Optimal design of $ PI^\rho D^\mu $-controller for artificial ventilation systems for COVID-19 patients

Iqbal M. Batiha; Reyad El-Khazali; Osama Y. Ababneh; Adel Ouannas; Radwan M. Batyha; Shaher Momani; Iqbal M. Batiha; Reyad El-Khazali; Osama Y. Ababneh; Adel Ouannas; Radwan M. Batyha; Shaher Momani

doi:10.3934/math.2023031

AIMS Mathematics

2023, Volume 8, Issue 1: 657-675. doi: 10.3934/math.2023031

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Optimal design of $ PI^\rho D^\mu $-controller for artificial ventilation systems for COVID-19 patients

1.
Department of Mathematics, Al Zaytoonah University of Jordan, Amman 11733, Jordan
2.
Nonlinear Dynamics Research Center (NDRC), Ajman University, Ajman, UAE
3.
EECS Department, Khalifa University, Abu-Dhabi, UAE
4.
Department of Mathematics, Zarqa University, Zarqa, Jordan
5.
Department of Mathematics and Computer Science, University of Larbi Ben M'hidi, Oum El Bouaghi, Algeria
6.
Department of Computer Science, Faculty of Science and Technology, Irbid National University, Irbid, Jordan
7.
Department of Mathematics, Faculty of Science, University of Jordan, Amman 11942, Jordan

Received: 14 July 2022 Revised: 22 August 2022 Accepted: 29 August 2022 Published: 09 October 2022
MSC : 47N70, 65K10

In light of the COVID-19 pandemic, many patients have suffered from Acute Respiratory Distress Syndrome (ARDS) in Intensive Care Units (ICUs) around the world. In the medical field, it is known that the so-called artificial ventilation device, which has become the mainstay of treatment of such syndrome, decreases mortality in critically ill COVID-19 patients. Due to the high reliability of this device, there is an emergency need to follow up the progress made on designing a robust controller for improving its performance. From this perspective, this work introduces different control design schemes for obtaining an optimal Fractional-order PID controller (or simply $ PI^\rho D^\mu $-controller) of the Artificial Ventilation (AV) system through two optimization algorithms: the Bacteria Foraging Optimization (BFO) and the Particle Swarm Optimization (PSO) algorithms. The realization of the controller is accomplished using four approximations: Oustaloup's approximation, the Continued Fractional Expansion (CFE) approximation and the $ 1^{st} $- and $ 2^{nd} $-order El-Khazali approximations. The validation of the controller design and the AV system behavior are verified via numerical simulation in order to demonstrate the effectiveness and the potency of all proposed schemes.
- $ PI^\rho D^\mu $-controller,
- particle swarm optimization algorithm,
- Bacteria Foraging Optimization,
- Laplacian operator
Citation: Iqbal M. Batiha, Reyad El-Khazali, Osama Y. Ababneh, Adel Ouannas, Radwan M. Batyha, Shaher Momani. Optimal design of $ PI^\rho D^\mu $-controller for artificial ventilation systems for COVID-19 patients[J]. AIMS Mathematics, 2023, 8(1): 657-675. doi: 10.3934/math.2023031

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Abstract

In light of the COVID-19 pandemic, many patients have suffered from Acute Respiratory Distress Syndrome (ARDS) in Intensive Care Units (ICUs) around the world. In the medical field, it is known that the so-called artificial ventilation device, which has become the mainstay of treatment of such syndrome, decreases mortality in critically ill COVID-19 patients. Due to the high reliability of this device, there is an emergency need to follow up the progress made on designing a robust controller for improving its performance. From this perspective, this work introduces different control design schemes for obtaining an optimal Fractional-order PID controller (or simply $ PI^\rho D^\mu $-controller) of the Artificial Ventilation (AV) system through two optimization algorithms: the Bacteria Foraging Optimization (BFO) and the Particle Swarm Optimization (PSO) algorithms. The realization of the controller is accomplished using four approximations: Oustaloup's approximation, the Continued Fractional Expansion (CFE) approximation and the $ 1^{st} $- and $ 2^{nd} $-order El-Khazali approximations. The validation of the controller design and the AV system behavior are verified via numerical simulation in order to demonstrate the effectiveness and the potency of all proposed schemes.

