THE ADVENT OF THE PROPORTIONAL INTEGRAL DERIVATIVE CONTROLLER: A REVIEW

Name of journalMuhandislik sohasidagi ilg’or texnologiyalar
Number of editionVol 2(10), 2023
View count 56

Web Address

DOI10.24412/2181-1431-2023-2-5-22

Date of creation in the UzSCI system 15-03-2024

Read count 56

Date of publication 20-04-2023

Main LanguageIngliz

Pages5

Tags

Ўзбек

Engineers have long sought to minimize human involvement in engineering processes by automating them, which reduces the likelihood of human error and imperfection. This not only lowers production costs but also minimizes the risk of life-endangering operations for humans. The control of engineering processes is critical to protecting devices from operating beyond their designed capabilities. This study investigates and presents a thorough review of the adventure of the Proportional-Integral-Derivative (PID) controller and its types. This entails the informative evolution of the controller’s birth and how it has become an essential tool for those working in the field of control systems, revolutionizing the way feedback control is used in a variety of engineering applications. This paper examines the efforts of eminent researchers and engineers who have made significant contributions to the development of this theory and actual use of this control approach. Apart from conceptualizing seven categories of control systems, this work addresses the benefits and drawbacks of the PID controller while highlighting its adaptability, clar ity, and durability. For researchers, practitioners, and students looking for a deeper understanding of this crucial control technique and its effects on various industries, the mathematical formulation and transfer function representation of the PID controller are presented and recommended, along with a comprehensive tabular review that serves as hands-on for any researcher in this area.

Tags

artificial intelligence

control systems

Machine Learning

Proportional-Integral-Derivative (PID)

№ Author name position Name of organisation

1 Mumuni Q.A. Dean Lagos State University

2 OLAYIWOLAMUMUNI A.I. professor Lagos State University

3 YUSSOUFF A.A. assistant professor Lagos State University

№ Name of reference

1 Control Engineering: What is it? (And its History) | Electrical4U

2 D. Lee, W. Yoo, and S. Won, “An integral control for synchronization of a class of unknown non-autonomous chaotic systems,” Physics Letters A, vol. 374, no. 41, pp. 4231 – 4237, 2010.

3 Who Made America? | Innovators | Elmer Sperry (pbs.org)

4 Z. Lendek, R. Babuska and B. De Schutter, “Stability of Cascaded Fuzzy Systems and Observers,” IEEE Transactions on Fuzzy Systems, vol. 17, no. 3, pp. 641–653, June 2009.

5 M. Chadli and T. M. Guerra, “LMI Solution for Robust Static Output Feedback Control of Takagi-Sugeno Fuzzy Models,” IEEE Trans. on Fuzzy Systems, vol. 20, no. 6, pp. 1160–1165, 2012

6 A. M. Nagy Kiss, B. Max, G. Mourot, G. Schutz and J. Ragot, “State estimation of two-time scale multiple models. Application to a wastewater treatment plant,” Journal of Control Engineering Practice, vol. 19, no. 11, pp. 1354–1362, 2011.

7 A. M. Nagy Kiss, B. Max, G. Mourot, G. Schutz and J. Ragot, “Observers design for uncertain Takagi-Sugeno systems with unmeasurable premise variables and unknown inputs. Application to a wastewater treatment plant,” Journal of Process Control, vol. 21, no. 7, pp. 1105–1114, 2011.

8 S. Aouaouda, M. Chadli, M. Tarek Khadir and T. Bouarar, “Robust fault tolerant tracking controller design for unknown inputs T–S models with unmeasurable premise variables,” Journal of Process Control, vol. 22, no. 5, pp. 261–872, 2012

9 Gao-jue, “Exploration and Design in Teaching of PID Control Based on Simulink Simulation”, Guangzhou Chemical Industry, vol.41, No.20, pp. 199-200, 212, October. 2013.

