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A review of PID control, tuning methods and applications

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Abstract

This article provides a study of modern and classical approaches used for PID tuning and its applications in various domains. Most of the control systems that are implemented to date with the use of PID control because of its simple structure, ease of implementation, and active research in tuning the PID for a long time. The techniques reviewed in the paper are in the order from classical to modern optimization rules used for the PID tuning. This paper attempts to address the literature review of PID control in an era of control system and bio-medical applications. The development of classical PID to the integration of intelligent control to it, has been surveyed by consideration of various application domains. The primary purpose of this document is to provide a detailed point of information for the people to understand the command of PID in different application areas.

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References

  1. Kang C-G (2016) Origin of stability analysis: “on governors” [historical perspectives ]. IEEE Control Syst Mag 36(5):77–88

    Google Scholar 

  2. Medaglia JD (2019) Clarifying cognitive control and the controllable connectome. Wiley Interdiscip Rev Cognit Sci 10(1):1471

    Google Scholar 

  3. Åström KJ, Kumar PR (2014) Control: a perspective. Automatica 50(1):3–43

    MathSciNet  MATH  Google Scholar 

  4. Bennett S (2000) The past of PID controllers. Ann Rev Control 25:43–53

    Google Scholar 

  5. Bennett S (1993) Development of the PID controller. IEEE Control Syst Mag 13(6):58–62

    Google Scholar 

  6. Fong-Chwee T, Sirisena HR (1988) Self-tuning PID controllers for dead time processes. IEEE Trans Ind Electr 35(1):119–125

    Google Scholar 

  7. Besharati Rad A, Lo WL, Tsang KM (1997) Self-tuning PID controller using Newton–Raphson search method. IEEE Trans Ind Electr 44(5):717–725

    Google Scholar 

  8. Leva A (1993) PID autotuning algorithm based on relay feedback. In: IEE Proceedings D (Control Theory and Applications), vol 140. pp 328–338. IET

  9. Zhuang M, Atherton DP (1993) Automatic tuning of optimum PID controllers. In IEE Proceedings D (Control Theory and Applications), vol 140. pp 216–224. IET

  10. Åström KJ, Hägglund T, Hang CC, Ho WK (1993) Automatic tuning and adaptation for PID controllers-a survey. Contr Eng Pract 1(4):699–714

    Google Scholar 

  11. Gawthrop P (1986) Self-tuning PID controllers: algorithms and implementation. IEEE Trans Autom Contr 31(3):201–209

    MATH  Google Scholar 

  12. Brown RE, Maliotis GN, Gibby JA (1993) PID self-tuning controller for aluminum rolling mill. IEEE Trans Ind Appl 29(3):578–583

    Google Scholar 

  13. Vega P, Prada C, Aleixandre V (1991) Self-tuning predictive PID controller. In: IEE Proceedings D (Control Theory and Applications), vol 138, pp 303–312. IET

  14. Khodadadi H, Ghadiri H (2018) Self-tuning PID controller design using fuzzy logic for half car active suspension system. Int J Dyn Control 6(1):224–232

    MathSciNet  Google Scholar 

  15. Porter B, Jones AH (1992) Genetic tuning of digital PID controllers. Electr Lett 28(9):843–844

    Google Scholar 

  16. Kristiansson B, Lennartson B (2002) Robust and optimal tuning of PI and PID controllers. IEE Proc Contr Theory Appl 149(1):17–25

    MATH  Google Scholar 

  17. Gundes AN, Ozguler AB (2007) PID stabilization of MIMO plants. IEEE Trans Autom Contr 52(8):1502–1508

    MathSciNet  MATH  Google Scholar 

  18. Hsieh C-H, Chou J-H (2007) Design of optimal PID controllers for pwm feedback systems with bilinear plants. IEEE Trans Contr Syst Technol 15(6):1075–1079

    Google Scholar 

  19. Chan YF, Moallem M, Wang W (2007) Design and implementation of modular FPGA-based PID controllers. IEEE Trans Ind Electro 54(4):1898–1906

