The dilemma of PID tuning

Abstract A lot of automatic feedback control and learning tasks carried out on many dynamical systems still fundamentally rely on a form of proportional–integral–derivative (PID) control law. The PID law is often viewed as a simplistic computational control algorithm. However just like all non-convex optimization problems, tuning the PID algorithm for accurate and stable closed-loop control becomes a NP-Hard Problem. This leads to a dilemma, for both users and designers, most especially in practise. It is then no wonder that tuning software is a big business in the industrial automation sector. In this review, we present and classify PID tuning methods till date into three general areas. Finally, we then present a proposal to minimize the dilemma of complexity and cost that has become associated with tuning the three main parameters of the PID control law. Hopefully, continuous attempts at the minimization of this dilemma can lead to both a money-savings investment and a significant improvement in the field of PID control design.

[1]  Sigurd Skogestad,et al.  Optimal PI and PID control of first-order plus delay processes and evaluation of the original and improved SIMC rules , 2018, Journal of Process Control.

[2]  Karl Johan Åström,et al.  Computer-Controlled Systems: Theory and Design , 1984 .

[3]  Kumpati S. Narendra,et al.  Adaptation and learning in automatic systems , 1974 .

[4]  Anastasios I. Dounis,et al.  Online Tuning of a PID Controller with a Fuzzy Reinforcement Learning MAS for Flow Rate Control of a Desalination Unit , 2019, Electronics.

[5]  Sushant N. Pawar,et al.  A review of PID control, tuning methods and applications , 2020, International Journal of Dynamics and Control.

[6]  Edward J. Davison,et al.  Controller Design for Multivariable Linear Time-Invariant Unknown Systems , 2013, IEEE Transactions on Automatic Control.

[7]  Kayode Akingbade,et al.  Speed Control of DC Motors: Optimal Closed PID-Loop Model Predictive Control , 2020 .

[8]  Samer S. Saab,et al.  A MIMO Sampling-Rate-Dependent Controller , 2015, IEEE Transactions on Industrial Electronics.

[9]  Yossi Peretz,et al.  A Randomized Algorithm for Optimal PID Controllers , 2018, Algorithms.

[10]  I. Podlubny.  Fractional-Order Systems and -Controllers , 1999 .

[11]  Keqin Gu,et al.  Control of Dead- Time Processes , 2008 .

[12]  Yun-Joo Nam.  Comparison study of time delay control (TDC) and uncertainty and disturbance estimation (UDE) based control , 2016, 2016 16th International Conference on Control, Automation and Systems (ICCAS).

[13]  Ivo Petráš,et al.  Tuning and implementation methods for fractional-order controllers , 2012 .

[14]  Jan Jantzen,et al.  Turning PID controller tuning into a simple consideration of settling time , 2016, 2016 European Control Conference (ECC).

[15]  Tariq Samad,et al.  A Survey on Industry Impact and Challenges Thereof [Technical Activities] , 2017, IEEE Control Systems.

[16]  Li Li,et al.  On the Crossroad of Artificial Intelligence: A Revisit to Alan Turing and Norbert Wiener , 2019, IEEE Transactions on Cybernetics.

[17]  Indra Narayan Kar,et al.  Time-Delayed Control (TDC): Design Issues and Solutions , 2020 .

[18]  Lei Zhang,et al.  PID Controller-Based Stochastic Optimization Acceleration for Deep Neural Networks , 2020, IEEE Transactions on Neural Networks and Learning Systems.

[19]  Mikulas Huba,et al.  Introduction to the Discrete Time PIDmn Control for the IPDT Plant , 2018 .

[20]  Richard Stobart,et al.  Design of UDE‐based controllers from their two‐degree‐of‐freedom nature , 2011 .

[21]  Baran Hekimoglu,et al.  Opposition based Henry gas solubility optimization as a novel algorithm for PID control of DC motor , 2020 .

[22]  Benjamin Recht,et al.  A Tour of Reinforcement Learning: The View from Continuous Control , 2018, Annu. Rev. Control. Robotics Auton. Syst..

[23]  W. Hershberger.  Control Theory and Learning Theory , 1990 .

[24]  Geoffrey E. Hinton,et al.  Deep Learning , 2015, Nature.

[25]  Derek P. Atherton.  Setting the Parameters of Proportional–Integral–Derivative Controllers , 2015 .

[26]  Wei Sun,et al.  A Proposal of Adaptive PID Controller Based on Reinforcement Learning , 2007 .