10 Li-lan.,” Review of adaptive fuzzy control”, Shandong Industrial Technology, vol.10, pp.209-210, October. 2015.

11 Alireza Fereidouni, “A new adaptive configuration of PID type fuzzy logic controller”, ISA Transactions, vol.56, pp.222-240, 2015.

12 J. L. Piquero et al., “A New Sliding Mode Controller Implementation On An Autonomous Qquadcopter System,” Int. J. Autom. Smart Technol., vol. 9, no. 2, pp. 53–63, Jun. 2019.

13 "National Instruments," 5 March 2019. [Online]. Available: https://www.ni.com/en-ph/innovations/white-papers/06/pidtheory-explained.html. [Accessed 10 August 2019].

14 M. A. Lukmana and H. Nurhadi, “Preliminary study on Unmanned Aerial Vehicle (UAV) Quadcopter using PID controller,” ICAMIMIA 2015 - Int. Conf. Adv. Mechatronics, Intell. Manuf. Ind. Autom. Proceeding - conjunction with Ind. Mechatronics Autom. Exhib. IMAE, pp. 34–37, 2016.

15 A. Visioli, “Practical PID Control”, Springer-Verlag, London 2006

16 G. K. & E. B. S. ANUSHA, “Comparison of Tuning Methods of Pid Controller,” BEST Int. J. Manag. Inf. Technol. Eng. (BEST IJMITE), vol. 2, no. 8, pp. 1–8, 2014.

17 M. Ruel, “Closed Loop Tuning Vs Open Loop Tuning : Tuning All Your Loops While the Process Is Running Is Now Possible,” Control, 2010.

18 I. May and Y. Joglekar, “Dynamic Performance Analysis of PID Controller with one Memristor,” Sci. Technol., pp. 1234–1237, 2011.

19 V. Vindhya and V. Reddy, “PID-Fuzzy Logic hybrid Controller for a Digitally Controlled DC-DC Converter,” Int. Conf. Commun. Conserv. Energy, pp. 362–366, 2013.

20 W. Li, “Design of a hybrid fuzzy logic proportional plus conventional integral-derivative controller,” IEEE Trans. Fuzzy Syst., vol. 6, no. 4, pp. 449–463, 1998.

21 H. He, F. Liu, L. Li, J.-R. Yang, L. Su, and Y. Wu, “Study of PID Control System for Ant Colony Algorithm,” in 2009 WRI Global Congress on Intelligent Systems, 2009, vol. 1, pp. 9–12.

22 C. C. Lee, “Fuzzy logic in control systems: fuzzy logic controller. II,” IEEE Trans. Syst. Man. Cybern., vol. 20, no. 2, 1990.

23 M. Petrov, I. Ganchev, and A. Taneva, “Fuzzy PID Control of Nonlinear Plants,” Structure, no. September, pp. 0–5, 2002.

24 W. L. W. Li, X. C. X. Chang, and J. Farrell, “Stability and performance analysis of an enhanced hybrid fuzzy P+IDcontroller,” Proc. 2001 Am. Control Conf. (Cat. No.01CH37148), vol. 5, no. 3, pp. 3855–3860, 2001.

25 M. Brahim, A. Abdelkarim, and M. Benrejeb, “On the design of process fuzzy PID controller,” in 2014 International Conference on Control, Decision and Information Technologies (CoDIT), 2014, no. 1, pp. 483–487

26 I. N’Doye, S. Asiri, A. Aloufi, A. Al-Awan, and T-M. Laleg-Kirati, “Intelligent proportional-integral-derivative control-based modulating functions for laser beam pointing and stabilization,” IEEE Transactions on Control System Technology. (2019).

27 M. J. Er and Y. L. Sun, “Hybrid fuzzy proportional-integral plus conventional derivative control of linear and nonlinear systems,” IEEE Transactions on Industrial Electronics, VOL. 48, NO. 6, December 2001.

