Abstract
The conventional PID controller has static parameters that cannot be changed at different operating conditions. As a result, the term ‘adaptive PID controller’ has appeared to solve this problem. This controller can be tuned using intelligent techniques such as Fuzzy Logic Control, Neural Network Control, or Adaptive Neuro-Fuzzy Inference Systems. However, the choice of the suitable parameters for these intelligent controllers has a direct effect on their performance. Metaheuristics algorithms—with their powerful performance, speed, and optimal parameter selection—can be applied for choosing controller parameters efficiently. In this paper, a hybrid of genetic algorithm and particle swarm optimization is proposed to tune the parameters of different adaptive PID controllers. To evaluate the performance of the proposed hybrid optimization method on the different adaptive PID controllers, these controllers are applied to control the operation of one of the most difficult chemical processes, the divided wall distillation column. The proposed column used in this work separates a ternary mixture of ethanol, propanol, and n-butanol. Our proposed hybrid optimization technique is compared with the genetic algorithm, and simulation results show that our proposed hybrid genetic-particle swarm technique outperforms genetic algorithm for different disturbances.
This is a preview of subscription content, log in via an institution to check access.
(Khanam 2014)
Similar content being viewed by others
Abbreviations
- B :
-
Bottom product flow rate (kmol/min)
- D :
-
Distillate product flow rate (kmol/min)
- l :
-
Reflux flow rate (kmol/min)
- F :
-
Feed flow rate (kmol/min)
- S :
-
Side stream flow rate (kmol/min)
- V :
-
Boilup flow rate (kmol/min)
- R L :
-
Liquid split ratio
- R V :
-
Vapor split ratio
- M i :
-
Total liquid holdup on the ith tray (kmol)
- L i :
-
Liquid flow rate from the ith tray (kmol/min)
- V i :
-
Vapor flow rate from the ith tray (kmol/min)
- x i,j :
-
Mole fraction of the jth component in the liquid phase at the ith tray
- y i,j :
-
Mole fraction of the jth component in the vapor phase at the ith tray
- \( \alpha_{j} \) :
-
Relative volatility of the jth component
- q :
-
Feed condition
- \( T_{{{\text{B}},j}} \) :
-
Boiling point temperature of the jth component
- \( T_{i} \) :
-
Temperature of the ith tray
- N :
-
Number of trays
- \( x_{\text{A}} \) :
-
Top composition, component A
- \( x_{\text{B}} \) :
-
Side composition, component B
- \( x_{\text{C}} \) :
-
Bottom composition, component C
- \( z_{1} \) :
-
Feed composition, component A
- \( z_{2} \) :
-
Feed composition, component B
- Subscript \( i \) :
-
Tray number \( i \in \left\{ {1, \ldots , N} \right\} \)
- Subscript \( j \) :
-
Component \( j \in \left\{ {1, 2, 3} \right\} \)
- \( u\left( t \right) \) :
-
The control signal
- \( K_{\text{p}} \) :
-
Proportional gain
- \( K_{\text{i}} \) :
-
Integral gain
- \( K_{\text{d}} \) :
-
Derivative gain
- \( e\left( t \right) \) :
-
Error between reference and actual temperatures
- \( \omega_{k + 1} \) :
-
The inertia factor
- \( c_{1} \) :
-
The cognitive scaling factor
- \( c_{2} \) :
-
The social scaling factor
- \( r_{1,k}^{i} , r_{2,k}^{i} , r_{3,k}^{i} \) :
-
Random numbers uniformly distributed in the interval \( \left[ {0 \,1} \right] \)
- \( p_{k}^{i} \) :
-
The best previously obtained position of the ith particle
- \( p_{k}^{g} \) :
-
The best obtained position in the entire swarm at the current iteration \( k \)
- \( k \) :
-
Iteration number
- \( v_{k + 1}^{i} \) :
-
The velocity update of a particle \( i \)
- \( v_{k}^{i} \) :
-
