Tree physiology optimization on SISO and MIMO PID control tuning

  • A. Hanif Halim
  • I. Ismail
Original Article


The tuning of proportional–integral–derivative (PID) controller is essential for any control application in order to ensure the best performance by step change or disturbance. This paper presents the tuning of PID controller for single-input single-output (SISO) and multiple-input multiple-output (MIMO) control systems using tree physiology optimization (TPO). TPO is a metaheuristic algorithm inspired from a plant growth system derived based on the idea of plant architecture and Thornley model (TM). The basic principle of TM simplifies the plant growth into shoots and roots part. The plant shoots grow towards sunlight with the help of nutrients supplied by the root system in order to undergo photosynthesis process, a process of converting light photon into carbon. The carbon gain from the shoots extension will be supplied to the root system in order for the root to grow and search for water plus nutrients. As a result, the nutrients are supplied upwards towards shoot system for further extension. This concept runs iteratively in order to ensure optimum plant growth. The iterative search of shoot towards better light supported by the root counterparts leads to an optimization idea of TPO algorithm. TPO also has a unique exploration strategy due to its multiple branches and shoots that can be defined by user. This concept may improve the search mechanism with a better trade-off between diversification and intensification search. A simulation of SISO control system and an industrial application of MIMO control are applied to demonstrate the effectiveness of the proposed algorithm and compared with other optimization methods such as particle swarm optimization, Ziegler–Nichols, Tyreus–Luyben and Chien–Hrones–Reswick methods. The results clearly exhibit the capability of TPO algorithm towards finding the optimum PID parameters for SISO and MIMO process with faster settling time and better performance with respect to other methods.


Single-input single-output Multiple-input multiple-output Tree physiology optimization Particle swarm optimization Ziegler–Nichols Tyreus–Luyben Chien–Hrones–Reswick 


Compliance with ethical standard

Conflict of interest

The authors declare that they have no conflict of interest.