28 B. Huang, B. Lu, Q. Li, and Y. Tong, “Average dwell time based smooth switching linear parameter-varying proportional-integral-derivative control for an F-16 aircraft,” Digital Object Identifier 10.1109/ACCESS.2021.3059900.

29 A. Salem, M. A. Moustafa Hassan, and M. E. Ammar, “Tuning PID controllers using artificial intelligence techniques applied to DC-motor and AVR system,” Asian Journal of Engineering and Technology (ISSN: 2321 – 2462), Volume 02 – Issue 02, April 2014.

30 G. Chengwei, and J. Qian, “Optimized proportional-integral-derivative control strategies and simulation for lower limb functional electrical simulation,” 2011 Fourth International Conference on Information and Computing.

31 Y. Cheng, Q. Nan, R. Wang, T. Dong, Z. Tian, “Fuzzy proportional integral derivative control of a radiofrequency ablation temperature control system,” 2017 10th International Congress on Image and Signal Processing, BioMedical Engineering and Informatics (CISP-BMEI).

32 “Spatial proportional-integral-derivative penalization of distributed consensus filters M. A. Demetriou for spatially distributed processes,” 2013 European Control Conferences (ECC) July 17-19, Zurich, Switzerland.

33 T. Youssef, M. Chadli, and M. Zelmat, “Synthesis of an unknown inputs proportional integral observation for TS fuzzy models,” 2013 European Control Conferences (ECC) July 17-19, Zurich, Switzerland.

34 H. Shan, H. Liu, L. Zhang, F. Li, and Q. Liu, “The control method of acceleration simulation mode emissions detection systems based on fuzzy proportional-integral-derivative control,” 2015 12th International Conference on Fuzzy Systems and Knowledge discovery (FSKD)

35 K. C. U. Obias, M. F. Q. Say, E. A. V. Fernandez, A. Y. Chua, and E. Sybingco, “A study of the interaction of proportional-integral-derivative control in a Quadcopter unmanned aerial vehicle using design of experiment,” 978-1-7281-3044-6/19/$31.00 (2019) IEEE.

36 N. S. A. Aziz, R. Adnan, and M. Tajjudin, “Design of fuzzy proportional plus fractional-order integral-derivative controller,” 2016 IEEE International Conference on Automatic Control and Intelligent Systems (I2CACIS), 22 October 2016, Shah Alam, Malaysia

37 A. P. S. Ramalakshmi, and P. S. Manoharan, “Non-linear modelling and PID control of twin rotor MIMO system,” 2012 IEEE International Conference on Advanced Communication Control and Computing Technologies (ICACCCT).

38 B. Y. Husodo and S. M. Ayob, “Design of proportional integral derivative controller for impedance-source inverter,” 2011 International Conference on Computer Applications and Industrial Electronics (ICCAIE 2011).

39 I. Kumiawan, A. I. Cahyadi, and I. Ardiyanto, “Tuning fractional order proportional integral derivative controller for DC motor control model using cross-entropy method,” 2018 3rd International Conference on Information Technology, Information Systems and Electrical Engineering (ICITISEE), Yogyakarta, Indonesia.

40 A. K. Srivastava, D. Kumar, S. M. Tripathi, and P. K. Sen, “Comparative study of proportional-integral and proportional-integral-derivative (PI and PID) controllers for Z-source inverter-fed induction motor drive,” 978-1-4673-1049-9/12/$31.00 ©2012 IEEE.

41 A. Gargioli, F. Rinaldi, and F. Quanglioti, “Proportional integral derivative and linear quadratic regulation of a multirotor attitude: mathematical modelling, simulations and experimental results,” 2013 International Conference on Unmanned Aircraft Systems (ICUAS) May 28-31, 2013, Grand Hyatt Atlanta, Atlanta, GA.

42 D. Sharma, R. Kumar, and V. Verma, “Fuzzy tuned proportional integral derivative control of paper machine headbox,” IEEE INDICON 2015 1570190789.

