Abstract
In this paper, heuristic algorithm based optimization approach is proposed to design the PID controller in Double Feedback Control Loop (DFCL) for a class of stable and unstable Single Input Single Output (SISO) process models. In this work, a three dimensional search is attempted and the heuristic algorithm is employed to find the best possible values for inner loop proportional gain (Kp1), outer loop integral gain (Ki), and derivative gain (Kd). A weighted sum of Objective Function (OF) is considered to guide the optimization search in order to attain the global best values. A comparative analysis is presented between heuristic algorithms, such as Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Bacterial Foraging Optimization (BFO) and Firefly Algorithm (FA). From this experimental study, it is confirmed that, FA based DFCL offers better performance in reference tracking and disturbance rejection operations with reduced error values for most of the considered process models compared with the alternatives. The statistical significance of the FA is also verified using Wilcoxon’s rank test.
Nomenclature
- Kp
Proportional gain
- Ki
Integral gain
- Kd
Derivative gain
- Gp
Process model
- Gc1
Inner loop (P) controller
- Gc2
Outer loop (PID) controller
- w1,... wn
Weighting parameter
- Mp
Overshoot
- ts
Settling time
- R1,R2, rand
Random number [0, 1]
- C1, C2
Cognitive and global parameters
- D
Dimension of search
- N
Population of agents
- Jmin
Objective function to be minimized
Initial position
Updated position
Greek Symbols
- α
randomization operator
- γ
Light absorption coefficient
- β
Attractiveness coefficient
- β0
Attractiveness at r = 0
- Ψ
Randomization parameter
Abbreviations
- PID
Proportional + Integral + Derivative
- SISO
Single Input Single Output
- DOF
Degree Of Freedom
- ACO
Ant Colony Optimization
- GA
Genetic Algorithm
- PSO
Particle Swarm Optimization
- BFO
Bacterial Foraging Optimization
- FA
Firefly Algorithm
- ITAE
Integral Time Absolute Error
- ITSE
Integral Time Square Error
References
1. Panda RC. Synthesis of PID controller for unstable and integrating processes. Chem Eng Sci 2009;64:2807–16.10.1016/j.ces.2009.02.051Search in Google Scholar
2. O’Dwyer A. Handbook of PI and PID controller tuning rules, 3rd ed. London: Imperial College Press, 2009.10.1142/p575Search in Google Scholar
3. Padmasree R, Chidambaram M. Control of unstable systems. India: Narosa Publishing House, 2006.Search in Google Scholar
4. Lahiri SK, Khalfe NM. Hybrid particle swarm optimization and ant colony optimization technique for the optimal design of shell and tube heat exchangers. Chem Product Process Model 2015;10:81–96. doi: 10.1515/cppm-2014-0039.doi: 10.1515/cppm-2014-0039Search in Google Scholar
5. Araki M, Taguchi H. Two-degree-of-freedom PID controllers. Int J Control Autom Syst 2003;1:401–11.Search in Google Scholar
6. Rajinikanth V, Latha K. Setpoint weighted PID controller tuning for unstable system using heuristic algorithm. Archives Control Sci 2012;22:481–505.10.2478/v10170-011-0037-8Search in Google Scholar
7. Vijayan V, Panda RC. Design of a simple setpoint filter for minimizing overshoot for low order processes. ISA Trans 2012;51:271–6.10.1016/j.isatra.2011.10.006Search in Google Scholar PubMed
8. Vijayan V, Panda RC. Design of PID controllers in double feedback loops for SISO systems with set-point filters. ISA Trans 2012;51:514–21.10.1016/j.isatra.2012.03.003Search in Google Scholar PubMed
9. Bensenouci A, Besheer AH. Voltage and power regulation for a sample power system using Heuristics population search based PID Design. Int Rev Autom Control (IRACO) 2012;5:737–48.Search in Google Scholar
10. Bensenouci A, Besheer AH. Voltage and power regulation for a sample power system using ant colony system based PID controller. J Electric Syst 2012;8:397–410.Search in Google Scholar
11. Besheer AH. Wind driven induction generator regulation using ant system Approach to Takagi Sugeno Fuzzy PID control. W Trans Syst Control 2011;6:427–39.Search in Google Scholar
