Open Access Open Access  Restricted Access Subscription or Fee Access

Open and Closed Loop Identification and Control of a Thermal System

Rubens Eduardo Hauser Novicki(1), Emersom Martim(2), Ervin Kaminski Lenzi(3), Florindo Antônio de Carvalho Ayres Jr.(4), Thiago Dalgalo de Quadros(5), Alisson Luan Daga(6), Marcelo Kaminski Lenzi(7*)

(1) Departamento de Engenharia Química, Universidade Federal do Paraná, Setor de Tecnologia, Jardim das América, Brazil
(2) Pontifícia Universidade Católica do Paraná, Departamento de Engenharia Química, Brazil
(3) Universidade Estadual de Ponta Grossa, Departamento de Física, Avenida Carlos Cavalcanti, 4748 - Campus Uvaranas, Brazil
(4) Universidade Federal do Amazonas, Departamento de Engenharia Elétrica, Avenida General Rodrigo Octavio, Brazil
(5) Departamento de Engenharia Química, Universidade Federal do Paraná, Setor de Tecnologia, Jardim das América, Brazil
(6) Departamento de Engenharia Química, Universidade Federal do Paraná, Setor de Tecnologia, Jardim das América, Brazil
(7) Departamento de Engenharia Química, Universidade Federal do Paraná, Setor de Tecnologia, Jardim das América, Brazil
(*) Corresponding author

DOI's assignment:
the author of the article can submit here a request for assignment of a DOI number to this resource!
Cost of the service: euros 10,00 (for a DOI)


The use of mathematical models has been longly recognized as a fundamental step for in-depth process studies. Aimed at process control applications, the use of transfer functions identified from plant data represents an interesting modeling approach when compared to the derivation of first-principles-based models. Thermal systems are widely present in scientific and industrial scenarios, with applications in different fields, representing an important component of a cost operation. Towards this, the development of low-cost thermal systems has been reported aimed at understanding basic phenomena and validating modeling and control strategies. In the first part of the work, open loop identification was performed, leading to a fractional order transfer function, with order (=0.838(0.009. In the second part, a classical closed loop identification, using an integer order PI (proportional-integral) controlled, was used to identify an integer order transfer function. In the third part, the closed loop identified transfer function was employed to successfully preview the experimental closed loop behavior of the controlled and manipulated variables using different PI controllers.
Copyright © 2019 Praise Worthy Prize - All rights reserved.


Thermal System; Arduino; Fractional Calculus; Closed Loop

Full Text:



O. Levenspiel, Modeling in chemical engineering, Chem. Eng. Sci. 57 (2000) 4691–4696.

R. Aris, Ends and beginnings in the mathematical modelling of chemical engineering systems, Chem. Eng. Sci. 48 (1993) 2507–2517.

R. B. Bird, Five Decades of Transport Phenomena, AIChE J. 50 (2004) 273–287

S. Ahmed, Identification from step response – The integral equation approach. Can. J. Chem. Eng. 94 (2016), 2243–2256.

D. M. Dimiduk, E. A. Holm, S. R. Niezgoda, Perspectives on the Impact of Machine Learning, Deep Learning, and Artificial Intelligence on Materials, Processes, and Structures Engineering. Integrat. Mat. Manufact. Innov 7 (2018) 157–172.

L.-L. Shao, L. Yang, L.-X. Zhao, C.-L. Zhang, Hybrid steady-state modeling of a residential air-conditioner system using neural network component models. Energ. Buildings 50 (2012) 189–195.

C. Ionescu, A. Lopes, D. Copot, J. A. T. Machado, J. H. Tu. Bates, The role of fractional calculus in modeling biological phenomena: A review. Commun. Nonlinear Sci. 51 (2017) 141–159.

F. Ayres Junior, C. Costa Junior, R. Medeiros, W. Barra Junior, C. Neves, M. K. Lenzi, G. Veroneze, A Fractional Order Power System Stabilizer Applied on a Small-Scale Generation System. Energies, 11 (2018) 2052.

J. Hristov, Fourth-order fractional diffusion model of thermal grooving: integral approach to approximate closed form solution of the Mullins model. Math. Model. Nat. Phenom 13 (2018) 6.

E. M. Bainy, E. K. Lenzi, M. L. Corazza, M. K. Lenzi, Mathematical modeling of fish burger baking using fractional calculus. Therm. Sci. 21 (2017) 41–50.

W. P. do Carmo, M. K. Lenzi, E. K. Lenzi, M. Fortuny, A. F. Santos, A fractional model to relative viscosity prediction of water-in-crude oil emulsions. J. Petrol. Sci. Eng. 172 (2019) 493–501.

I. C. Kemp, Pinch Analysis and Process Integration (Butterworth-Heinemann, 2007).

H. Malek, Y. Luo, Y. Chen, Identification and tuning fractional order proportional integral controllers for time delayed systems with a fractional pole. Mechatronics, 23 (2013) 746–754.

S. Ahmed, Parameter and delay estimation of fractional order models from step response. IFAC PapersOnLine, 28 (2015) 942–947.

W. L. Torres, I. B. Q. Araujo, J. B. M. Filho, A. G. C. Junior, Mathematical Modeling and PID Controller Parameter Tuning in a Didactic Thermal Plant. IEEE Lat. Am. T. 15 (2017) 1250–1256.

O. Nelles, O. Nonlinear System Identification (Springer, 2001).

A. M. Almeida, G. S. Silva, I. Neitzel, M. K. Lenzi, Closed-Loop Identification and Performance Indexes of an Industrial Paperboard Machine. Int. Review. Chem. Eng. 1 (2014) 15–21.

D. E. Seborg, T. F. Edgar, D. A. Mellichamp, F. J. Doyle III, Process Dynamics and Control (John Wiley & Sons, 2011).

I. Podlubny, Fractional Differential Equations (Academic Press, 1998).

E. K. Lenzi, A. Ryba, A., M. K. Lenzi, Monitoring Liquid-Liquid Mixtures Using Fractional Calculus and Image Analysis, Fractal Fract 2 (2018) 11.

J. C .Lagarias, J. A. Reeds, M. H. Wright, P. E. Wright, Convergence properties of the Nelder–Mead simplex method in low dimensions, SIAM J. Optim. 9 (1998) 112–147.


  • There are currently no refbacks.

Please send any question about this web site to
Copyright © 2005-2020 Praise Worthy Prize