References

[1]	E. Fan, J. R. Beitler, L. Brochard, C. S. Calfee, N. D. Ferguson, A. S. Slutsky, et al., COVID-19-associated acute respiratory distress syndrome: is a different approach to management warranted? Lancet Resp. Med., 8 (2020), 816–821. https://doi.org/10.1016/S2213-2600(20)30304-0 doi: 10.1016/S2213-2600(20)30304-0
[2]	H. D. Poor, C. E. Ventetuolo, T. Tolbert, G. Chun, G. Serrao, A. Zeidman, et al., COVID-19 critical illness pathophysiology driven by diffuse pulmonary thrombi and pulmonary endothelial dysfunction responsive to thrombolysis, Lancet Resp. Med., 10 (2020), e44. https://doi.org/10.1002/ctm2.44 doi: 10.1002/ctm2.44
[3]	J. Guay, E. A. Ochroch, S. Kopp, Intraoperative use of low volume ventilation to decrease postoperative mortality, mechanical ventilation, lengths of stay and lung injury in adults without acute lung injury, Cochrane Database Syst. Rev., 2018 (2018), CD011151. https://doi.org/10.1002/14651858.CD011151.pub3 doi: 10.1002/14651858.CD011151.pub3
[4]	T. Yoshida, S. Nakahashi, M. A. M. Nakamura, Y. Koyama, R. Roldan, V. Torsani, et al., Volume-controlled ventilation does not prevent injurious inflation during spontaneous effort, Am. J. Resp. Cri. Care, 196 (2017), 590–601. https://doi.org/10.1164/rccm.201610-1972OC doi: 10.1164/rccm.201610-1972OC
[5]	Y. Shi, B. Zhang, M. Cai, X. D. Zhang, Numerical simulation of volume-controlled mechanical ventilated respiratory system with 2 different lungs, Int. J. Numer. Meth. Bio., 33 (2017), e2852. https://doi.org/10.1002/cnm.2852 doi: 10.1002/cnm.2852
[6]	S. S. Vidhya, K. Keerthana, M. Janaki, J. Kanimozhi, A survey of control algorithms used in physiological closed loop control for oxygen therapy, Int. J. Appl. Eng. Res., 14 (2019), 694–702.
[7]	C. Kirakli, I. Naz, O. Ediboglu, D. Tatar, A. Budak, E. Tellioglu, A randomized controlled trial comparing the ventilation duration between adaptive support ventilation and pressure assist/control ventilation in medical patients in the ICU, Chest, 147 (2015), 1503–1509. https://doi.org/10.1378/chest.14-2599 doi: 10.1378/chest.14-2599
[8]	S. Mesic, R. Babuska, H. C. Hoogsteden, A. F. Verbraak, Computer-controlled mechanical simulation of the artificially ventilated human respiratory system, IEEE T. Biomed. Eng., 50 (2003), 731–743. https://doi.org/10.1109/TBME.2003.812166 doi: 10.1109/TBME.2003.812166
[9]	M. E. Shahri, S. Balochian, H. Balochian, Y. Zhang, Design of fractional–order PID controllers for time delay systems using differential evolution, Indian J. Sci. Technol., 7 (2014), 1307–1315. https://doi.org/10.17485/ijst/2014/v7i9.28 doi: 10.17485/ijst/2014/v7i9.28
[10]	N. Nasirpour, S. Balochian, Optimal design of fractional-order PID controllers for multi-input multi-output (variable air volume) air-conditioning system using particle swarm optimization, Intell. Build. Int., 9 (2017), 107–119. https://doi.org/10.1080/17508975.2016.1170659 doi: 10.1080/17508975.2016.1170659
[11]	J. Kennedy, R. Eberhart, Particle swarm optimization, In: Proceedings of ICNN'95-international conference on neural networks, 1995, 1942–1948. https://doi.org/10.1109/ICNN.1995.488968