    Google Scholar 

  20. Yamamoto T, Takao K, Yamada T (2008) Design of a data-driven PID controller. IEEE Trans Contr Syst Technol 17(1):29–39

    Google Scholar 

  21. Sio KC, Lee CK (1998) Stability of fuzzy PID controllers. IEEE Trans Syst Man Cybern Part A Syst Humans 28(4):490–495

    Google Scholar 

  22. Tzafestas S, Papanikolopoulos NP (1990) Incremental fuzzy expert PID control. IEEE Trans Ind Electr 37(5):365–371

    Google Scholar 

  23. Zhao Z-Y, Tomizuka M, Isaka S (1993) Fuzzy gain scheduling of PID controllers. IEEE Trans Syst Man Cybern 23(5):1392–1398

    Google Scholar 

  24. Minh Vu K (1992) Optimal setting for discrete PID controllers. In: IEE Proceedings D (Control Theory and Applications), vol 139. pp 31–40. IET

  25. Tang K-S, Man KF, Chen G, Kwong S (2001) An optimal fuzzy PID controller. IEEE Trans Ind Electr 48(4):757–765

    Google Scholar 

  26. Verma B, Padhy PK (2018a) Optimal PID controller design with adjustable maximum sensitivity. IET Contr Theory Appl 12(8):1156–1165

    MathSciNet  Google Scholar 

  27. Zolotas AC, Halikias GD (1999) Optimal design of PID controllers using the QFT method. IEE Proc Contr Theory Appl 146(6):585–589

    Google Scholar 

  28. Kaya Y, Yamamura S (1962) A self-adaptive system with a variable-parameter PID controller. Trans Am Instit Electr Eng Part II Appl Ind 80(6):378–386

    Google Scholar 

  29. Zhenbin W, Zhenlei W, Guangyi C, Xinjian Z (2005) Digital implementation of fractional order PID controller and its application. J Syst Eng Electr 16(1):116–122

    Google Scholar 

  30. Viola J, Angel L (2015) Factorial design for robustness evaluation of fractional PID controllers. IEEE Lat Am Trans 13(5):1286–1293

    Google Scholar 

  31. Ranjbaran K, Tabatabaei M (2018) Fractional order [PI],[PD] and [PI][PD] controller design using Bode’s integrals. Int J Dyn Contr 6(1):200–212

    MathSciNet  Google Scholar 

  32. Bongulwar MR, Patre BM (2018) Design of FOPID controller for fractional-order plants with experimental verification. Int J Dyn Contr 6(1):213–223

    MathSciNet  Google Scholar 

  33. Åström KJ, Hägglund T (2001) The future of PID control. Contr Eng Pract 9(11):1163–1175

    Google Scholar 

  34. Díaz-Rodríguez Iván D, Sangjin H, Bhattacharyya Shankar P (2019) Analytical design of PID controllers. Springer, Berlin. ISBN 978–3–030–18227–4

  35. Ziegler John G, Nichols Nancy B (1942) Optimum settings for automatic controllers. J Dyn Syst Meas Control Trans ASME 115:220–222

    Google Scholar 

  36. Åström KJ, Hägglund T (1984) Automatic tuning of simple regulators. IFAC Proc Vol 17(2):1867–1872

    MATH  Google Scholar 

  37. Ho WK, Gan OP, Tay EB, Ang EL (1996) Performance and gain and phase margins of well-known PID tuning formulas. IEEE Trans Contr Syst Technol 4(4):473–477

    Google Scholar 

  38. Koivo HN, Tanttu JT (1991) Tuning of PID conrollers: Survey of SISO and MIMO techniques. In: Devanathan R (ed) Intelligent tuning and adaptive control, pp 75–80. Elsevier

  39. Ruano AEB, Fleming PJ, Jones DI (1992) Connectionist approach to PID autotuning. In: IEE Proceedings D (Control Theory and Applications), vol 139, pp 279–285. IET