43 M. F. N. Tajuddin and N. A. Rahim, “Small-signal AC modelling technique of buck converter with DSP based proportional-integral-derivative (PID) controller,” 2009 IEEE Symposium on Industrial Electronics and Applications (ISIEA 2009), October 4-6, 2009, Kuala Lumpur, Malaysia

44 W-H. Lai and S-F Liang, “An F0 control model for singing synthesis based on proportional-integral-derivative controller,” 978-1-4244-9991-5/11/$26.00 ©2011 IEEE

45 K. Qiu, Z. Zheng, and T.Y. Chen, “Testing proportional-integral-derivative (PID) controller with metamorphic testing,” 2017 IEEE 28th International Symposium on Software Reliability Engineering Workshops.

46 T. A. B. Alves, F. R. Durand, B. A. Angelico, and T. Abrao, “Power allocation scheme for OCDMA NG-PON with proportional-integral-derivative algorithms,” VOL. 8, NO. 9/SEPTEMBER 2016/JOURNAL OF OPTICAL. COMMUNITY. NETWORK. 1943-0620/16/090645-11 Journal © 2016 Optical Society of America.

47 S. K. Pandey and V. Laxmi,” Control of twin rotor MIMO system using PID controller with derivative filter coefficient,” 2014 IEEE Students' Conference on Electrical, Electronics and Computer Science

48 H. Naccache and G. C. Gannod, “Using proportional-integral-derivative control in self-healing adaptive content systems,” 978-0-7695-3708-5/09 $25.00 © 2009 IEEE, 2009 Congress on Services – I

49 C-A. B-Dragos, S. Preitl, R-E. Precup, S. Hergane, E. G. Hughiet, and A.-L. S-Stinean, “State feedback and proportional-integral-derivative control of a magnetic levitation system,” SISY 2016 • IEEE 14th International Symposium on Intelligent Systems and Informatics • August 29-31, 2016, Subotica, Serbia.

50 J. Li and Y. Yuan, “A nonlinear proportional integral derivative-incorporated stochastic gradient descent-based latent factor model,” 2020 IEEE International Conference on Systems, Man, and Cybernetics (SMC) October 11-14, 2020. Toronto, Canada.

51 Q.-X. Wang, S.-L Chen, X. Luo, “An adaptive latent factor model via particle swarm optimization,” Neuro-computing, vol. 369, no. 5, pp. 176- 184, 2019.

52 H-C. Yu, T-C. Chen, and C-S. Liu,”Adaptive fuzzy logic proportional-integral-derivative control for a miniature autofocus voice coil motor actuator with retaining force,” IEEE TRANSACTIONS ON MAGNETICS, VOL. 50, NO. 11, NOVEMBER 2014.

53 K. Gao, J. Song, X. Wang, and H. Li, “Fractional-order proportional-integral-derivative linear active disturbance rejection control design and parameter optimization for hypersonic vehicles with actuator faults,” TSINGHUA SCIENCE AND TECHNOLOGY ISSNll1007-0214 02/10 pp9– 23 DOI: 1 0. 2 6 5 9 9/T ST. 2 0 1 9. 9 0 1 0 0 4 1 Volume 26, Number 1, February 2021.

54 D. Nan and Y. Zhang, “Predictive modelling based on proportional integral derivative neutral networks and quantum computation,” Proceedings of the 7th World Congress on Intelligent Control and Automation June 25 - 27, 2008, Chongqing, China.

55 B. B. M. Pinto, J. G. R. Mota, and O. M. Almeida, “PID self-adjustable fuzzy logic MIMO case: method and application,” 2010 9th IEEE/IAS International Conference on Industry Applications - INDUSCON 2010.

56 J-G. Juang, M-T. Huang, and W-K. Liu, “PID control using researched genetic algorithms for MIMO system,” IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS—PART C: APPLICATIONS AND REVIEWS, VOL. 38, NO. 5, SEPTEMBER 2008.