[27]  Mikulas Huba.  Filter choice for an effective measurement noise attenuation in PI and PID controllers , 2015, 2015 IEEE International Conference on Mechatronics (ICM).

[28]  Leszek Koszalka,et al.  An Idea of Using Reinforcement Learning in Adaptive Control Systems , 2006, International Conference on Networking, International Conference on Systems and International Conference on Mobile Communications and Learning Technologies (ICNICONSMCL'06).

[29]  Stuart Bennett,et al.  The past of pid controllers , 2000, Annu. Rev. Control..

[30]  Anuradha M. Annaswamy,et al.  New Edition of CSS's "The Impact of Control Technology" Report [Publication Activities] , 2013 .

[31]  Lennart Ljung,et al.  Guest Editorial: Special Issue on System Identification , 2005, IEEE Trans. Autom. Control..

[32]  Wei Wang.  The New Design Strategy on PID Controllers , 2012 .

[33]  Yun Li,et al.  PID control system analysis, design, and technology , 2005, IEEE Transactions on Control Systems Technology.

[34]  Fatemeh Nasiri,et al.  Air Condition's PID Controller Fine-Tuning Using Artificial Neural Networks and Genetic Algorithms , 2018, Comput..

[35]  Shiro Masuda,et al.  Direct PID Tuning from Closed-Loop Data and Its Application to Unstable Processes , 2009 .

[36]  Tore Hägglund,et al.  Control signal constraints and filter order selection for PI and PID controllers , 2011, Proceedings of the 2011 American Control Conference.

[37]  S. Hassan HosseinNia,et al.  Linear fractional order controllers; A survey in the frequency domain , 2019, Annu. Rev. Control..

[38]  Tomislav B. Sekara,et al.  Optimization of PID Controller Based on Maximization of the Proportional Gain Under Constraints on Robustness and Sensitivity to Measurement Noise , 2009, IEEE Transactions on Automatic Control.

[39]  N. Munro,et al.  PID controllers: recent tuning methods and design to specification , 2002 .

[40]  Tore Hägglund,et al.  Measurement noise filtering for PID controllers , 2014 .

[41]  Chen Peng,et al.  Research on Improved Auto-Tuning of a PID Controller Based on Phase Angle Margin , 2019, Energies.

[42]  Juha T. Tanttu,et al.  TUNING OF PID CONROLLERS: SURVEY OF SISO AND MIMO TECHNIQUES , 1991 .

[43]  Marialena Vagia.  PID Controller Design Approaches - Theory, Tuning and Application to Frontier Areas , 2012 .

[44]  Aidan O'Dwyer,et al.  Handbook of PI and PID controller tuning rules , 2003 .

[45]  Sangjin Han,et al.  PID Controller Synthesis Using a $\sigma$ -Hurwitz Stability Criterion , 2018, IEEE Control Systems Letters.

[46]  Eduard Petlenkov,et al.  Towards Industrialization of FOPID Controllers: A Survey on Milestones of Fractional-Order Control and Pathways for Future Developments , 2021, IEEE Access.

[47]  Tianshi Chen,et al.  A shift in paradigm for system identification , 2019, Int. J. Control.

[48]  Lei Guo,et al.  Theory and Design of PID Controller for Nonlinear Uncertain Systems , 2019, IEEE Control Systems Letters.

[49]  Dennis S. Bernstein,et al.  Naive control of the double integrator , 2001 .

[50]  K. Moore,et al.  Editorial: Special issue on iterative learning control , 2000 .

[51]  Thomas A. Fuhlbrigge,et al.  Controller parameter optimization for complex industrial system with uncertainties , 2019, Measurement and Control.

[52]  Eric C. Kerrigan,et al.  Feedback and Time are Essential for the Optimal Control of Computing Systems , 2015, ArXiv.

[53]  Gene F. Franklin,et al.  Feedback Control of Dynamic Systems , 1986 .

[54]  M. Araki,et al.  Two-Degree-of-Freedom PID Controllers , 2003 .

[55]  Michael A. Johnson,et al.  PID CONTROL: NEW IDENTIFICATION AND DESIGN METHODS , 2008 .

[56]  Anuradha M. Annaswamy,et al.  On Adaptive Control With Closed-Loop Reference Models: Transients, Oscillations, and Peaking , 2013, IEEE Access.