  40. Aguirre LA (1992) PID tuning based on model matching. Electr Lett 28(25):2269–2271

    Google Scholar 

  41. Zhuang M, Atherton DP (1994) PID controller design for a TITO system. IEE Proc Contr Theory Appl 141(2):111–120

    MATH  Google Scholar 

  42. Poulin E, Pomerleau A (1996) PID tuning for integrating and unstable processes. IEE Proc Contr Theory Appl 143(5):429–435

    MATH  Google Scholar 

  43. Tan W, Liu J, Tam PKS (1998) PID tuning based on loop-shaping \(H_\infty \) control. IEE Proc Contr Theory Appl 145(6):485–490

    Google Scholar 

  44. Wang Q-G, Lee T-H, Fung H-W, Bi Q, Zhang Y (1999) PID tuning for improved performance. IEEE Trans Contr Syst Technol 7(4):457–465

    Google Scholar 

  45. Mann GKI, Hu B-G, Gosine RG (2001) Time-domain based design and analysis of new PID tuning rules. IEE Proc Contr Theory Appl 148(3):251–261

    Google Scholar 

  46. Visioli A (2001a) Tuning of PID controllers with fuzzy logic. IEE Proc Contr Theory Appl 148(1):1–8

    MathSciNet  Google Scholar 

  47. Cominos P, Munro N (2002) PID controllers: recent tuning methods and design to specification. IEE Proc Contr Theory Appl 149(1):46–53

    Google Scholar 

  48. Huang H-P, Roan M-L, Jeng J-C (2002) On-line adaptive tuning for PID controllers. IEE Proc Contr Theory Appl 149(1):60–67

    Google Scholar 

  49. Lennartson B, Kristiansson B (2009) Evaluation and tuning of robust PID controllers. IET Contr Theory Appl 3(3):294–302

    MATH  Google Scholar 

  50. Stafford EM (1977) Design aid for approximate PD and PID on/off controllers. Electr Lett 13(6):163–164

    Google Scholar 

  51. Jacobs OLR, Hewkin PF, While C (1980) Online computer control of PH in an industrial process. In: IEE Proceedings D (Control Theory and Applications), vol 127. pp 161–168. IET

  52. Coppus GWM, Shah SL, Wood RK (1983) Robust multivariable control of a binary distillation column. In: IEE Proceedings D (Control Theory and Applications), vol 30. pp 201–208. IET

  53. Thomas HW, Sandoz DJ, Thomson M (1983) New desaturation strategy for digital PID controllers. In IEE Proceedings D (Control Theory and Applications), vol 130, pp 188–192. IET

  54. Yamamoto T, Shah SL (2004) Design and experimental evaluation of a multivariable self-tuning PID controller. IEE Proc Control Theory Appl 151(5):645–652

    Google Scholar 

  55. Gawthrop PJ, Nomikos PE, Smith LSPS (1990) Adaptive temperature control of industrial processes: a comparative study. In: IEE Proceedings D (Control Theory and Applications), vol 137. pp 137–144. IET

  56. Edwards C, Spurgeon SK (1994) Robust nonlinear control of heating plant. IEE Proc Contr Theory Appl 141(4):227–234

    MATH  Google Scholar 

  57. Dilhac J-M, Ganibal C, Bordeneuve J, Nolhier N (1992) Temperature control in a rapid thermal processor. IEEE Trans Electr Devices 39(1):201–203

    Google Scholar 

  58. Chen C-L, Chang F-Y (1996) Design and analysis of neural/fuzzy variable structural PID control systems. IEE Proc Contr Theory Appl 143(2):200–208

    MATH  Google Scholar 

  59. Scottedward Hodel A, Hall CE (2001) Variable-structure PID control to prevent integrator windup. IEEE Trans Ind Electr 48(2):442–451