57 TRMS 33-220 User Manual, 3-000M5, Feedback Company, E. Sussex, U.K. 1998.

58 M. H. Moradi, “State space representation of MIMO predictive PID controller,” Bu Ali Sina University, Dept of Electrical Engineering, Faculty of Engineering, University of Bu Ali Sina, Hamadan, Iran. IEEE XPLORE.

59 M. H. Moradi, M. R. Katebi, and M. A. Johnson, “Robust MIMO PID tuning method,” 0-7803-7386-3/02/$17.00 0 2002 IEEE.

60 K. J. Astrom, K. H. Johansson, and Q-G. Wang, "Design of decoupled PID controllers for MIMO systems," IEEE Transactions on Automatic Control, vol. 48, no. 4, pp. 679-686, April 2003.

Waiting

№	Author name	position	Name of organisation
1	Mumuni Q.A.	Dean	Lagos State University
2	OLAYIWOLAMUMUNI A.I.	professor	Lagos State University
3	YUSSOUFF A.A.	assistant professor	Lagos State University

№	Name of reference
1	Control Engineering: What is it? (And its History) \| Electrical4U
2	D. Lee, W. Yoo, and S. Won, “An integral control for synchronization of a class of unknown non-autonomous chaotic systems,” Physics Letters A, vol. 374, no. 41, pp. 4231 – 4237, 2010.
3	Who Made America? \| Innovators \| Elmer Sperry (pbs.org)
4	Z. Lendek, R. Babuska and B. De Schutter, “Stability of Cascaded Fuzzy Systems and Observers,” IEEE Transactions on Fuzzy Systems, vol. 17, no. 3, pp. 641–653, June 2009.
5	M. Chadli and T. M. Guerra, “LMI Solution for Robust Static Output Feedback Control of Takagi-Sugeno Fuzzy Models,” IEEE Trans. on Fuzzy Systems, vol. 20, no. 6, pp. 1160–1165, 2012
6	A. M. Nagy Kiss, B. Max, G. Mourot, G. Schutz and J. Ragot, “State estimation of two-time scale multiple models. Application to a wastewater treatment plant,” Journal of Control Engineering Practice, vol. 19, no. 11, pp. 1354–1362, 2011.
7	A. M. Nagy Kiss, B. Max, G. Mourot, G. Schutz and J. Ragot, “Observers design for uncertain Takagi-Sugeno systems with unmeasurable premise variables and unknown inputs. Application to a wastewater treatment plant,” Journal of Process Control, vol. 21, no. 7, pp. 1105–1114, 2011.
8	S. Aouaouda, M. Chadli, M. Tarek Khadir and T. Bouarar, “Robust fault tolerant tracking controller design for unknown inputs T–S models with unmeasurable premise variables,” Journal of Process Control, vol. 22, no. 5, pp. 261–872, 2012
9	Gao-jue, “Exploration and Design in Teaching of PID Control Based on Simulink Simulation”, Guangzhou Chemical Industry, vol.41, No.20, pp. 199-200, 212, October. 2013.
10	Li-lan.,” Review of adaptive fuzzy control”, Shandong Industrial Technology, vol.10, pp.209-210, October. 2015.
11	Alireza Fereidouni, “A new adaptive configuration of PID type fuzzy logic controller”, ISA Transactions, vol.56, pp.222-240, 2015.
12	J. L. Piquero et al., “A New Sliding Mode Controller Implementation On An Autonomous Qquadcopter System,” Int. J. Autom. Smart Technol., vol. 9, no. 2, pp. 53–63, Jun. 2019.
13	"National Instruments," 5 March 2019. [Online]. Available: https://www.ni.com/en-ph/innovations/white-papers/06/pidtheory-explained.html. [Accessed 10 August 2019].
14	M. A. Lukmana and H. Nurhadi, “Preliminary study on Unmanned Aerial Vehicle (UAV) Quadcopter using PID controller,” ICAMIMIA 2015 - Int. Conf. Adv. Mechatronics, Intell. Manuf. Ind. Autom. Proceeding - conjunction with Ind. Mechatronics Autom. Exhib. IMAE, pp. 34–37, 2016.