[57]  Shin Wakitani,et al.  Design of an Implicit Self-tuning PID Controller Based on the Generalized Output , 2017 .

[58]  J. G. Ziegler,et al.  Optimum Settings for Automatic Controllers , 1942, Journal of Fluids Engineering.

[59]  Pyung Hun Chang,et al.  A Systematic Method for Gain Selection of Robust PID Control for Nonlinear Plants of Second-Order Controller Canonical Form , 2009, IEEE Trans. Control. Syst. Technol..

[60]  Fernando Reyes-Cortés,et al.  A generalised PID-type control scheme with simple tuning for the global regulation of robot manipulators with constrained inputs , 2015, Int. J. Control.

[61]  N. Minorsky.,et al.  DIRECTIONAL STABILITY OF AUTOMATICALLY STEERED BODIES , 2009 .

[62]  Benjamin Recht,et al.  Analysis and Design of Optimization Algorithms via Integral Quadratic Constraints , 2014, SIAM J. Optim..

[63]  Paulo Paz,et al.  Extremum Seeking-based Adaptive PID Control applied to Neuromuscular Electrical Stimulation. , 2019, Anais da Academia Brasileira de Ciencias.

[64]  Stefan Bucz,et al.  Advanced Methods of PID Controller Tuning for Specified Performance , 2018, PID Control for Industrial Processes.

[65]  K. Åström,et al.  Problems of Identification and Control , 1971 .

[66]  Saurabh Srivastava,et al.  A PI/PID controller for time delay systems with desired closed loop time response and guaranteed gain and phase margins , 2016 .

[67]  Anastasios I. Dounis,et al.  Fast Tuning of the PID Controller in An HVAC System Using the Big Bang-Big Crunch Algorithm and FPGA Technology , 2018, Algorithms.

[68]  Alexandru Forrai.  Embedded Control System Design: A Model Based Approach , 2012 .

[69]  Sergio M. Savaresi,et al.  Non-iterative direct data-driven controller tuning for multivariable systems: theory and application , 2012 .

[70]  Lei Guo,et al.  Towards a Theoretical Foundation of PID Control for Uncertain Nonlinear Systems. , 2020 .

[71]  Firooz Bakhtiari-Nejad,et al.  Development of neural fractional order PID controller with emulator. , 2020, ISA transactions.

[72]  Lei Guo,et al.  Exploring the maximum capability of adaptive feedback , 2002 .

[73]  Qiuqi Ruan,et al.  Facial Expression Recognition Based on Discriminant Neighborhood Preserving Nonnegative Tensor Factorization and ELM , 2014 .

[74]  Lei Guo,et al.  Feedback and uncertainty: Some basic problems and results , 2020, Annu. Rev. Control..

[75]  Reza Jafari,et al.  Adaptive PID Control of a Nonlinear Servomechanism Using Recurrent Neural Networks , 2011 .

[76]  M. Krstic,et al.  PID tuning using extremum seeking: online, model-free performance optimization , 2006, IEEE Control Systems.

[77]  K. Åström,et al.  Performance and robustness trade-offs in PID control , 2014 .

[78]  Rosdiazli Ibrahim,et al.  A comparative study of 2DOF PID and 2DOF fractional order PID controllers on a class of unstable systems , 2023, Archives of Control Sciences.

[79]  Ahmed Hassan Ahmed,et al.  Fixed Set Point Weighting 2DOF PID Controller for Control Processes , 2018 .

[80]  Baran Hekimoglu,et al.  Optimal Tuning of Fractional Order PID Controller for DC Motor Speed Control via Chaotic Atom Search Optimization Algorithm , 2019, IEEE Access.

[81]  A. N. Gundes,et al.  PID Stabilization of MIMO Plants , 2007 .

[82]  Bin Hu,et al.  Control interpretations for first-order optimization methods , 2017, 2017 American Control Conference (ACC).

[83]  Tore Hägglund,et al.  Design methods : PID Control , 2017 .

[84]  Michel Gevers,et al.  Identification for control , 1996 .

[85]  Paul M. J. Van den Hof,et al.  Identification and control - Closed-loop issues , 1995, Autom..

[86]  Morimasa Ogawa,et al.  Practical direct PID/I-PD controller tuning and its application to chemical processes , 2010, 2010 IEEE International Conference on Control Applications.

[87]  Michal Kvasnica,et al.  MPC-Based Reference Governors: Theory and Case Studies , 2019 .