    Google Scholar 

  60. Visioli A (2001b) Optimal tuning of PID controllers for integral and unstable processes. IEE Proc Contr Theory Appl 148(2):180–184

    Google Scholar 

  61. Daley S, Liu GP (1999) Optimal PID tuning using direst search algorithms. Comput Contr Eng J 10(2):51–56

    Google Scholar 

  62. Grassi E, Tsakalis K (2000) PID controller tuning by frequency loop-shaping: application to diffusion furnace temperature control. IEEE Trans Contr Syst Technol 8(5):842–847

    Google Scholar 

  63. Katebi MR, Moradi MH (2001) Predictive PID controllers. IEE Proc Contr Theory Appl 148(6):478–487

    Google Scholar 

  64. Pfeiffer BM (2003) PID control of batch processes along pre-optimised trajectories. Comput Contr Eng J 14(5):16–21

    Google Scholar 

  65. Skoczowski S, Domek S, Pietrusewicz K, Broel-Plater B (2005) A method for improving the robustness of PID control. IEEE Trans Ind Electr 52(6):1669–1676

    Google Scholar 

  66. Dinca MP, Gheorghe M, Galvin P (2008) Design of a PID controller for a pcr micro reactor. IEEE Trans Edu 52(1):116–125

    Google Scholar 

  67. Papadopoulos KG, Papastefanaki EN, Margaris NI (2012) Explicit analytical PID tuning rules for the design of Type-III control loops. IEEE Trans Ind Electr 60(10):4650–4664

    Google Scholar 

  68. Gil P, Lucena C, Cardoso A, Palma LB (2014) Gain tuning of fuzzy PID controllers for mimo systems: a performance-driven approach. IEEE Trans Fuzzy Syst 23(4):757–768

    Google Scholar 

  69. Torres WL, Araujo IBQ, Filho JBM, Junior AGC (2017) Mathematical modeling and PID controller parameter tuning in a didactic thermal plant. IEEE Lat Am Trans 15(7):1250–1256

    Google Scholar 

  70. Eslami M, Shayesteh MR, Pourahmadi M (2018) Optimal design of PID-based low-pass filter for gas turbine using intelligent method. IEEE Access 6:15335–15345

    Google Scholar 

  71. Razvarz S, Vargas-Jarillo C, Jafari R, Gegov A (2019) Flow control of fluid in pipelines using PID controller. IEEE Access 7:25673–25680

    Google Scholar 

  72. Garran PT, Garcia G (2017) Design of an optimal PID controller for a coupled tanks system employing adrc. IEEE Lat Am Trans 15(2):189–196

    Google Scholar 

  73. Verma B, Padhy PK (2018b) Indirect IMC-PID controller design. IET Contr Theory Appl 13(2):297–305

    MathSciNet  MATH  Google Scholar 

  74. Bestaoui Y (1989) Decentralised PD and PID robotic regulators. In: IEE Proceedings D (Control Theory and Applications), vol 136. pp 133–145. IET

  75. Zhang H, Trott G, Paul RP (1990) Minimum delay PID control of interpolated joint trajectories of robot manipulators. IEEE Trans Ind Electr 37(5):358–364

    Google Scholar 

  76. Rocco P (1996) Stability of PID control for industrial robot arms. IEEE Trans Robot Autom 12(4):606–614

    Google Scholar 

  77. Sun D, Songyu H, Shao X, Liu C (2009) Global stability of a saturated nonlinear PID controller for robot manipulators. IEEE Trans Contr Syst Technol 17(4):892–899

    Google Scholar 

  78. Feng W, O’reilly J, Ballance DJ (2002) Mimo nonlinear PID predictive controller. IEE Proc Contr Theory Appl 149(3):203–208

    Google Scholar 

  79. Parra-Vega V, Arimoto S, Liu Y-H, Hirzinger G, Akella P (2003) Dynamic sliding PID control for tracking of robot manipulators: theory and experiments. IEEE Trans Robot Autom 19(6):967–976