15	A. Visioli, “Practical PID Control”, Springer-Verlag, London 2006
16	G. K. & E. B. S. ANUSHA, “Comparison of Tuning Methods of Pid Controller,” BEST Int. J. Manag. Inf. Technol. Eng. (BEST IJMITE), vol. 2, no. 8, pp. 1–8, 2014.
17	M. Ruel, “Closed Loop Tuning Vs Open Loop Tuning : Tuning All Your Loops While the Process Is Running Is Now Possible,” Control, 2010.
18	I. May and Y. Joglekar, “Dynamic Performance Analysis of PID Controller with one Memristor,” Sci. Technol., pp. 1234–1237, 2011.
19	V. Vindhya and V. Reddy, “PID-Fuzzy Logic hybrid Controller for a Digitally Controlled DC-DC Converter,” Int. Conf. Commun. Conserv. Energy, pp. 362–366, 2013.
20	W. Li, “Design of a hybrid fuzzy logic proportional plus conventional integral-derivative controller,” IEEE Trans. Fuzzy Syst., vol. 6, no. 4, pp. 449–463, 1998.
21	H. He, F. Liu, L. Li, J.-R. Yang, L. Su, and Y. Wu, “Study of PID Control System for Ant Colony Algorithm,” in 2009 WRI Global Congress on Intelligent Systems, 2009, vol. 1, pp. 9–12.
22	C. C. Lee, “Fuzzy logic in control systems: fuzzy logic controller. II,” IEEE Trans. Syst. Man. Cybern., vol. 20, no. 2, 1990.
23	M. Petrov, I. Ganchev, and A. Taneva, “Fuzzy PID Control of Nonlinear Plants,” Structure, no. September, pp. 0–5, 2002.
24	W. L. W. Li, X. C. X. Chang, and J. Farrell, “Stability and performance analysis of an enhanced hybrid fuzzy P+IDcontroller,” Proc. 2001 Am. Control Conf. (Cat. No.01CH37148), vol. 5, no. 3, pp. 3855–3860, 2001.
25	M. Brahim, A. Abdelkarim, and M. Benrejeb, “On the design of process fuzzy PID controller,” in 2014 International Conference on Control, Decision and Information Technologies (CoDIT), 2014, no. 1, pp. 483–487
26	I. N’Doye, S. Asiri, A. Aloufi, A. Al-Awan, and T-M. Laleg-Kirati, “Intelligent proportional-integral-derivative control-based modulating functions for laser beam pointing and stabilization,” IEEE Transactions on Control System Technology. (2019).
27	M. J. Er and Y. L. Sun, “Hybrid fuzzy proportional-integral plus conventional derivative control of linear and nonlinear systems,” IEEE Transactions on Industrial Electronics, VOL. 48, NO. 6, December 2001.
28	B. Huang, B. Lu, Q. Li, and Y. Tong, “Average dwell time based smooth switching linear parameter-varying proportional-integral-derivative control for an F-16 aircraft,” Digital Object Identifier 10.1109/ACCESS.2021.3059900.
29	A. Salem, M. A. Moustafa Hassan, and M. E. Ammar, “Tuning PID controllers using artificial intelligence techniques applied to DC-motor and AVR system,” Asian Journal of Engineering and Technology (ISSN: 2321 – 2462), Volume 02 – Issue 02, April 2014.
30	G. Chengwei, and J. Qian, “Optimized proportional-integral-derivative control strategies and simulation for lower limb functional electrical simulation,” 2011 Fourth International Conference on Information and Computing.
31	Y. Cheng, Q. Nan, R. Wang, T. Dong, Z. Tian, “Fuzzy proportional integral derivative control of a radiofrequency ablation temperature control system,” 2017 10th International Congress on Image and Signal Processing, BioMedical Engineering and Informatics (CISP-BMEI).
