Fractional order fuzzy PID optimal control in copper removal process of zinc hydrometallurgy

Abstract The copper removal process is the first stage of purification in zinc hydrometallurgy. Due to its dynamic characteristics and complex reaction mechanism, a robust and effective controller to maintain high quality and stability of the outlet-ion-concentration is in great need. In this paper, a fractional order fuzzy proportional integral derivative (FOFPID) controller based on fuzzy logic is proposed to meet this challenge. The proposed work is conducted through a combination of three novel interdependent efforts. First, controller design problem is transformed into a nonconvex optimization problem. Second, a novel method named state transition algorithm (STA) is employed to solve the aforementioned optimization problem. Furthermore, in order to evaluate the performance of the proposed control strategy, the response performance of the system is analyzed. Finally, further tests are carried out to evaluate the performance of FOFPID controller, where disturbances caused by the measurement, flow rate, and inlet-ion-concentration are all taken into account. The simulation results demonstrate the superiority of the FOFPID controller in copper removal process over the competing FOPID and manual control in the same application environment.

[1]  Weihua Gui,et al.  Control strategy for hydrometallurgical removal process based on modelling and evaluation , 2016 .

[2]  B. C. Nakra,et al.  A Review on Classical and Fuzzy PID Controllers , 2011 .

[3]  Kok Lay Teo,et al.  Optimal control for zinc solution purification based on interacting CSTR models , 2012 .

[4]  Koksal Erenturk,et al.  Fractional-Order $\hbox{PI}^{\lambda}\hbox{D}^{\mu}$ and Active Disturbance Rejection Control of Nonlinear Two-Mass Drive System , 2013, IEEE Transactions on Industrial Electronics.

[5]  L. Caccetta,et al.  An integrated predictive model with an on-line updating strategy for iron precipitation in zinc hydrometallurgy , 2015 .

[6]  J. C. Balarini,et al.  Importance of roasted sulphide concentrates characterization in the hydrometallurgical extraction of zinc , 2008 .

[7]  Yan Shi,et al.  Disturbance-Observer-Based Robust Synchronization Control for a Class of Fractional-Order Chaotic Systems , 2017, IEEE Transactions on Circuits and Systems II: Express Briefs.

[8]  Farshad Merrikh-Bayat,et al.  Discrete-time fractional-order PID controller: Definition, tuning, digital realization and some applications , 2014, International Journal of Control, Automation and Systems.

[9]  B. K. Sahu,et al.  Teaching-learning based optimization algorithm based fuzzy-PID controller for automatic generation control of multi-area power system , 2015, Appl. Soft Comput..

[10]  Xiaojun Zhou,et al.  Discrete state transition algorithm for unconstrained integer optimization problems , 2012, Neurocomputing.

[11]  Xiaojun Zhou,et al.  State Transition Algorithm , 2012, ArXiv.

[12]  Weihua Gui,et al.  Dynamic modeling and optimal control of goethite process based on the rate-controlling step , 2017 .

[13]  Feng Liu,et al.  FUZZY PID TRACKING CONTROLLER FOR TWO-AXIS AIRBORNE OPTOELECTRONIC STABILIZED PLATFORM , 2017 .

[14]  Xiaojie Su,et al.  Dissipativity-Based Filtering for Fuzzy Switched Systems With Stochastic Perturbation , 2016, IEEE Transactions on Automatic Control.

[15]  Richa Sharma,et al.  Design of two-layered fractional order fuzzy logic controllers applied to robotic manipulator with variable payload , 2016, Appl. Soft Comput..

[16]  W. Gui,et al.  A new multi-threshold image segmentation approach using state transition algorithm , 2017 .

[17]  Erkki Paatero,et al.  Copper removal by chelating adsorption in solution purification of hydrometallurgical zinc production , 2010 .

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

[19]  Weihua Gui,et al.  Kinetic Modeling and Parameter Estimation for Competing Reactions in Copper Removal Process from Zinc Sulfate Solution , 2013 .

[20]  Jun-yi Cao,et al.  Design of Fractional Order Controllers Based on Particle Swarm Optimization , 2006, 2006 1ST IEEE Conference on Industrial Electronics and Applications.

[21]  Jingqing Han,et al.  From PID to Active Disturbance Rejection Control , 2009, IEEE Trans. Ind. Electron..

[22]  Xiaojun Zhou,et al.  Fractional-order PID controller tuning using continuous state transition algorithm , 2018, Neural Computing and Applications.

[23]  Xiaojun Zhou,et al.  A Two-stage State Transition Algorithm for Constrained Engineering Optimization Problems , 2018 .

[24]  Saeed Balochian,et al.  Design of Optimal Fractional-Order PID Controllers Using Particle Swarm Optimization Algorithm for Automatic Voltage Regulator (AVR) System , 2013 .

[25]  B. Bose,et al.  Evaluation of membership functions for fuzzy logic controlled induction motor drive , 2002, IEEE 2002 28th Annual Conference of the Industrial Electronics Society. IECON 02.

[26]  Xiaojun Zhou,et al.  Dynamic optimization based on state transition algorithm for copper removal process , 2017, Neural Computing and Applications.

[27]  Vineet Kumar,et al.  Nonlinear adaptive fractional order fuzzy PID control of a 2-link planar rigid manipulator with payload , 2017, J. Frankl. Inst..

[28]  Qiang Gao,et al.  Multiobjective Optimization Design of a Fractional Order PID Controller for a Gun Control System , 2013, TheScientificWorldJournal.

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

[30]  Xiaojun Zhou,et al.  A dynamic state transition algorithm with application to sensor network localization , 2015, Neurocomputing.

[31]  O. Ibidapo-Obe,et al.  On Development of Fuzzy Controller: The Case of Gaussian and Triangular Membership Functions , 2011 .

[32]  Mehmet Önder Efe,et al.  Neural Network Assisted Computationally Simple PI$^\lambda$D$^\mu$ Control of a Quadrotor UAV , 2011, IEEE Transactions on Industrial Informatics.

[33]  Weihua Gui,et al.  State-transition-algorithm-based resolution for overlapping linear sweep voltammetric peaks with high signal ratio , 2016 .

[34]  Vineet Kumar,et al.  Performance analysis of fractional order fuzzy PID controllers applied to a robotic manipulator , 2014, Expert Syst. Appl..

[35]  B. Cosenza,et al.  Control of a distillation column by type-2 and type-1 fuzzy logic PID controllers , 2014 .

[36]  Xiaojun Zhou,et al.  Dynamic multi-objective optimization arising in iron precipitation of zinc hydrometallurgy , 2017 .

[37]  Chunhua Yang,et al.  Intelligent optimal setting control of a cobalt removal process , 2014 .

[38]  Ebrahim H. Mamdani,et al.  An Experiment in Linguistic Synthesis with a Fuzzy Logic Controller , 1999, Int. J. Hum. Comput. Stud..

[39]  Weihua Gui,et al.  Evaluation strategy for the control of the copper removal process based on oxidation–reduction potential , 2016 .

[40]  Peng Shi,et al.  Robust reliable H∞ control for fuzzy systems with random delays and linear fractional uncertainties , 2016, Fuzzy Sets Syst..

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

[42]  Shantanu Das,et al.  Performance Comparison of Optimal Fractional Order Hybrid Fuzzy PID Controllers for Handling Oscillatory Fractional Order Processes with Dead Time , 2013, ISA transactions.

[43]  Vineet Kumar,et al.  A fractional order fuzzy PID controller for binary distillation column control , 2015, Expert Syst. Appl..