    Google Scholar 

  80. Jafarov EM, Alpaslan Parlakci MN, Istefanopulos Y (2004) A new variable structure PID-controller design for robot manipulators. IEEE Trans Contr Syst Technol 13(1):122–130

    Google Scholar 

  81. Li W, Chang XG, Wahl FM, Farrell J (2001) Tracking control of a manipulator under uncertainty by fuzzy P \(+\) ID controller. Fuzzy Sets Syst 122(1):125–137

    MathSciNet  MATH  Google Scholar 

  82. Kazemian HB (2002) The SOF-PID controller for the control of a MIMO robot arm. IEEE Trans Fuzzy Syst 10(4):523–532

    Google Scholar 

  83. Sun YL, Joo Er M (2004) Hybrid fuzzy control of robotics systems. IEEE Trans Fuzzy Syst 12(6):755–765

    Google Scholar 

  84. Yildirim S, Sukkar MF, Demirci R, Aslantas V (1996) Design of adaptive nns-robust-PID controller for a robot control. In: Proceedings of the 1996 IEEE International Symposium on Intelligent Control, pp 508–513. IEEE

  85. Kwok DP, Sheng F(1994) Genetic algorithm and simulated annealing for optimal robot arm PID control. In: Proceedings of the First IEEE Conference on Evolutionary Computation. IEEE World Congress on Computational Intelligence, pp 707–713. IEEE,

  86. Park J, Chung WK (2000a) Analytic nonlinear H/sub/spl infin//inverse-optimal control for Euler–Lagrange system. IEEE Trans Robot Autom 16(6):847–854

    Google Scholar 

  87. Park J, Chung W (2000b) Design of a robust \(H_\infty \) PID control for industrial manipulators. J Dyn Syst Meas Contr 122(4):803–812

    Google Scholar 

  88. Cervantes I, Alvarez-Ramirez J (2001) On the PID tracking control of robot manipulators. Syst Contr Lett 42(1):37–46

    MathSciNet  MATH  Google Scholar 

  89. Eriksson E, Jan Wikander (2002) Robust PID design of flexible manipulators through pole assignment. In: 7th International Workshop on Advanced Motion Control. Proceedings (Cat. No. 02TH8623), pp 420–425. IEEE

  90. Alavarez-Ramirezi J, Cervantes I, Bautista R (2002) Robust PID control for robots manipulators with elastic joints. In Proceedings of the 2001 IEEE International Conference on Control Applications (CCA’01)(Cat. No. 01CH37204), pp 542–547. IEEE

  91. Yuxin S, Muller PC, Zheng C (2009) Global asymptotic saturated PID control for robot manipulators. IEEE Trans Contr Syst Technol 18(6):1280–1288

    Google Scholar 

  92. Chang PH, Jung JH (2008) A systematic method for gain selection of robust PID control for nonlinear plants of second-order controller canonical form. IEEE Trans Contr Syst Technol 17(2):473–483

    Google Scholar 

  93. Kumar Pradhan S, Subudhi B (2020) Position control of a flexible manipulator using a new nonlinear self tuning PID controller. IEEE/CAA J Automat Sin 7:136–149

    MathSciNet  Google Scholar 

  94. Shaban EM, Sayed H, Abdelhamid A (2019) A novel discrete PID + controller applied to higher order/time delayed nonlinear systems with practical implementation. Int J Dyn Contr 7(3):888–900

    MathSciNet  Google Scholar 

  95. Liaw CM, Chao KH, Chen YK, Chen HC (1998) Quantitative design and implementation of PI-D controller with model-following response for motor drive. IEE Proc Electr Power Appl 145(2):98–104

    Google Scholar 

  96. Tan KK, Lee TH, Zhou HX (2001) Micro-positioning of linear-piezoelectric motors based on a learning nonlinear PID controller. IEEE/ASME Trans Mech 6(4):428–436

