Optimal Nash tuning rules for robust PID controllers

Abstract In this paper, we propose tuning rules for one degree-of-freedom proportional-integral-derivative controllers, by considering important aspects such as the trade-off in the performance in the servo and regulation operation modes and the control system robustness by constraining the maximum sensitivity peak. The different conflicting objectives are dealt with by using a multi-objective optimization algorithm to generate the trade-off optimal solutions. In this context, a simple tuning rule is determined by using the Nash solutions as a multi-criteria decision making technique. The Nash criteria is shown to provide convenient trade-off solutions for the controller tuning problem. Illustrative simulation examples show the effectiveness of the method.

[1]  Kaisa Miettinen,et al.  Nonlinear multiobjective optimization , 1998, International series in operations research and management science.

[2]  Vilfredo Pareto,et al.  Manuale di economia politica , 1965 .

[3]  Qingfu Zhang,et al.  Multiobjective evolutionary algorithms: A survey of the state of the art , 2011, Swarm Evol. Comput..

[4]  Tore Hägglund,et al.  Software-based optimal PID design with robustness and noise sensitivity constraints , 2015 .

[5]  K.J. ÅSTRÖM,et al.  Design of PI Controllers based on Non-Convex Optimization , 1998, Autom..

[6]  Ramon Vilanova,et al.  PID autotuning for weighted servo/regulation control operation , 2010 .

[7]  Carlos A. Coello Coello,et al.  Evolutionary multi-objective optimization: a historical view of the field , 2006, IEEE Comput. Intell. Mag..

[8]  Shiow-Fen Hwang,et al.  A Novel Intelligent Multiobjective Simulated Annealing Algorithm for Designing Robust PID Controllers , 2008, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[9]  Guoqiang Zeng,et al.  Design of fractional order PID controller for automatic regulator voltage system based on multi-objective extremal optimization , 2015, Neurocomputing.

[10]  Akira Okada,et al.  The Nash bargaining solution in general n-person cooperative games , 2010, J. Econ. Theory.

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

[12]  R. Toscano.  A simple robust PI/PID controller design via numerical optimization approach , 2004 .

[13]  R. Vilanova,et al.  PID controller tuning rules for robust step response of first-order-plus-dead-time models , 2006, 2006 American Control Conference.

[14]  John E. Dennis,et al.  Normal-Boundary Intersection: A New Method for Generating the Pareto Surface in Nonlinear Multicriteria Optimization Problems , 1998, SIAM J. Optim..

[15]  C. Kravaris,et al.  Nonlinear state feedback control of second-order nonminimum-phase nonlinear systems , 1990 .

[16]  Ramon Vilanova,et al.  On the model matching approach to PID design: Analytical perspective for robust Servo/Regulator tradeoff tuning , 2010 .

[17]  R. Vilanova,et al.  Optimality comparison of 2DoF PID implementations , 2014, 2014 18th International Conference on System Theory, Control and Computing (ICSTCC).

[18]  Julián Arévalo.  Gradual Nash bargaining with endogenous agenda: a path-dependent model , 2005 .

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

[20]  Carlos A. Coello Coello,et al.  Multi-objective Optimization Using Differential Evolution: A Survey of the State-of-the-Art , 2008 .

[21]  Riccardo Poli,et al.  Particle swarm optimization , 1995, Swarm Intelligence.

[22]  Gilberto Reynoso-Meza,et al.  Controller tuning using evolutionary multi-objective optimisation: Current trends and applications , 2014 .

[23]  J. V. Vusse.  Plug-flow type reactor versus tank reactor , 1964 .

[24]  David W. Coit,et al.  Multi-objective optimization using genetic algorithms: A tutorial , 2006, Reliab. Eng. Syst. Saf..

[25]  Ramon Vilanova,et al.  PID Control in the Third Millennium , 2012 .

[26]  R. Vilanova,et al.  Analysis of the claimed robustness for PI/PID robust tuning rules , 2010, 18th Mediterranean Conference on Control and Automation, MED'10.

[27]  Tore Hägglund,et al.  Design of PID controllers based on constrained optimization , 1999 .

[28]  Dervis Karaboga,et al.  A comprehensive survey: artificial bee colony (ABC) algorithm and applications , 2012, Artificial Intelligence Review.

[29]  R.H.C. Takahashi,et al.  H2/H∞ Robust PID Synthesis for Uncertain Systems , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[30]  Ponnuthurai N. Suganthan,et al.  Multi-objective robust PID controller tuning using two lbests multi-objective particle swarm optimization , 2011, Inf. Sci..

[31]  Xavier Blasco Ferragud,et al.  Multiobjective evolutionary algorithms for multivariable PI controller design , 2012, Expert Syst. Appl..

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

[33]  Min-Sen Chiu,et al.  Robust PID controller design via LMI approach , 2002 .

[34]  A. Messac,et al.  Generating Well-Distributed Sets of Pareto Points for Engineering Design Using Physical Programming , 2002 .

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

[36]  J. Nash.  THE BARGAINING PROBLEM , 1950, Classics in Game Theory.

[37]  Gilberto Reynoso-Meza,et al.  Algoritmos Evolutivos y su empleo en el ajuste de controladores del tipo PID: Estado Actual y Perspectivas , 2013 .

[38]  D. P. Atherton,et al.  Automatic tuning of optimum PID controllers , 1993 .

[39]  Antonio Visioli,et al.  Nash tuning for optimal balance of the servo/regulation operation in robust PID control , 2015, 2015 23rd Mediterranean Conference on Control and Automation (MED).

[40]  Rainer Storn,et al.  Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces , 1997, J. Glob. Optim..

[41]  P. N. Suganthan,et al.  Differential Evolution: A Survey of the State-of-the-Art , 2011, IEEE Transactions on Evolutionary Computation.

[42]  Thomas Stützle,et al.  Ant Colony Optimization: Overview and Recent Advances , 2018, Handbook of Metaheuristics.

[43]  Lalit M. Patnaik,et al.  Genetic algorithms: a survey , 1994, Computer.

[44]  A. Messac,et al.  The normalized normal constraint method for generating the Pareto frontier , 2003 .

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