12. Kanthaswamy G, Jovitha J. Control of dead-time systems using hybrid ant colony optimization. Appl Artif Intell: Int J 2011;25:609–34.10.1080/08839514.2011.595282Search in Google Scholar
13. Kotteeswaran R, Sivakumar L. Performance evaluation of optimal PI controller for ALSTOM gasifier during coal quality variations. J Process Control 2014;24:27–36.10.1016/j.jprocont.2013.10.006Search in Google Scholar
14. Roeva O, Slavov T. PID Controller Tuning based on metaheuristic algorithms for bioprocess control. Biotechnol Biotechnol Equip 2012;26:3267–77.10.5504/BBEQ.2012.0065Search in Google Scholar
15. Rajinikanth V, Latha K. Controller Parameter Optimization for Nonlinear Systems Using Enhanced Bacteria Foraging Algorithm. Appl Comput Intell Soft Comput 2012;2012:12. Article ID 214264.10.1155/2012/214264Search in Google Scholar
16. Park JH, Sung SW, Lee IB. An enhanced PID control strategy for unstable processes. Automatica 1998;34:751–6.10.1016/S0005-1098(97)00235-5Search in Google Scholar
17. Yang X-S. Firefly algorithm, stochastic test functions and design optimisation. Int J Bio-inspired Comput 2010;2:78–84.10.1504/IJBIC.2010.032124Search in Google Scholar
18. Yang XS. Nature-inspired metaheuristic algorithms. UK: Luniver Press, 2008.Search in Google Scholar
19. Fister I, Fister Jr I, Yang X-S, Brest J. A comprehensive review of firefly algorithms. Swarm Evol Comput 2013;13:34–46.10.1016/j.swevo.2013.06.001Search in Google Scholar
20. Sri Madhava Raja N, Rajinikanth V, Latha K. Otsu based optimal multilevel image thresholding using firefly algorithm. Modell Simul Eng 2014;2014:17. Article ID 794574.10.1155/2014/794574Search in Google Scholar
21. Sri Madhava Raja N, Suresh Manic K, Rajinikanth V. Firefly algorithm with various randomization parameters: an analysis, in Proceedings of the 4th International Conference on Swarm, Evolutionary, and Memetic Computing (SEMCCO ‘13), In: Panigrahi, BK, Suganthan, PN, Das S, Dash SS, editors. vol. 8297 of Lecture Notes in Computer Science, 2013:110–21.Search in Google Scholar
22. Fayyazi E, Ghobadian B, Najafi G, Hosseinzadeh B. Genetic algorithm approach to optimize biodiesel production by ultrasonic system. Chem Product Process Model 2014;9:59–70. doi: 10.1515/cppm-2013-0043.doi: 10.1515/cppm-2013-0043Search in Google Scholar
23. Singh AK, Tyagi B, Kumar V. Classical and neural network–based approach of model predictive control for binary continuous distillation column. Chem Product Process Model 2014;9:71–87. doi: 10.1515/cppm-2013-0013.doi: 10.1515/cppm-2013-0013Search in Google Scholar
24. Kennedy J, Eberhart RC. Particle swarm optimization. In Proceedings of IEEE international conference on neural networks. 1995:1942–8.Search in Google Scholar
25. Saad MS, Jamaluddin H, Darus IZ. PID controller tuning using evolutionary algorithms. Wseas Trans System Control 2012;7:139–49.Search in Google Scholar
26. Passino KM. Biomimicry of bacterial foraging for distributed optimization and control. IEEE Control Syst Mag 2002;22:52–67.10.1109/MCS.2002.1004010Search in Google Scholar
27. Rajinikanth V, Latha K. Modeling, analysis, and intelligent controller tuning for a bioreactor: a simulation study. ISRN Chem Eng 2012;2012:15. Article ID 413657.10.5402/2012/413657Search in Google Scholar
28. Padhy PK, Majhi S. Relay based PI-PD design for stable and unstable FOPDT processes. Comput Chem Eng 2006;30:790–6.10.1016/j.compchemeng.2005.12.013Search in Google Scholar
29. Chen CC, Huang H-P, Liaw H-J. Set-point weighted PID controller tuning for time-delayed unstable processes. Ind Eng Chem Res 2008;47:6983–90.10.1021/ie800001mSearch in Google Scholar
30. Oliva D, Osuna-Enciso V, Cuevas E, Pajares G, Marco Pérez-Cisneros M, Zaldívar D. Improving segmentation velocity using an evolutionary method. Expert Syst Appl 2015;42:5874–86.10.1016/j.eswa.2015.03.028Search in Google Scholar
©2015 by De Gruyter