    Google Scholar 

  97. Lin C-L, Jan H-Y (2002) Multiobjective PID control for a linear brushless DC motor: an evolutionary approach. IEE Proc Electr Power Appl 149(6):397–406

    Google Scholar 

  98. Lin C-L, Jan H-Y, Shieh N-C (2003) Ga-based multiobjective PID control for a linear brushless DC motor. IEEE/ASME Trans Mech 8(1):56–65

    Google Scholar 

  99. Kelly R, Moreno J (2001) Learning PID structures in an introductory course of automatic control. IEEE Trans Edu 44(4):373–376

    Google Scholar 

  100. Zhang G, Furusho J (2000) Speed control of two-inertia system by PI/PID control. IEEE Trans Ind Electr 47(3):603–609

    Google Scholar 

  101. Angel L, Viola J (2015) Design and statistical robustness analysis of FOPID, IOPID and SIMC PID controllers applied to a motor-generator system. IEEE Lat Am Trans 13(12):3724–3734

    Google Scholar 

  102. Jung J-W, Leu VQ, Do TD, Kim E-K, Choi HH (2014) Adaptive PID speed control design for permanent magnet synchronous motor drives. IEEE Trans Power Electr 30(2):900–908

    Google Scholar 

  103. Viola J, Angel L, Sebastian JM (2017) Design and robust performance evaluation of a fractional order PID controller applied to a dc motor. IEEE/CAA J Automatica Sinica 4(2):304–314

    MathSciNet  Google Scholar 

  104. Hekimoğlu B (2019) Optimal tuning of fractional order PID controller for DC motor speed control via chaotic atom search optimization algorithm. IEEE Access 7:38100–38114

    Google Scholar 

  105. Gaing Z-L (2004) A particle swarm optimization approach for optimum design of PID controller in AVR system. IEEE Trans Energy Convers 19(2):384–391

    Google Scholar 

  106. Kim K, Rao P, Burnworth JA (2010) Self-tuning of the PID controller for a digital excitation control system. IEEE Trans Ind Appl 46(4):1518–1524

    Google Scholar 

  107. Hasanien HM (2012) Design optimization of PID controller in automatic voltage regulator system using taguchi combined genetic algorithm method. IEEE Syst J 7(4):825–831

    Google Scholar 

  108. Kapat S, Krein PT (2011) Formulation of PID control for DC-DC converters based on capacitor current: a geometric context. IEEE Trans Power Electr 27(3):1424–1432

    Google Scholar 

  109. Seo S-W, Choi HH (2019) Digital implementation of fractional order PID-type controller for boost DC-DC converter. IEEE Access 7:142652–142662

    Google Scholar 

  110. Natarajan K (2005) Robust PID controller design for hydroturbines. IEEE Trans Energy Convers 20(3):661–667

    Google Scholar 

  111. Behera A, Panigrahi TK, Ray PK, Sahoo AK (2019) A novel cascaded PID controller for automatic generation control analysis with renewable sources. IEEE/CAA J Automatica Sinica 6(6):1438–1451

    Google Scholar 

  112. Osinski C, Leandro GV, Henrique G Oliveira (2019) Fuzzy PID controller design for lfc in electric power systems. IEEE Lat Am Trans 17(01:147–154

    Google Scholar 

  113. Glickman S, Kulessky R, Nudelman G (2004) Identification-based PID control tuning for power station processes. IEEE Trans Contr Syst Technol 12(1):123–132

    MATH  Google Scholar 

  114. Slate JB, Sheppard LC (1982) Automatic control of blood pressure by drug infusion. IEE Proc A Phys Sci Meas Instrum Manag Edu Rev 129(9):639–645

    Google Scholar 

  115. Isaka S, Sebald AV (1993) Control strategies for arterial blood pressure regulation. IEEE Trans Biomed Eng 40(4):353–363

    Google Scholar 

  116. Denai M, Linkens DA, Asbury AJ, MacLeod AD, Gray WM (1990) Self-tuning PID control of atracurium-induced muscle relaxation in surgical patients. In: IEE Proceedings D (Control Theory and Applications), vol 137. pp 261–272. IET