32	“Spatial proportional-integral-derivative penalization of distributed consensus filters M. A. Demetriou for spatially distributed processes,” 2013 European Control Conferences (ECC) July 17-19, Zurich, Switzerland.
33	T. Youssef, M. Chadli, and M. Zelmat, “Synthesis of an unknown inputs proportional integral observation for TS fuzzy models,” 2013 European Control Conferences (ECC) July 17-19, Zurich, Switzerland.
34	H. Shan, H. Liu, L. Zhang, F. Li, and Q. Liu, “The control method of acceleration simulation mode emissions detection systems based on fuzzy proportional-integral-derivative control,” 2015 12th International Conference on Fuzzy Systems and Knowledge discovery (FSKD)
35	K. C. U. Obias, M. F. Q. Say, E. A. V. Fernandez, A. Y. Chua, and E. Sybingco, “A study of the interaction of proportional-integral-derivative control in a Quadcopter unmanned aerial vehicle using design of experiment,” 978-1-7281-3044-6/19/$31.00 (2019) IEEE.
36	N. S. A. Aziz, R. Adnan, and M. Tajjudin, “Design of fuzzy proportional plus fractional-order integral-derivative controller,” 2016 IEEE International Conference on Automatic Control and Intelligent Systems (I2CACIS), 22 October 2016, Shah Alam, Malaysia
37	A. P. S. Ramalakshmi, and P. S. Manoharan, “Non-linear modelling and PID control of twin rotor MIMO system,” 2012 IEEE International Conference on Advanced Communication Control and Computing Technologies (ICACCCT).
38	B. Y. Husodo and S. M. Ayob, “Design of proportional integral derivative controller for impedance-source inverter,” 2011 International Conference on Computer Applications and Industrial Electronics (ICCAIE 2011).
39	I. Kumiawan, A. I. Cahyadi, and I. Ardiyanto, “Tuning fractional order proportional integral derivative controller for DC motor control model using cross-entropy method,” 2018 3rd International Conference on Information Technology, Information Systems and Electrical Engineering (ICITISEE), Yogyakarta, Indonesia.
40	A. K. Srivastava, D. Kumar, S. M. Tripathi, and P. K. Sen, “Comparative study of proportional-integral and proportional-integral-derivative (PI and PID) controllers for Z-source inverter-fed induction motor drive,” 978-1-4673-1049-9/12/$31.00 ©2012 IEEE.
41	A. Gargioli, F. Rinaldi, and F. Quanglioti, “Proportional integral derivative and linear quadratic regulation of a multirotor attitude: mathematical modelling, simulations and experimental results,” 2013 International Conference on Unmanned Aircraft Systems (ICUAS) May 28-31, 2013, Grand Hyatt Atlanta, Atlanta, GA.
42	D. Sharma, R. Kumar, and V. Verma, “Fuzzy tuned proportional integral derivative control of paper machine headbox,” IEEE INDICON 2015 1570190789.
43	M. F. N. Tajuddin and N. A. Rahim, “Small-signal AC modelling technique of buck converter with DSP based proportional-integral-derivative (PID) controller,” 2009 IEEE Symposium on Industrial Electronics and Applications (ISIEA 2009), October 4-6, 2009, Kuala Lumpur, Malaysia
44	W-H. Lai and S-F Liang, “An F0 control model for singing synthesis based on proportional-integral-derivative controller,” 978-1-4244-9991-5/11/$26.00 ©2011 IEEE
45	K. Qiu, Z. Zheng, and T.Y. Chen, “Testing proportional-integral-derivative (PID) controller with metamorphic testing,” 2017 IEEE 28th International Symposium on Software Reliability Engineering Workshops.