[12]	K. M. Passino, Distributed optimization and control using only a germ of intelligence, In: The 2000 IEEE international symposium on intelligent control. Held jointly with the 8th IEEE Mediterranean conference on control and automation (Cat. No.00CH37147), 2000, 5–13. https://doi.org/10.1109/ISIC.2000.882888
[13]	S. Momani, I. M. Batiha, R. El-Khazali, Design of $PI^\lambda D^\delta$-heart rate controllers for cardiac pacemaker, In: 2019 IEEE international symposium on signal processing and information technology (ISSPIT), 2019. https://doi.org/10.1109/ISSPIT47144.2019.9001785
[14]	I. M. Batiha, R. El-Khazali, S. Momani, Dynamic responses of $PI^\lambda$, $PD^\delta$, and $PI^\lambda D^\delta$ controllers for prosthetic hand model using PSO algorithm, In: 2019 IEEE international symposium on signal processing and information technology (ISSPIT), 2019. https://doi.org/10.1109/ISSPIT47144.2019.9001835
[15]	I. M. Batiha, S. A. Njadat, R. M. Batyha, A. Zraiqat, A. Dababneh, S. Momani, Design fractional-order PID controllers for single-joint robot arm model, Int. J. Advance Soft Compu. Appl., 14 (2022), 96–114. https://doi.org/10.15849/IJASCA.220720.07 doi: 10.15849/IJASCA.220720.07
[16]	S. Momani, I. M. Batiha, Tuning of the fractional-order PID controller for some real-life industrial processes using particle swarm optimization, Prog. Fract. Differ. Appl., 8 (2022), 377–391. https://doi.org/10.18576/pfda/080303 doi: 10.18576/pfda/080303
[17]	R. El-Khazali, I. M. Batiha, S. Momani, The drug administration via fractional-order $PI^\lambda D^\delta$-controller, Prog. Fract. Differ. Appl., 8 (2022), 53–62. https://doi.org/10.18576/pfda/080103 doi: 10.18576/pfda/080103
[18]	I. M. Batiha, J. Oudetallah, A. Ouannas, A. A. Al-Nana, I. H. Jebril, Tuning the fractional-order PID-controller for blood glucose level of diabetic patients, Int. J. Advance Soft Compu. Appl., 13 (2021), 1–10.
[19]	A. K. Gil'mutdinov, P. A. Ushakov, R. El-Khazali, Fractal elements and their applications, Switzerland: Springer International Publishing, 2017. https://doi.org/10.1007/978-3-319-45249-4
[20]	R. El-Khazali, I. M. Batiha, S. Momani, Approximation of fractional-order operators, In: Fractional calculus, Singapore: Springer, 2019,121–151. https://doi.org/10.1007/978-981-15-0430-3_8
[21]	B. T. Krishna, Studies on fractional order differentiators and integrators: A survey, Signal Process., 91 (2011), 386–426. https://doi.org/10.1016/j.sigpro.2010.06.022 doi: 10.1016/j.sigpro.2010.06.022
[22]	R. El-Khazali, Fractional-order $LC^\alpha L$ filter-based grid connected PV systems, In: 2019 IEEE 62nd international midwest symposium on circuits and systems (MWSCAS), 2019,533–536. https://doi.org/10.1109/MWSCAS.2019.8885133
[23]	R. El-Khazali, On the biquadratic approximation of fractional-order Laplacian operators, Analog Integr. Circ. Sig. Procss., 82 (2015), 503–517. https://doi.org/10.1007/s10470-014-0432-8 doi: 10.1007/s10470-014-0432-8
[24]	I. Podlubny, Fractional-order systems and $PI^\lambda D^\mu$-controllers, In: IEEE transactions on automatic control, 1999,208–214. https://doi.org/10.1109/9.739144
[25]	I. M. Batiha, R. El-Khazali, A. AlSaedi, S. Momani, The general solution of singular fractional-order linear time-invariant continuous systems with regular pencils, Entropy, 20 (2018), 400. https://doi.org/10.3390/e20060400 doi: 10.3390/e20060400