  117. Veltink PH, Chizeck HJ, Crago PE, El-Bialy A (1992) Nonlinear joint angle control for artificially stimulated muscle. IEEE Trans Biomed Eng 39(4):368–380

    Google Scholar 

  118. Chee F, Fernando TL, Savkin AV, Van Heeden V (2003) Expert PID control system for blood glucose control in critically ill patients. IEEE Trans Inf Technol Biomed 7(4):419–425

    Google Scholar 

  119. Marchetti G, Barolo M, Jovanovic L, Zisser H, Seborg DE (2008) An improved PID switching control strategy for type 1 diabetes. IEEE Trans Biomed Eng 55(3):857–865

    Google Scholar 

  120. O’Hara DA, Hexem JG, Derbyshire GJ, Overdyk FJ, Chen B, Henthorn TK, Li JK-J (1997) The use of a PID controller to model vecuronium pharmacokinetics and pharmacodynamics during liver transplantation. IEEE Trans Biomed Eng 44(7):610–619

    Google Scholar 

  121. Van Heusden K, Dumont GA, Soltesz K, Petersen CL, Umedaly A, West N, Mark Ansermino J (2013) Design and clinical evaluation of robust PID control of propofol anesthesia in children. IEEE Trans Contr Syst Technol 22(2):491–501

    Google Scholar 

  122. Marttinen A, Virkkunen JOUKO, Salminen RT (1990) Control study with a pilot crane. IEEE Trans Edu 33(3):298–305

    Google Scholar 

  123. Homberg D, Weiss W (2006) PID control of laser surface hardening of steel. IEEE Trans Contr Syst Technol 14(5):896–904

    Google Scholar 

  124. Juang J-G, Huang M-T, Liu W-K (2008) PID control using presearched genetic algorithms for a MIMO system. IEEE Trans Syst Man Cybern Part C Appl Rev 38(5):716–727

    Google Scholar 

  125. Romero JG, Ortega R, Donaire A (2016) Energy shaping of mechanical systems via PID control and extension to constant speed tracking. IEEE Trans Autom Contr 61(11):3551–3556

    MathSciNet  MATH  Google Scholar 

  126. Wei C, Söffker D (2015) Optimization strategy for PID-controller design of amb rotor systems. IEEE Trans Contr Syst Technol 24(3):788–803

    Google Scholar 

  127. Paul S, Morales-Menendez R (2018) Active control of chatter in milling process using intelligent PD/PID control. IEEE Access 6:72698–72713

    Google Scholar 

  128. Ortiz JP, Minchala LI, Reinoso MJ (2016) Nonlinear robust H-infinity PID controller for the multivariable system quadrotor. IEEE Lat Am Trans 14(3):1176–1183

    Google Scholar 

  129. Wai R-J, Lee J-D, Chuang K-L (2010) Real-time PID control strategy for maglev transportation system via particle swarm optimization. IEEE Trans Ind Electr 58(2):629–646

    Google Scholar 

  130. Chen Q, Tan Y, Li J, Mareels I (2017) Decentralized PID control design for magnetic levitation systems using extremum seeking. IEEE Access 6:3059–3067

    Google Scholar 

  131. Duan X-G, Deng H, Li H-X (2012) A saturation-based tuning method for fuzzy PID controller. IEEE Trans Ind Electr 60(11):5177–5185

    Google Scholar 

  132. Meng F, Liu S, Liu K (2020) Design of an optimal fractional order PID for constant tension control system. IEEE Access 8:58933–58939. https://doi.org/10.1109/ACCESS.2020.2983059

    Article  Google Scholar 

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Borase, R.P., Maghade, D.K., Sondkar, S.Y. et al. A review of PID control, tuning methods and applications. Int. J. Dynam. Control 9, 818–827 (2021). https://doi.org/10.1007/s40435-020-00665-4

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