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.
Similar content being viewed by others
References
Kang C-G (2016) Origin of stability analysis: “on governors” [historical perspectives ]. IEEE Control Syst Mag 36(5):77–88
Medaglia JD (2019) Clarifying cognitive control and the controllable connectome. Wiley Interdiscip Rev Cognit Sci 10(1):1471
Åström KJ, Kumar PR (2014) Control: a perspective. Automatica 50(1):3–43
Bennett S (2000) The past of PID controllers. Ann Rev Control 25:43–53
Bennett S (1993) Development of the PID controller. IEEE Control Syst Mag 13(6):58–62
Fong-Chwee T, Sirisena HR (1988) Self-tuning PID controllers for dead time processes. IEEE Trans Ind Electr 35(1):119–125
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
Leva A (1993) PID autotuning algorithm based on relay feedback. In: IEE Proceedings D (Control Theory and Applications), vol 140. pp 328–338. IET
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
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
Gawthrop P (1986) Self-tuning PID controllers: algorithms and implementation. IEEE Trans Autom Contr 31(3):201–209
Brown RE, Maliotis GN, Gibby JA (1993) PID self-tuning controller for aluminum rolling mill. IEEE Trans Ind Appl 29(3):578–583
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
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
Porter B, Jones AH (1992) Genetic tuning of digital PID controllers. Electr Lett 28(9):843–844
Kristiansson B, Lennartson B (2002) Robust and optimal tuning of PI and PID controllers. IEE Proc Contr Theory Appl 149(1):17–25
Gundes AN, Ozguler AB (2007) PID stabilization of MIMO plants. IEEE Trans Autom Contr 52(8):1502–1508
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
Chan YF, Moallem M, Wang W (2007) Design and implementation of modular FPGA-based PID controllers. IEEE Trans Ind Electro 54(4):1898–1906
Yamamoto T, Takao K, Yamada T (2008) Design of a data-driven PID controller. IEEE Trans Contr Syst Technol 17(1):29–39
Sio KC, Lee CK (1998) Stability of fuzzy PID controllers. IEEE Trans Syst Man Cybern Part A Syst Humans 28(4):490–495
Tzafestas S, Papanikolopoulos NP (1990) Incremental fuzzy expert PID control. IEEE Trans Ind Electr 37(5):365–371
Zhao Z-Y, Tomizuka M, Isaka S (1993) Fuzzy gain scheduling of PID controllers. IEEE Trans Syst Man Cybern 23(5):1392–1398
Minh Vu K (1992) Optimal setting for discrete PID controllers. In: IEE Proceedings D (Control Theory and Applications), vol 139. pp 31–40. IET
Tang K-S, Man KF, Chen G, Kwong S (2001) An optimal fuzzy PID controller. IEEE Trans Ind Electr 48(4):757–765
Verma B, Padhy PK (2018a) Optimal PID controller design with adjustable maximum sensitivity. IET Contr Theory Appl 12(8):1156–1165
Zolotas AC, Halikias GD (1999) Optimal design of PID controllers using the QFT method. IEE Proc Contr Theory Appl 146(6):585–589
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
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
Viola J, Angel L (2015) Factorial design for robustness evaluation of fractional PID controllers. IEEE Lat Am Trans 13(5):1286–1293
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
Bongulwar MR, Patre BM (2018) Design of FOPID controller for fractional-order plants with experimental verification. Int J Dyn Contr 6(1):213–223
Åström KJ, Hägglund T (2001) The future of PID control. Contr Eng Pract 9(11):1163–1175
Díaz-Rodríguez Iván D, Sangjin H, Bhattacharyya Shankar P (2019) Analytical design of PID controllers. Springer, Berlin. ISBN 978–3–030–18227–4
Ziegler John G, Nichols Nancy B (1942) Optimum settings for automatic controllers. J Dyn Syst Meas Control Trans ASME 115:220–222
Åström KJ, Hägglund T (1984) Automatic tuning of simple regulators. IFAC Proc Vol 17(2):1867–1872
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
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
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
Aguirre LA (1992) PID tuning based on model matching. Electr Lett 28(25):2269–2271
Zhuang M, Atherton DP (1994) PID controller design for a TITO system. IEE Proc Contr Theory Appl 141(2):111–120
Poulin E, Pomerleau A (1996) PID tuning for integrating and unstable processes. IEE Proc Contr Theory Appl 143(5):429–435
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
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
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
Visioli A (2001a) Tuning of PID controllers with fuzzy logic. IEE Proc Contr Theory Appl 148(1):1–8
Cominos P, Munro N (2002) PID controllers: recent tuning methods and design to specification. IEE Proc Contr Theory Appl 149(1):46–53
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
Lennartson B, Kristiansson B (2009) Evaluation and tuning of robust PID controllers. IET Contr Theory Appl 3(3):294–302
Stafford EM (1977) Design aid for approximate PD and PID on/off controllers. Electr Lett 13(6):163–164
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
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
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
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
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
Edwards C, Spurgeon SK (1994) Robust nonlinear control of heating plant. IEE Proc Contr Theory Appl 141(4):227–234
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
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
Scottedward Hodel A, Hall CE (2001) Variable-structure PID control to prevent integrator windup. IEEE Trans Ind Electr 48(2):442–451