[88]  Kartik B. Ariyur,et al.  Adaptive Systems: History, Techniques, Problems, and Perspectives , 2014, Syst..

[89]  Filippo Neri,et al.  PID Tuning with Neural Networks , 2019, ACIIDS.

[90]  Stefan Preitl,et al.  Iterative Feedback and Learning Control. Servo systems applications , 2007 .

[91]  Eugenius Kaszkurewicz,et al.  A Control-Theoretic Approach to the Design of Zero Finding Numerical Methods , 2007, IEEE Transactions on Automatic Control.

[92]  Kaspar Althoefer,et al.  Stability analysis of a three-term backpropagation algorithm , 2005, Neural Networks.

[93]  Su Whan Sung,et al.  ProportionalIntegralDerivative Controller Tuning , 2009 .

[94]  Samer S. Saab.  Development of multivariable PID controller gains in presence of measurement noise , 2017, Int. J. Control.

[95]  Ying Bai,et al.  Classical and Modern Controls with Microcontrollers , 2018, Advances in Industrial Control.

[96]  Jürgen Schmidhuber,et al.  Deep learning in neural networks: An overview , 2014, Neural Networks.

[97]  Ravi Kumar Mandava,et al.  An optimal PID controller for a biped robot walking on flat terrain using MCIWO algorithms , 2018, Evol. Intell..

[98]  Olivier Lequin.  Optimal closed-loop PID tuning in the process industry with the "iterative feedback tuning" scheme , 1997, 1997 European Control Conference (ECC).

[99]  Sigurd Skogestad,et al.  Tuning for Smooth PID Control with Acceptable Disturbance Rejection , 2006 .

[100]  Diego Eckhard,et al.  Data-driven model reference control design by prediction error identification , 2017, J. Frankl. Inst..

[101]  Michel Gevers,et al.  Identification for Control: From the Early Achievements to the Revival of Experiment Design , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[102]  Serdar Ekıncı,et al.  Improved Kidney-Inspired Algorithm Approach for Tuning of PID Controller in AVR System , 2019, IEEE Access.

[103]  Shankar P. Bhattacharyya,et al.  PID Controllers for Time Delay Systems , 2004 .

[104]  J. Mendel.  Uncertain Rule-Based Fuzzy Logic Systems: Introduction and New Directions , 2001 .

[105]  Reza Katebi.  MODELLING, SIMULATION AND CONTROL OF LARGE POWER PLANTS , 2007 .

[106]  Shankar P. Bhattacharyya,et al.  Analytical Design of PID Controllers , 2019 .

[107]  Tore Hägglund,et al.  Robust PID Design Based on QFT and Convex–Concave Optimization , 2017, IEEE Transactions on Control Systems Technology.

[108]  Antonin Vitecek,et al.  2DOF Controller Tuning , 2015 .

[109]  Weng Khuen Ho,et al.  Relay auto-tuning of PID controllers using iterative feedback tuning , 2003, Autom..

[110]  W. Guan,et al.  Iterative Learning Control Design and Application for Linear Continuous Systems with Variable Initial States Based on 2-D System Theory , 2014 .

[111]  Tiago Roux Oliveira,et al.  Model-Free Neuromuscular Electrical Stimulation by Stochastic Extremum Seeking , 2020, IEEE Transactions on Control Systems Technology.

[112]  Vilma A. Oliveira,et al.  Modern design of classical controllers: Digital PID controllers , 2015, 2015 IEEE 24th International Symposium on Industrial Electronics (ISIE).

[113]  Xavier Blasco Ferragud,et al.  Controller Tuning by Means of Multi-Objective Optimization Algorithms: A Global Tuning Framework , 2013, IEEE Transactions on Control Systems Technology.

[114]  Li Sun,et al.  An Approach for Setting Parameters for Two-Degree-of-Freedom PID Controllers , 2018, Algorithms.

[115]  Antonio Visioli,et al.  Practical PID Control , 2006 .

[116]  Norbert Wiener,et al.  The human use of human beings - cybernetics and society , 1988 .

[117]  D.Y. Abramovitch,et al.  Semi-automatic tuning of PID gains for Atomic Force Microscopes , 2008, 2008 American Control Conference.

[118]  Anuradha M. Annaswamy,et al.  Adaptive Output Feedback Based on Closed-Loop Reference Models , 2014, IEEE Transactions on Automatic Control.

