Optimal Fractional Order PID Controller Design for Fractional Order Systems by Stochastic Multi Parameter Divergence Optimization Method with Different Random Distribution Functions

This paper modifies Stochastic Multi Parameter Divergence Optimization Method (SMDO) by using some types of random distribution functions in order to show effects of different random distribution functions on optimization performance. SMDO is a parameter wise random search algorithm in random walk class. A prominent feature of SMDO method lies in using random number with standard uniform distribution while diverging a parameter of solution point in backward and forward directions to reach an optimal solution. SMDO method benefits from the success of random backward and forward divergences. This study investigates effects of four types of random distribution functions on performance of SMDO algorithm for controller tuning problem. These distributions are Chi-Square Distribution (CSD), Rayleigh Distribution (RD), Log Normal Distribution (LND) and Uniform random (UD) distribution. To illustrate effects of these random distribution functions, SMDO is employed to fractional order PID (FOPID) controller tuning problems for fractional order model (FOM) and results obtained for different distribution functions are demonstrated.

[1]  Abdullah Ates,et al.  Online Tuning of Two Degrees of Freedom Fractional Order Control Loops , 2016 .

[2]  Muhammad Asghar,et al.  Performance comparison of wind turbine based doubly fed induction generator system using fault tolerant fractional and integer order controllers , 2018 .

[3]  Javad Mahmoudimehr,et al.  A novel multi-objective Dynamic Programming optimization method: Performance management of a solar thermal power plant as a case study , 2019, Energy.

[4]  YangQuan Chen,et al.  Optimal random search, fractional dynamics and fractional calculus , 2013, Fractional Calculus and Applied Analysis.

[5]  Aleksei Tepljakov,et al.  Fractional-Order PID Controller Design , 2017 .

[6]  Jing J. Liang,et al.  A survey on multi-objective evolutionary algorithms for the solution of the environmental/economic dispatch problems , 2018, Swarm Evol. Comput..

[7]  Celaleddin Yeroğlu,et al.  Modified Artificial Physics Optimization for Multi-parameter Functions , 2018 .

[8]  Abdullah Ates,et al.  A stochastic multi-parameters divergence method for online auto-tuning of fractional order PID controllers , 2014, J. Frankl. Inst..

[9]  YangQuan Chen,et al.  A new collection of real world applications of fractional calculus in science and engineering , 2018, Commun. Nonlinear Sci. Numer. Simul..

[10]  Yin-Fu Jin,et al.  Optimization techniques for identifying soil parameters in geotechnical engineering: Comparative study and enhancement , 2018 .

[12]  Liesbet Geris,et al.  Bayesian Multiobjective Optimisation With Mixed Analytical and Black-Box Functions: Application to Tissue Engineering , 2019, IEEE Transactions on Biomedical Engineering.

[13]  Celaleddin Yeroglu,et al.  Optimal fractional order PID design via Tabu Search based algorithm. , 2016, ISA transactions.

[14]  Abdullah Ates,et al.  Implementation of fractional order filters discretized by modified Fractional Order Darwinian Particle Swarm Optimization , 2017 .

[15]  P ? ? ? ? ? ? ? % ? ? ? ? , 1991 .

[16]  Varun Punnathanam,et al.  Optimization of Multi-objective Dynamic Optimization Problems with Front-Based Yin-Yang-Pair Optimization , 2018, Smart Innovations in Communication and Computational Sciences.

[17]  Abdullah Ates,et al.  Auto-tuning of PID controller according to fractional-order reference model approximation for DC rotor control , 2013 .

[18]  Soheyl Khalilpourazari,et al.  An efficient hybrid algorithm based on Water Cycle and Moth-Flame Optimization algorithms for solving numerical and constrained engineering optimization problems , 2017, Soft Computing.

[19]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[20]  Luca Maria Gambardella,et al.  A survey on metaheuristics for stochastic combinatorial optimization , 2009, Natural Computing.

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

[22]  YangQuan Chen,et al.  Disturbance Rejection FOPID Control of Rotor by Multi-Objective BB-BC Optimization Algorithm , 2017 .

[23]  Frederick Stern,et al.  Stochastic optimization methods for ship resistance and operational efficiency via CFD , 2018 .