Design of a fractional order PID controller for hydraulic turbine regulating system using chaotic non-dominated sorting genetic algorithm II

Fractional-order PID (FOPID) controller is a generalization of traditional PID controller using fractional calculus. Compared to the traditional PID controller, in FOPID controller, the order of derivative portion and integral portion is not integer, which provides more flexibility in achieving control objectives. Design stage of such an FOPID controller consists of determining five parameters, i.e. proportional, integral and derivative gains {Kp, Ki, Kd}, and extra integration and differentiation orders {λ,μ}, which has a large difference comparing with the conventional PID tuning rules, thus a suitable optimization algorithm is essential to the parameters tuning of FOPID controller. This paper focuses on the design of the FOPID controller using chaotic non-dominated sorting genetic algorithm II (NSGAII) for hydraulic turbine regulating system (HTRS). The parameters chosen of the FOPID controller is formulated as a multi-objective optimization problem, in which the objective functions are composed by the integral of the squared error (ISE) and integral of the time multiplied squared error (ITSE). The chaotic NSGAII algorithm, which is an incorporation of chaotic behaviors into NSGAII, is used as the optimizer to search true Pareto-front of the FOPID controller and designers can implement each of them based on objective functions priority. The designed chaotic NSGAII based FOPID controller procedure is applied to a HTRS system. A comparison study between the optimum integer order PID controller and optimum fractional order PID controller is presented in the paper. The simulation and some experimental results validate the superiority of the fractional order controllers over the integer controllers.

[1]  Xiaohui Yuan,et al.  Optimal self-scheduling of hydro producer in the electricity market , 2010 .

[2]  Long Chen,et al.  Application of an improved PSO algorithm to optimal tuning of PID gains for water turbine governor , 2011 .

[3]  Kalyanmoy Deb,et al.  A combined genetic adaptive search (GeneAS) for engineering design , 1996 .

[4]  Alberto Herreros,et al.  Design of PID-type controllers using multiobjective genetic algorithms. , 2002, ISA transactions.

[5]  Chuanwen Jiang,et al.  PID controller parameters optimization of hydro-turbine governing systems using deterministic-chaotic-mutation evolutionary programming (DCMEP) , 2006 .

[6]  Cristina I. Muresan,et al.  Development and implementation of an FPGA based fractional order controller for a DC motor , 2013 .

[7]  Mohamed Karim Bouafoura,et al.  PI λ D μ controller design for integer and fractional plants using piecewise orthogonal functions , 2010 .

[8]  Kalyanmoy Deb,et al.  Simulated Binary Crossover for Continuous Search Space , 1995, Complex Syst..

[9]  Ching-Hung Lee,et al.  Fractional-order PID controller optimization via improved electromagnetism-like algorithm , 2010, Expert Syst. Appl..

[10]  I. Podlubny.  Fractional-order systems and PIλDμ-controllers , 1999, IEEE Trans. Autom. Control..

[11]  Saptarshi Das,et al.  Frequency Domain Design of Fractional Order PID Controller for AVR System Using Chaotic Multi-objective Optimization , 2013, ArXiv.

[12]  Inés Tejado,et al.  Data-driven fractional PID control: application to DC motors in flexible joints , 2012 .

[13]  Ajith Abraham,et al.  Design of fractional-order PIlambdaDµ controllers with an improved differential evolution , 2009, Eng. Appl. Artif. Intell..

[14]  Xiaohui Yuan,et al.  Application of enhanced discrete differential evolution approach to unit commitment problem , 2009 .

[15]  Xiaohui Yuan,et al.  Improved Self-Adaptive Chaotic Genetic Algorithm for Hydrogeneration Scheduling , 2008 .

[16]  Hassen T. Dorrah,et al.  Design of aerospace control systems using fractional PID controller , 2012 .

[17]  Joao P. S. Catalao,et al.  Fractional-order control and simulation of wind energy systems with PMSG/full-power converter topology , 2010 .