The current velocity of a particle \( i \)
- \( x_{k + 1}^{i} \) :
-
The position update of a particle \( i \)
- \( x_{k}^{i} \) :
-
The current position of a particle \( i \)
- \( N \) :
-
Dimension of the problem
References
Abd-El-Wahed WF, Mousa AA, El-Shorbagy MA (2011) Integrating particle swarm optimization with genetic algorithms for solving nonlinear optimization problems. J Comput Appl Math 235(5):1446–1453. https://doi.org/10.1016/j.cam.2010.08.030
Asadi E, da Silva MG, Antunes CH, Dias L, Glicksman L (2014) Multi-objective optimization for building retrofit: a model using genetic algorithm and artificial neural network and an application. Energy Build 81:444–456. https://doi.org/10.1016/j.enbuild.2014.06.009
Baloch MA, Ismail I, Hanif NHHBM, Baloch TM (2010) ANFIS identification model of an advanced process control (APC) pilot plant. In: 2010 international conference on intelligent and advanced systems, Manila, pp 1–5. https://doi.org/10.1109/icias.20https://doi.org/10.5716224
Bingi K, Ibrahim R, Karsiti MN, Hassan SM (2017) Fuzzy gain scheduled set-point weighted PID controller for unstable CSTR systems. In: 2017 IEEE international conference on signal and image processing applications (ICSIPA), Kuching, pp 289–293. https://doi.org/10.1109/icsipa.2017.8120623
Cheng H, Zhang Y, Kong L, Meng X (2017) The application of neural network PID controller to control the light gasoline etherification. In: IOP conference series earth and environmental science 69(1). https://doi.org/10.1088/1755-1315/69/1/012045
Chiew TH, Jamaludin Z, Bani Hashim AY, Leo KJ, Abdullah L, Rafan NA (2012) Analysis of tracking performance in machine tools for disturbance forces compensation using sliding mode control and PID controller. Int J Mech Mechatron Eng 12(6):34–40
Chopra V, Singla S, Dewan L (2014) Comparative analysis of tuning a PID controller using intelligent methods. Acta Polytechn Hung 11(8):235–249. https://doi.org/10.12700/APH.11.08.2014.08.13
Deng W, Zhao H, Zou L, Li G, Yang X, Wu D (2017a) A novel collaborative optimization algorithm in solving complex optimization problems. Soft Comput 21(15):4387–4398. https://doi.org/10.1007/s00500-016-2071-8
Deng W, Zhao H, Yang X, Xiong J, Sun M, Li B (2017b) Study on an improved adaptive PSO algorithm for solving multi-objective gate assignment. Appl Soft Comput 59:288–302. https://doi.org/10.1016/j.asoc.2017.06.004
Deng W, Zhang S, Zhao H, Yang X (2018) A novel fault diagnosis method based on integrating empirical wavelet transform and fuzzy entropy for motor bearing. IEEE Access 6:35042–35056. https://doi.org/10.1109/ACCESS.2018.2834540
Deng W, Yao R, Zhao H, Yang X, Li G (2019a) A novel intelligent diagnosis method using optimal LS-SVM with improved PSO algorithm. Soft Comput 23(7):2445–2462. https://doi.org/10.1007/s00500-017-2940-9
Deng W, Xu J, Zhao H (2019b) An improved ant colony optimization algorithm based on hybrid strategies for scheduling problem. IEEE Access 7:20281–20292. https://doi.org/10.1109/ACCESS.2019.2897580
Diggelen RCV, Kiss AA, Heemink AW (2010) Comparison of control strategies for dividing-wall columns. Ind Eng Chem Res 49(1):288–307. https://doi.org/10.1021/ie9010673
Dohare RK, Singh K, Kumar R (2015a) Modeling and model predictive control of dividing wall column for separation of Benzene–Toluene-o-Xylene. Syst Sci Control Eng 3(1):142–153. https://doi.org/10.1080/21642583.2014.996301
Dohare RK, Singh K, Kumar R, Upadhyaya S (2015b) Simulation-based artificial neural network predictive control of BTX dividing wall column. Arab J Sci Eng 40:3393–3407. https://doi.org/10.1007/s13369-015-1846-z