[26]	R. El-Khazali, Fractional-order $PI^\lambda D^\mu$ controller design, Comput. Math. Appl., 66 (2013), 639–646. https://doi.org/10.1016/j.camwa.2013.02.015 doi: 10.1016/j.camwa.2013.02.015
[27]	S. Momani, R. El-Khazali, I. M. Batiha, Tuning PID and $PI^\lambda D^\delta$ controllers using particle swarm optimization algorithm via El-Khazali's approach, AIP Conf. Proc., 2172 (2019), 050003. https://doi.org/10.1063/1.5133522 doi: 10.1063/1.5133522
[28]	I. Podlubny, L. Dorcak, I. Kostial, On fractional derivatives, fractional-order dynamic systems and $PI^\lambda D^\mu$ -controllers, In: Proceedings of the 36th IEEE conference on decision and control, 1997, 4985–4990. https://doi.org/10.1109/CDC.1997.649841
[29]	T. Hamadneh, I. Abu-Falahah, M. AlQudah, Numerical optimization and positivity certificates for polynomials and rationals over simplices, J. Comput. Appl. Math., 414 (2022), 114430. https://doi.org/10.1016/j.cam.2022.114430 doi: 10.1016/j.cam.2022.114430
[30]	W. Lin, Z. Chongquan, Design of optimal fractional-order PID controllers using particle swarm optimization algorithm for DC motor system, In: 2015 IEEE advanced information technology, electronic and automation control conference (IAEAC), 2015,175–179. https://doi.org/10.1109/IAEAC.2015.7428542
[31]	S. Das, A. Biswas, S. Dasgupta, A. Abraham, Bacterial foraging optimization algorithm: Theoretical foundations, analysis, and applications, In: Foundations of computational intelligence, Heidelberg: Springer, 2009, 23–55. https://doi.org/10.1007/978-3-642-01085-9_2
[32]	M. Nasri, H. Nezamabadi-pour, M. Maghfoori, A PSO-based optimum design of PID controller for a linear brushless DC motor, Proceedings of World Academy of Science, Engineering and Technology, 20 (2007), 211–215.
[33]	B. D. Halilu, E. C. Anene, E. E. Omigzegba, L. Maijama'a, S. A. Baraza, Optimization of PID controller gains for identified magnetic levitation plant using bacteria foraging algorithm, Int. J. Eng. Modern Technol., 5 (2019), 12–18.
[34]	M. A. Muñoz, S. K. Halgamuge, W. Alfonso, E. F. Caicedo, Simplifying the bacteria foraging optimization algorithm, In: IEEE congress on evolutionary computation, 2010, 1–7. https://doi.org/10.1109/CEC.2010.5586025
[35]	K. E. Dagher, Design of an auto-tuning PID controller for systems based on slice genetic algorithm, IJCCCE, 13 (2013), 1–9.
[36]	A. Oustaloup, F. Levron, B. Mathieu, F. M. Nanot, Frequency band complex noninteger differentiator: characterization and synthesis, IEEE T. Circuits Syst. I, 47 (2000), 25–39. https://doi.org/10.1109/81.817385 doi: 10.1109/81.817385
[37]	I. Dimeas, Design of an integrated fractional-order controller, Patras: University of Patras, 2017.
[38]	A. T. Yimchunger, D. Acharya, D. K. Das, Particle swarm optimization based PID-controller design for volume control of artificial ventilation system, In: 2020 IEEE calcutta conference (CALCON), 2020,278–282. https://doi.org/10.1109/CALCON49167.2020.9106480
[39]	M. Walter, S. Leonhardt, Control applications in artificial ventilation, In: 2007 Mediterranean conference on control & automation, 2007, 1–6. https://doi.org/10.1109/MED.2007.4433762

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