[18]  T. Niknam,et al.  A modified teaching–learning based optimization for multi-objective optimal power flow problem , 2014 .

[19]  Cem Celal Tutum,et al.  A new PI tuning method for an industrial process: A case study from a micro-cogeneration system , 2013 .

[20]  Meng Xiuyun,et al.  Freestyle Fractional Order Controller Design with PSO for Weapon System , 2011 .

[21]  Ivo Petraÿs,et al.  FRACTIONAL - ORDER FEEDBACK CONTROL OF A DC MOTOR , 2009 .

[22]  İlyas Eker,et al.  Governors for hydro-turbine speed control in power generation: a SIMO robust design approach , 2004 .

[23]  Nand Kishor,et al.  Dynamic simulations of hydro turbine and its state estimation based LQ control , 2006 .

[24]  Di He,et al.  A chaotic map with infinite collapses , 2000, 2000 TENCON Proceedings. Intelligent Systems and Technologies for the New Millennium (Cat. No.00CH37119).

[25]  Shantanu Das,et al.  Fractional Order Fuzzy Control of Nuclear Reactor Power with Thermal-Hydraulic Effects in the Presence of Random Network Induced Delay and Sensor Noise having Long Range Dependence , 2013, ArXiv.

[26]  Luigi Fortuna,et al.  Does chaos work better than noise , 2002 .

[27]  G. Griva,et al.  Design of fractional order PID controller for boost converter based on Multi-Objective optimization , 2010, Proceedings of 14th International Power Electronics and Motion Control Conference EPE-PEMC 2010.

[28]  Amir H. Mohammadi,et al.  Optimal design of a solar driven heat engine based on thermal and thermo-economic criteria , 2013 .

[29]  Yanbin Yuan,et al.  Unit commitment problem using enhanced particle swarm optimization algorithm , 2011, Soft Comput..

[30]  Saptarshi Das,et al.  Chaotic multi-objective optimization based design of fractional order PIλDμ controller in AVR system , 2012, ArXiv.

[31]  D. Valerio,et al.  Rule-based fractional control of an irrigation canal , 2009, 2009 35th Annual Conference of IEEE Industrial Electronics.

[32]  F. Van De Meulebroeke,et al.  Hydro turbine model for system dynamic studies , 1994 .

[33]  Nasser Sadati,et al.  Design of a fractional order PID controller for an AVR using particle swarm optimization , 2009 .

[34]  Ali Jamali,et al.  Modelling and multi-objective optimization of a variable valve-timing spark-ignition engine using polynomial neural networks and evolutionary algorithms , 2007 .

[35]  Xiaohui Yuan,et al.  Hydrothermal scheduling using chaotic hybrid differential evolution , 2008 .

[36]  YangQuan Chen,et al.  Tuning and auto-tuning of fractional order controllers for industry applications , 2008 .

[37]  Igor Podlubny,et al.  Fractional-order systems and PI/sup /spl lambda//D/sup /spl mu//-controllers , 1999 .

[38]  Danqing Guo,et al.  Chaotic-NSGA-II: An effective algorithm to solve multi-objective optimization problems , 2010, 2010 International Conference on Intelligent Computing and Integrated Systems.

[39]  Antonio Visioli,et al.  Tuning rules for optimal PID and fractional-order PID controllers , 2011 .

[40]  Kalyanmoy Deb,et al.  A fast and elitist multiobjective genetic algorithm: NSGA-II , 2002, IEEE Trans. Evol. Comput..

[41]  Zhengyun Ren,et al.  Computation of stabilizing PI and PID controllers by using Kronecker summation method , 2009 .

[42]  Diyi Chen,et al.  Nonlinear dynamical analysis of hydro-turbine governing system with a surge tank , 2013 .

[43]  Xiaohui Yuan,et al.  Improved gravitational search algorithm for parameter identification of water turbine regulation system , 2014 .

[44]  Xiaohui Yuan,et al.  Multi-objective optimization of short-term hydrothermal scheduling using non-dominated sorting gravitational search algorithm with chaotic mutation , 2014 .