46	T. A. B. Alves, F. R. Durand, B. A. Angelico, and T. Abrao, “Power allocation scheme for OCDMA NG-PON with proportional-integral-derivative algorithms,” VOL. 8, NO. 9/SEPTEMBER 2016/JOURNAL OF OPTICAL. COMMUNITY. NETWORK. 1943-0620/16/090645-11 Journal © 2016 Optical Society of America.
47	S. K. Pandey and V. Laxmi,” Control of twin rotor MIMO system using PID controller with derivative filter coefficient,” 2014 IEEE Students' Conference on Electrical, Electronics and Computer Science
48	H. Naccache and G. C. Gannod, “Using proportional-integral-derivative control in self-healing adaptive content systems,” 978-0-7695-3708-5/09 $25.00 © 2009 IEEE, 2009 Congress on Services – I
49	C-A. B-Dragos, S. Preitl, R-E. Precup, S. Hergane, E. G. Hughiet, and A.-L. S-Stinean, “State feedback and proportional-integral-derivative control of a magnetic levitation system,” SISY 2016 • IEEE 14th International Symposium on Intelligent Systems and Informatics • August 29-31, 2016, Subotica, Serbia.
50	J. Li and Y. Yuan, “A nonlinear proportional integral derivative-incorporated stochastic gradient descent-based latent factor model,” 2020 IEEE International Conference on Systems, Man, and Cybernetics (SMC) October 11-14, 2020. Toronto, Canada.
51	Q.-X. Wang, S.-L Chen, X. Luo, “An adaptive latent factor model via particle swarm optimization,” Neuro-computing, vol. 369, no. 5, pp. 176- 184, 2019.
52	H-C. Yu, T-C. Chen, and C-S. Liu,”Adaptive fuzzy logic proportional-integral-derivative control for a miniature autofocus voice coil motor actuator with retaining force,” IEEE TRANSACTIONS ON MAGNETICS, VOL. 50, NO. 11, NOVEMBER 2014.
53	K. Gao, J. Song, X. Wang, and H. Li, “Fractional-order proportional-integral-derivative linear active disturbance rejection control design and parameter optimization for hypersonic vehicles with actuator faults,” TSINGHUA SCIENCE AND TECHNOLOGY ISSNll1007-0214 02/10 pp9– 23 DOI: 1 0. 2 6 5 9 9/T ST. 2 0 1 9. 9 0 1 0 0 4 1 Volume 26, Number 1, February 2021.
54	D. Nan and Y. Zhang, “Predictive modelling based on proportional integral derivative neutral networks and quantum computation,” Proceedings of the 7th World Congress on Intelligent Control and Automation June 25 - 27, 2008, Chongqing, China.
55	B. B. M. Pinto, J. G. R. Mota, and O. M. Almeida, “PID self-adjustable fuzzy logic MIMO case: method and application,” 2010 9th IEEE/IAS International Conference on Industry Applications - INDUSCON 2010.
56	J-G. Juang, M-T. Huang, and W-K. Liu, “PID control using researched genetic algorithms for MIMO system,” IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS—PART C: APPLICATIONS AND REVIEWS, VOL. 38, NO. 5, SEPTEMBER 2008.
57	TRMS 33-220 User Manual, 3-000M5, Feedback Company, E. Sussex, U.K. 1998.
58	M. H. Moradi, “State space representation of MIMO predictive PID controller,” Bu Ali Sina University, Dept of Electrical Engineering, Faculty of Engineering, University of Bu Ali Sina, Hamadan, Iran. IEEE XPLORE.
59	M. H. Moradi, M. R. Katebi, and M. A. Johnson, “Robust MIMO PID tuning method,” 0-7803-7386-3/02/$17.00 0 2002 IEEE.
60	K. J. Astrom, K. H. Johansson, and Q-G. Wang, "Design of decoupled PID controllers for MIMO systems," IEEE Transactions on Automatic Control, vol. 48, no. 4, pp. 679-686, April 2003.