Dounis AI, Kofinas P, Alafodimos C, Tseles D (2013) Adaptive fuzzy gain scheduling PID controller for maximum power point tracking of photovoltaic system. Renew Energy 60:202–214. https://doi.org/10.1016/j.renene.2013.04.014
Dwivedi D, Strandberg JP, Halvorsen IJ, Preisig HA, Skogestad S (2012) Active vapor split control for dividing-wall columns. Ind Eng Chem Res 51(46):15176–15183. https://doi.org/10.1021/ie3014346
Elbelady SA, Fawaz H, Abdul Aziz A (2016) Online self tuning PID control using neural network for tracking control of a pneumatic cylinder using pulse width modulation piloted digital valves. Int J Mech Mechatron Eng IJMME-IJENS 16(3):123–136
Ferdiansyah I, Era P, Windarko A (2016) Fuzzy gain scheduling of PID (FGS-PID) for speed control three phase induction motor based on indirect field oriented control (IFOC). EMITTER Int J Eng Technol 4(2):237–258. https://doi.org/10.24003/emitter.v4i2.147
Fu YY, Wu CJ, Chien TL, Ko CN (2008) Integration of PSO and GA for optimum design of fuzzy PID controllers in a pendubot system. Artif Life Robot 13(1):223–227. https://doi.org/10.1007/s10015-008-0512-x
Gritli W, Gharsallaoui H, Benrejeb M (2016) PID-type fuzzy scaling factors tuning using genetic algorithm and Simulink Design Optimization for Electronic Throttle Valve. In: 2016 international conference on control, decision and information technologies (CoDIT), St. Julian’s, pp 216–221. https://doi.org/10.1109/codit.2016.7593563
Jali MH, Mustafa NES, Izzuddina TA, Ghazali R, Jaafar HI (2015) ANFIS-PID controller for arm rehabilitation device. Int J Eng Technol (IJET) 7(5):1589–1597
Jia S, Qian X, Yuan X, Skogestad S (2018) Control structure comparison for three-product Petlyuk column. Chin J Chem Eng 26(8):1621–1630. https://doi.org/10.1016/j.cjche.2017.10.018
John AK, Krishnakumar K (2017) Performing multiobjective optimization on perforated plate matrix heat exchanger surfaces using genetic algorithm. Int J Simul Multidiscip Des Optim. https://doi.org/10.1051/smdo/2016011
Jouda A, Elyes F, Rabhi A, Abdelkader M (2017) Optimization of scaling factors of fuzzy–MPPT controller for stand-alone photovoltaic system by particle swarm optimization. Energy Proc 111:954–963. https://doi.org/10.1016/j.egypro.2017.03.258
Jung J, Leu VQ, Do TD, Kim E, Choi HH (2015) Adaptive PID speed control design for permanent magnet synchronous motor drives. IEEE Trans Power Electron 30(2):900–908. https://doi.org/10.1109/TPEL.2014.2311462
Kanagasabai N, Jaya N (2014) Fuzzy gain scheduling of PID controller for a MIMO process. Int J Comput Appl 91(10):13–20. https://doi.org/10.5120/15916-4803
Khanam A (2014) Control strategies for divided wall (Petlyuk) columns, thesis, Norwegian University of Science and Technology
Kinoshita K, Ohno S, Wakitani S (2017) Design of neural network PID controller based on E-FRIT. In: 2017 56th annual conference of the society of instrument and control engineers of Japan (SICE), Kanazawa, pp 1183–1186. https://doi.org/10.23919/sice.2017.8105555
Kiss AA, Bildea CS (2011) A control perspective on process intensification in dividing wall columns. Chem Eng Process 50(3):281–292. https://doi.org/10.1016/j.cep.2011.01.011
Kuo RJ, Han YS (2011) A hybrid of genetic algorithm and particle swarm optimization for solving bi-level linear programming problem—a case study on supply chain model. Appl Math Model 35(8):3905–3917. https://doi.org/10.1016/j.apm.2011.02.008
Kuo RJ, Hong CW (2013) Integration of genetic algorithm and particle swarm optimization for investment portfolio optimization. Appl Math Inf Sci 7(6):2397–2408. https://doi.org/10.12785/amis/070633