Visioli A (2001b) Optimal tuning of PID controllers for integral and unstable processes. IEE Proc Contr Theory Appl 148(2):180–184
Daley S, Liu GP (1999) Optimal PID tuning using direst search algorithms. Comput Contr Eng J 10(2):51–56
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
Katebi MR, Moradi MH (2001) Predictive PID controllers. IEE Proc Contr Theory Appl 148(6):478–487
Pfeiffer BM (2003) PID control of batch processes along pre-optimised trajectories. Comput Contr Eng J 14(5):16–21
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
Dinca MP, Gheorghe M, Galvin P (2008) Design of a PID controller for a pcr micro reactor. IEEE Trans Edu 52(1):116–125
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
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
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
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
Razvarz S, Vargas-Jarillo C, Jafari R, Gegov A (2019) Flow control of fluid in pipelines using PID controller. IEEE Access 7:25673–25680
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
Verma B, Padhy PK (2018b) Indirect IMC-PID controller design. IET Contr Theory Appl 13(2):297–305
Bestaoui Y (1989) Decentralised PD and PID robotic regulators. In: IEE Proceedings D (Control Theory and Applications), vol 136. pp 133–145. IET
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
Rocco P (1996) Stability of PID control for industrial robot arms. IEEE Trans Robot Autom 12(4):606–614
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
Feng W, O’reilly J, Ballance DJ (2002) Mimo nonlinear PID predictive controller. IEE Proc Contr Theory Appl 149(3):203–208
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
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
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
Kazemian HB (2002) The SOF-PID controller for the control of a MIMO robot arm. IEEE Trans Fuzzy Syst 10(4):523–532
Sun YL, Joo Er M (2004) Hybrid fuzzy control of robotics systems. IEEE Trans Fuzzy Syst 12(6):755–765
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
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,
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
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
Cervantes I, Alvarez-Ramirez J (2001) On the PID tracking control of robot manipulators. Syst Contr Lett 42(1):37–46
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
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
Yuxin S, Muller PC, Zheng C (2009) Global asymptotic saturated PID control for robot manipulators. IEEE Trans Contr Syst Technol 18(6):1280–1288
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
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
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
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
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
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
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
Kelly R, Moreno J (2001) Learning PID structures in an introductory course of automatic control. IEEE Trans Edu 44(4):373–376
Zhang G, Furusho J (2000) Speed control of two-inertia system by PI/PID control. IEEE Trans Ind Electr 47(3):603–609
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
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
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
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
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
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
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
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
Seo S-W, Choi HH (2019) Digital implementation of fractional order PID-type controller for boost DC-DC converter. IEEE Access 7:142652–142662
Natarajan K (2005) Robust PID controller design for hydroturbines. IEEE Trans Energy Convers 20(3):661–667
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
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
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
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
Isaka S, Sebald AV (1993) Control strategies for arterial blood pressure regulation. IEEE Trans Biomed Eng 40(4):353–363
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
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
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
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
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
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
Marttinen A, Virkkunen JOUKO, Salminen RT (1990) Control study with a pilot crane. IEEE Trans Edu 33(3):298–305
Homberg D, Weiss W (2006) PID control of laser surface hardening of steel. IEEE Trans Contr Syst Technol 14(5):896–904
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
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
Wei C, Söffker D (2015) Optimization strategy for PID-controller design of amb rotor systems. IEEE Trans Contr Syst Technol 24(3):788–803
Paul S, Morales-Menendez R (2018) Active control of chatter in milling process using intelligent PD/PID control. IEEE Access 6:72698–72713
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
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
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
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
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
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
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
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40435-020-00665-4