2019;44:320–34.10.1016/j.swevo.2018.04.008Search in Google Scholar

[6] Menhas MI, Wang L, Fei M, Pan H. Comparative performance analysis of various binary coded PSO algorithms in multivariable PID controller design. Expert Syst Appl. 2012;39:4390–401.10.1016/j.eswa.2011.09.152Search in Google Scholar

[7] Zeng GQ, Lu KD, Dai YX, Zhang ZJ, Chen MR, Zheng CW, et al. Binary-coded extremal optimization for the design of PID controllers. Neurocomputing. 2014;138:180–8.10.1016/j.neucom.2014.01.046Search in Google Scholar

[8] Zeng GQ, Chen J, Chen MR, Dai YX, Li LM, Lu KD, et al. Design of multivariable PID controllers using real-coded population-based extremal optimization. Neurocomputing. 2015;151:1343–53.10.1016/j.neucom.2014.10.060Search in Google Scholar

[9] S. Saab. A stochastic PID controller for a class of MIMO systems A stochastic PID controller for a class of MIMO systems. International Journal of Control. 2017;90:447–62.10.1080/00207179.2016.1183176Search in Google Scholar

[10] Rajapandiyan C, Chidambaram M. Controller design for MIMO processes based on simple decoupled equivalent transfer functions and simplified decoupler. Ind Eng Chem Res. 2012;51:12398–410.10.1021/ie301448cSearch in Google Scholar

[11] Iruthayarajan MW, Baskar S. Evolutionary algorithms based design of multivariable PID controller. Expert Syst Appl. 2009;36:9159–67.10.1016/j.eswa.2008.12.033Search in Google Scholar

[12] Dhanraj AV, Nanjundappan D. Design of optimized PI controller with ideal decoupler for a non linear multivariable system using particle swarm optimization technique. Int J Innovative Comput Inf Control. 2013;10:341–55.Search in Google Scholar

[13] Viola J, Angel L, Sebastian JM. Design and robust performance evaluation of a fractional order PID controller applied to a DC motor. IEEE/CAA J Autom Sin. 2017;4:304–14.10.1109/JAS.2017.7510535Search in Google Scholar

[14] Li Zhuo, Chen YangQuan. Ideal, Simplified and Inverted Decoupling of Fractional Order TITO Processes. IFAC Proceedings Volumes. 2014;47:2897–902. DOI: 10.3182/20140824-6-ZA-1003.02107.Search in Google Scholar

[15] Raviteja K, Dasari PR, Seshagiri Rao A. Improved controller design for two-input-two-output (TITO) unstable processes. Resour-Efficient Technol. 2016;2:S76–S86.10.1016/j.reffit.2016.10.009Search in Google Scholar

[16] Besta CS, Chidambaram M. Tuning of multivariable PI controllers by BLT method for TITO systems. Chem Eng Commun. 2016;203:527–38.10.1080/00986445.2015.1039121Search in Google Scholar

[17] Suresh A, Kiran MV, Kumar CS. Design PID controller for TITO process based on least square optimization tuning method. In: 2014 IEEE International Conference on Computational Intelligence and Computing Research, 2014:1–4.10.1109/ICCIC.2014.7238444Search in Google Scholar

[18] Besta CS, Chidambaram M. Decentralized PID controllers by synthesis method for multivariable unstable systems. IFAC-PapersOnLine. 2016;49:504–9.10.1016/j.ifacol.2016.03.104Search in Google Scholar

[19] Nasirpour N, Balochian S. Optimal design of fractional-order PID controllers for multi-input-multi-output air-conditioning system using particle swarm optimization. Intell Build Int. 2017;9:107–19.10.1080/17508975.2016.1170659Search in Google Scholar

[20] Chen Z, Yuan X, Ji B, Wang P, Tian H. Design of a fractional order PID controller for hydraulic turbine regulating system using chaotic non-dominated sorting genetic algorithm II. Energy Convers Manage. 2014;84:390–404.10.1016/j.enconman.2014.04.052Search in Google Scholar

[21] Zeng GQ, Chen J, Dai YX, Li LM, Zheng CW, Chen MR. Design of fractional order PID controller for automatic regulator voltage system based on multi-objective extremal optimization. Neurocomputing. 2015;160:173–84.10.1016/j.neucom.2015.02.051Search in Google Scholar

[22] Rao RV, Savsani VJ, Vakharia DP. Teaching–learning-based optimization: a novel method for constrained mechanical design optimization problems. Computer-Aided Design. 2011;43:303–15. DOI:10.1016/j.cad.2010.12.015.Search in Google Scholar

[23] Nenavath H, Jatoth RK. Hybrid SCA–TLBO: a novel optimization algorithm for global optimization and visual tracking. Neural Comput Appl. 1–30. DOI: 10.1007/s00521-018-3376-6.Search in Google Scholar

[24] Wang H, Zeng G, Dai Y, Bi D, Sun J, Xie X. Design of a fractional order frequency PID controller for an islanded microgrid: a multi-objective extremal optimization method. Energies. 2017;10:1502.10.3390/en10101502Search in Google Scholar

Received: 2019-04-19
Revised: 2019-09-23
Accepted: 2019-10-24
Published Online: 2019-12-21

© 2019 Walter de Gruyter GmbH, Berlin/Boston

Downloaded on 15.9.2025 from https://www.degruyterbrill.com/document/doi/10.1515/cppm-2019-0061/html
Scroll to top button