[119]  Karl Johan Åström,et al.  PID Controllers: Theory, Design, and Tuning , 1995 .

[120]  Wen Yu.  PID Admittance Control in Task Space , 2018 .

[121]  William J. Shipman,et al.  Reinforcement Learning and Deep Neural Networks for PI Controller Tuning , 2019 .

[122]  Tore Hägglund,et al.  Automatic Tuning and Adaptation for PID Controllers—A Survey , 1992 .

[123]  George Ellis,et al.  Control System Design Guide , 2012 .

[124]  Joseba Quevedo,et al.  Automatic design of robust PID controllers based on QFT specifications , 2012 .

[125]  Nam Nguyen,et al.  Overshoot and settling time assignment with PID for first‐order and second‐order systems , 2018, IET Control Theory & Applications.

[126]  A. J. Calderón,et al.  Fractional PID Controllers for Industry Application. A Brief Introduction , 2007 .

[127]  Shankar P. Bhattacharyya,et al.  Structure and synthesis of PID controllers , 2000 .

[128]  Aydogan Savran,et al.  A fuzzy model based adaptive PID controller design for nonlinear and uncertain processes. , 2014, ISA transactions.

[129]  In-Beum Lee,et al.  Process Identification and PID Control , 2009 .

[130]  Shankar P. Bhattacharyya,et al.  Robust, fragile, or optimal? , 1997, IEEE Trans. Autom. Control..

[131]  Y. Cao,et al.  An Output-Tracking-Based Discrete PID-Sliding Mode Control for MIMO Systems , 2014, IEEE/ASME Transactions on Mechatronics.

[132]  Monika Gupta,et al.  A comparative study of PID and neuro-fuzzy based control schemes for a 6-DoF robotic arm , 2018, J. Intell. Fuzzy Syst..

[133]  Una-May O'Reilly,et al.  A Self-Tuning Analog Proportional-Integral-Derivative (PID) Controller , 2006, First NASA/ESA Conference on Adaptive Hardware and Systems (AHS'06).

[134]  Abdelkader Chaari,et al.  Tuning optimal PID controller , 2015, Int. J. Model. Identif. Control..

[135]  S. Hassan HosseinNia,et al.  Tuning guidelines for fractional order PID controllers: Rules of thumb , 2018, Mechatronics.

[136]  P. Werbos,et al.  Beyond Regression : "New Tools for Prediction and Analysis in the Behavioral Sciences , 1974 .

[137]  Sheng Zhong,et al.  A parameter formula connecting PID and ADRC , 2020, Science China Information Sciences.

[138]  Serdar Ekinci,et al.  Optimal FOPID Speed Control of DC Motor via Opposition-Based Hybrid Manta Ray Foraging Optimization and Simulated Annealing Algorithm , 2021 .

[139]  Gianluigi Pillonetto,et al.  System identification using kernel-based regularization: New insights on stability and consistency issues , 2018, Autom..

[140]  Shankar P. Bhattacharyya,et al.  Robustness and fragility of high order controllers: A tutorial , 2016, 2016 IEEE Conference on Control Applications (CCA).

[141]  Davut Izci,et al.  Comparative Performance Analysis of Slime Mould Algorithm For Efficient Design of Proportional–Integral–Derivative Controller , 2021 .

[142]  Ramon Vilanova,et al.  PID control in the Third Millennium : lessons learned and new approaches , 2012 .

[143]  Shuxia Li,et al.  Research on Engineering Tuning Methods of PID Controller Parameters and Its Application , 2016, ICIC.

[144]  Pavel Zítek,et al.  Dimensional analysis approach to dominant three-pole placement in delayed PID control loops , 2013 .

[145]  Qing-Long Han,et al.  Discrete-time filter proportional-integral-derivative controller design for linear time-invariant systems , 2020, Autom..

[146]  Ashish Tewari.  Modern Control Design With MATLAB and SIMULINK , 2002 .

[147]  Antonio Visioli,et al.  Optimized Retuning of PID Controllers for TITO Processses , 2018 .

[148]  Tore Hägglund,et al.  Advanced PID Control , 2005 .

[149]  Andrzej Koszewnik,et al.  Experimental Studies of the Fractional PID and TID Controllers for Industrial Process , 2021, International Journal of Control, Automation and Systems.

[150]  Toru Yamamoto,et al.  Design and Application of a Database-Driven PID Controller with Data-Driven Updating Algorithm , 2019 .