  1. 1.
    Paz MA et al (2017) Adaptive proportional-integral controller using OLE for process control for industrial applications. Int J Adv Robot Syst 1–11Google Scholar
  2. 2.
    Miranda MF, Vamvoudakis KG (2016) Online optimal auto-tuning of PID controllers for tracking in a special class of linear systems. In: American control conference (ACC), Boston, pp. 5443–5448Google Scholar
  3. 3.
    Boyd S, Hast M, Åström KJ (2015) MIMO PID tuning via iterated LMI restriction. Int J Robust Nonlinear Control 26(8):1718–1731MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Dalen C, Ruscio DD (2017) PD/PID controller tuning based on model approximations: model reduction of some unstable and higher order nonlinear models. Model Identif Control 38(4):185–197CrossRefGoogle Scholar
  5. 5.
    Doerr A et al (2017) Model-based policy search for automatic tuning of multivariate PID controllers. In: Proceedings IEEE international conference on robotics and automation. ICRA, Singapore, pp 5925–5301Google Scholar
  6. 6.
    Ziegler JG, Nichols NB (1942) Optimum settings for automatic controllers. Trans ASME 64:759–768Google Scholar
  7. 7.
    Åström KJ, Hägglund T (1995) PID controllers: theory, design and tuning, 2nd edn. ISA, Research Triangle Park, pp 134–149Google Scholar
  8. 8.
    Sebord DE, Edgar TF, Mellichamp DA, Doyle FJ (2016) Process dynamics and control, 4th edn. Wiley, New YorkGoogle Scholar
  9. 9.
    Walter H (2001) Kompaktkurs regelungstechnik, chap 8. Vieweg, Germany, pp 183CrossRefGoogle Scholar
  10. 10.
    Sariyildiz E, Yu H, Ohnishi K (2015) A practical tuning method for the robust PID controller with velocity feed-back. Machines 3:208–222CrossRefGoogle Scholar
  11. 11.
    Bingi K, Ibrahim R, Karsiti MN, Chung TD, Hassan SM (2016) Optimal PID control of pH neutralization plant. In: IEEE symposium on robotics and manufacturing automation (ROMA), Ipoh, MalaysiaGoogle Scholar
  12. 12.
    Roeva Olympia, Slavov Tsonyo (2014) PID controller tuning based on Metaheuristic algorithms for bioprocess control. Biotechnol Biotechnol Equip 26(5):3267–3277CrossRefGoogle Scholar
  13. 13.
    Şen MA, Kalyoncu M (2018) Optimal tuning of PID controller using grey wolf optimizer algorithm for quadruped robot. Balkan J Electr Comput Eng 6(1):29–35Google Scholar
  14. 14.
    Holland JH (1992) Adaptation in natural and artificial systems, an introductory analysis with applications to biology, control, and artificial intelligence, vol 10. MIT Press, Massachusetts, pp 171–184Google Scholar
  15. 15.
    Storn R, Price K (1997) Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces. J Global Optim 11:341–359MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Kirkpatrick S et al (1983) Optimization by simulated annealing. Science 220:671–680MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Yang XS (2009) Firefly algorithms for multimodal optimization, in stochastic algorithms: foundations and applications. Lect Not Comput Sci 5792:169–178CrossRefzbMATHGoogle Scholar
  18. 18.
    Yang XS (2010) A new metaheuristic bat-inspired algorithm, nature inspired cooperative strategies for optimization, NISCO 2010. Stud Comput Intell 284:65–74Google Scholar
  19. 19.
    Kennedy J, Eberhardt R (1995) Particle swarm optimization. In: Proceedings of the 1995 IEEE international conference on neural networks, Perth, Australia, pp 1942–1948Google Scholar
  20. 20.
    Wafa G, Hajer G, Mohamed B (2016) PID-type fuzzy scaling factors tuning using genetic algorithm and simulink design optimization for electronic throttle valve. In: International conference on control, decision and information technologies (CoDIT)Google Scholar
  21. 21.
    Sheng L, Li W (2018) Optimization design by genetic algorithm controller for trajectory control of a 3-RRR parallel robot. Algorithms 11(1):1–13MathSciNetGoogle Scholar
  22. 22.
    Kishnani M, Pareek S, Gupta R (2014) Optimal tuning of PID controller using meta heuristic approach. Int J Electron Electric Eng 7(2):171–176Google Scholar
  23. 23.
    Villarreal-Cervantes MG et al (2018) Differential evolution based adaptation for the direct current motor velocity control parameters. Math Comput Simul 150:122–141MathSciNetCrossRefGoogle Scholar
  24. 24.
    Cheng Z, Lu Z (2018) Research on PID control of the ESP system of tractor based on improved AFSA and improved SA. Comput Electron Agric 148:142–147CrossRefGoogle Scholar
  25. 25.