Mosaad MI, Salem F (2014) LFC based adaptive PID controller using ANN and ANFIS techniques. J Electr Syst Inf Technol 1(3):212–222. https://doi.org/10.1016/j.jesit.2014.12.004
Osório L, Mendes J, Araújo R, Matias T (2013) A comparison of adaptive PID methodologies controlling a DC motor with a varying load. In: 2013 IEEE 18th conference on emerging technologies and factory automation (ETFA), Cagliari, pp 1–6. https://doi.org/10.1109/etfa.2013.6648093
Premkumar K, Manikandan BV (2015) GA-PSO optimized online ANFIS based speed controller for Brushless DC motor. J Intell Fuzzy Syst 28(6):2839–2850. https://doi.org/10.3233/IFS-151563
Rahmat MF (2009) Application of self-tuning fuzzy PID controller on industrial hydraulic actuator using system identification approach. Int J Smart Sens Intell Syst 2(2):246–261. https://doi.org/10.21307/ijssis-2017-349
Ryu H, Son SH, Lee JM (2018) Application of dividing wall column in silane off-gas recovery process: optimal design and control. J Chem Eng Jpn 51(3):253–263. https://doi.org/10.1252/jcej.16we386
Singh S, Kaur M (2016) Gain scheduling of PID controller based on fuzzy systems. In: MATEC web of conferences 57. https://doi.org/10.1051/matecconf/20165701008
Skogestad S (2003) Simple analytic rules for model reduction and PID controller tuning. J Process Control 13(4):291–309. https://doi.org/10.1016/S0959-1524(02)00062-8
Soyguder S, Karakose M, Alli H (2009) Design and simulation of self-tuning PID-type fuzzy adaptive control for an expert HVAC system. Expert Syst Appl 36(3):4566–4573. https://doi.org/10.1016/j.eswa.2008.05.031
Wang G, Fong C, Chang KJ (2001) Neural-network-based self-tuning PI controller for precise motion control of PMAC motors. IEEE Trans Industr Electron 48(2):408–415. https://doi.org/10.1109/41.915420
Wang J, Yu N, Chen M, Cong L, Sun L (2018) Composition control and temperature inferential control of dividing wall column based on model predictive control and PI strategies. Chin J Chem Eng 26(5):1087–1101. https://doi.org/10.1016/j.cjche.2017.12.005
Whitley D (1994) A genetic algorithm tutorial. Stat Comput 4(2):65–85. https://doi.org/10.1007/BF00175354
Xiaolong G, Botong L, Xigang Y, Yiqing L, Kuo-Ksong Y (2017) Application of the dividing wall column to olefin separation in fluidization methanol to propylene (FMTP) process. Chin J Chem Eng 25(8):1069–1078. https://doi.org/10.1016/j.cjche.2017.03.018
Yu W, Li B, Jia H, Zhang M, Wang D (2015) Application of multi-objective genetic algorithm to optimize energy efficiency and thermal comfort in building design. Energy Build 88:135–143. https://doi.org/10.1016/j.enbuild.2014.11.063
Zhang J (2001) A nonlinear gain scheduling control strategy based on neuro-fuzzy networks. Ind Eng Chem Res 40(14):3164–3170. https://doi.org/10.1021/ie990866h
Zhao H, Sun M, Deng W, Yang X (2017) A new feature extraction method based on EEMD and multi-scale fuzzy entropy for motor bearing. Entropy 19(1):14. https://doi.org/10.3390/e19010014
Zhao H, Yao R, Xu L, Yuan Y, Li G, Deng W (2018) Study on a novel fault damage degree identification method using high-order differential mathematical morphology gradient spectrum entropy. Entropy 20(9):682. https://doi.org/10.3390/e20090682
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare no conflict of interest.
Additional information
Communicated by V. Loia.
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
El-Gendy, E.M., Saafan, M.M., Elksas, M.S. et al. Applying hybrid genetic–PSO technique for tuning an adaptive PID controller used in a chemical process. Soft Comput 24, 3455–3474 (2020). https://doi.org/10.1007/s00500-019-04106-z
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00500-019-04106-z