    Debnath MK et al (2017) Design of fuzzy-PID controller with derivative filter and its application using firefly algorithm to automatic generation control. In: 6th International conference on computer applications in electrical engineering-recent advances (CERA), Roorkee, India, pp 353–358Google Scholar
  26. 26.
    Nor’azlan NA et al (2018) Multivariable PID controller design tuning using bat algorithm for activated sludge process. IOP Conf Ser Mater Sci Eng 342:1–9Google Scholar
  27. 27.
    Hanifah RA et al (2018) Swarm intelligence tuned current reduction for power-assisted steering control in electric vehicles. IEEE Trans Ind Electron 65(9):7202–7210CrossRefGoogle Scholar
  28. 28.
    Connor J, Seyedmahmoudian M, Horan B (2017) Using particle swarm optimization for PID optimization for altitude control on a quadrotor. In: IEEE Australasian universities power engineering conference (AUPEC), Melbourne, Australia, pp 1–6Google Scholar
  29. 29.
    Bingul Z, Karahan O (2018) Comparison of PID and FOPID controllers tuned by PSO and ABC algorithms for unstable and integrating systems with time delay. Opt Control Appl Methods. Google Scholar
  30. 30.
    Oliveira MOF, Fernandes MR, Souto RF (2017) Implementation of a low-cost prototype of twin rotor for academic studies in identification, optimal control and stochastic filtering. In: IEEE 6th international conference on systems and control (ICSC), Batna, Algeria, pp 193–198Google Scholar
  31. 31.
    Xin-yue L et al (2016) The research on the coordinated control system of PID neural network based on artificial fish swarm algorithm. In: Chinese control and decision conference, Yinchuan, China, pp 3065–3068Google Scholar
  32. 32.
    Dharan ST et al (2017) Tuning pf PID controller using optimization techniques for a MIMO process. IOP Conf Ser Mater Sci Eng 263:1–17Google Scholar
  33. 33.
    Fard NA, Shahbazian M, Hadian M (2016) Adaptive fuzzy controller based on cuckoo optimization algorithm for a distillation column. In: IEEE international conference on computer intelligent application (ICCIA), Jeju, Korea, pp 1–6Google Scholar
  34. 34.
    Yang XS (2010) Nature-inspired metaheuristic algorithms, vol 2. Luniver Press, EnglandGoogle Scholar
  35. 35.
    Halim AH, Ismail I (2013) Nonlinear plant modeling using neuro-fuzzy system with tree physiology optimization. In: IEEE student conference on research and development (SCOReD), Putrajaya, Malaysia, pp 295–300Google Scholar
  36. 36.
    Halim AH, Ismail I (2017) Tree physiology optimization in benchmark function and travelling salesman problem. J Intell Syst. Google Scholar
  37. 37.
    Durand J-B et al (2004) Analysis pf the plant architecture via tree-structured statistical models: the hidden Markov tree models. N Phytol 166:813–825CrossRefGoogle Scholar
  38. 38.
    Barthélémy D (1991) Levels of organization and repetition phenomena in seed plants. Acta Biotheor 39:309–323CrossRefGoogle Scholar
  39. 39.
    Thornley JHM (1976) Mathematical models in plant physiology, a qualitative approach to problems in plant and crop physiology, vol 9. Academic Press, London, pp 173–174Google Scholar
  40. 40.
    Thornley JHM (1998) Modelling shoot: root relations: The only way forward? Ann Bot 81:165–171CrossRefGoogle Scholar
  41. 41.
    Jang JSR (1993) ANFIS: adaptive-network-based fuzzy inference system. IEEE Trans Syst Man Cybern 23(3):665–685CrossRefGoogle Scholar
  42. 42.
    Halim AH, Ismail I (2016) Online PID controller tuning using tree physiology optimization. In: International conference on intelligent and advanced systems (ICIAS), Kuala Lumpur, Malaysia, pp 1–5Google Scholar
  43. 43.
    Hanif Halim A, Ismail I (2017) Single and multiple variables control using tree physiology optimization. MATEC Web Conf 131:1–8Google Scholar
  44. 44.
    Ismail I, Halim AH (2017) Comparative study of meta-heuristics optimization algorithm using benchmark function. Int J Electric Comput Eng 7(3):1643–1650Google Scholar
  45. 45.
    Hanif Halim A, Ismail I (2018) Tree physiology optimization in constrained optimized problem. Telkomnika 16(2):876–882CrossRefGoogle Scholar
  46. 46.
    Doicin B, Popescu M, Patrascioiu C (2016) PID controller optimal tuning. In: 8th International conference on electronics, computers and artificial intelligence, ECAI, Ploiesti, Romania, pp 1–4Google Scholar

Copyright information

© The Natural Computing Applications Forum 2018

Authors and Affiliations

  1. 1.Electrical and Electronic Engineering DepartmentUniversiti Teknologi PETRONASTronohMalaysia

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