Application of Grey Wolf Optimizer for Optimization of Fractional Order Controllers for a Non-monotonic Phase System

In this paper, an optimized fractional order proportional-integral (FOPI), proportional-derivative (FOPD) and proportional-integral-derivative (FOPID) controllers are proposed for controlling the non-monotonic phase DC-buck regulator system. The parameters of controllers are optimized using a new meta-heuristic technique known as Grey Wolf Optimizer (GWO). Integral time absolute error (ITAE) has been taken as the fitness function for optimizing the parameters of the controller. Output response shows that the FOPI controller provides faster closed-loop performance and enhances the robustness of the system. Moreover, the FOPI controller also preserves the monotonic phase behavior of the system within the desired bandwidth. The results have validated by comparing the time domain as well as frequency domain characteristics of the system with another technique in the literature.

[1]  YangQuan Chen,et al.  Fractional order PID control of a DC-motor with elastic shaft: a case study , 2006, 2006 American Control Conference.

[2]  R. Coppinger,et al.  Wolf-pack (Canis lupus) hunting strategies emerge from simple rules in computational simulations , 2011, Behavioural Processes.

[3]  S. K. Nagar,et al.  Optimization of Fractional Order PID Controller Using Grey Wolf Optimizer , 2017, Journal of Control, Automation and Electrical Systems.

[4]  I. Podlubny.  Fractional differential equations : an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications , 1999 .

[5]  Luis Henrique de Carvalho Ferreira,et al.  An Improved Analytical PID Controller Design for Non-Monotonic Phase LTI Systems , 2012, IEEE Transactions on Control Systems Technology.

[6]  José António Tenreiro Machado,et al.  Fractional-order hybrid control of robot manipulators , 1998, SMC'98 Conference Proceedings. 1998 IEEE International Conference on Systems, Man, and Cybernetics (Cat. No.98CH36218).

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

[8]  Andrew Lewis,et al.  Grey Wolf Optimizer , 2014, Adv. Eng. Softw..

[9]  Shyam Krishna Nagar,et al.  Reduction and controller design for fractional order Spherical tank system using GWO , 2016, 2016 International Conference on Emerging Trends in Electrical Electronics & Sustainable Energy Systems (ICETEESES).

[10]  H. Srivastava,et al.  Theory and Applications of Fractional Differential Equations , 2006 .

[11]  C. Halijak,et al.  Approximation of Fractional Capacitors (1/s)^(1/n) by a Regular Newton Process , 1964 .

[12]  Shyam Krishna Nagar,et al.  Controlling of an automatic voltage regulator using optimum integer and fractional order PID controller , 2015, 2015 IEEE Workshop on Computational Intelligence: Theories, Applications and Future Directions (WCI).

[13]  YangQuan Chen,et al.  Fractional-order Systems and Controls , 2010 .

[14]  Alain Oustaloup,et al.  Fractional order sinusoidal oscillators: Optimization and their use in highly linear FM modulation , 1981 .

[15]  Seyed Mohammad Mirjalili,et al.  Evolutionary population dynamics and grey wolf optimizer , 2015, Neural Computing and Applications.

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

[17]  Shyam Krishna Nagar,et al.  Optimal fractional order PID controller for magnetic levitation system , 2015, 2015 39th National Systems Conference (NSC).

[18]  Shyam Krishna Nagar,et al.  Fractional Order PI Controller Design for Non-Monotonic Phase Systems , 2016 .

[19]  M. H. Sulaiman,et al.  Grey Wolf Optimizer for solving economic dispatch problems , 2014, 2014 IEEE International Conference on Power and Energy (PECon).

[20]  Shantanu Das,et al.  Improved Model Reduction and Tuning of Fractional Order PIλDμ Controllers for Analytical Rule Extraction with Genetic Programming , 2012, ISA transactions.

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

[22]  Santosh Kumar Choudhary,et al.  Stability and Performance Analysis of Fractional Order Control Systems , 2014 .

[23]  Eduard Petlenkov,et al.  FOMCON: Fractional-order modeling and control toolbox for MATLAB , 2011, Proceedings of the 18th International Conference Mixed Design of Integrated Circuits and Systems - MIXDES 2011.

[24]  S. Das,et al.  Functional Fractional Calculus for System Identification and Controls , 2007 .

[25]  Alain Oustaloup,et al.  The CRONE toolbox for Matlab , 2000, CACSD. Conference Proceedings. IEEE International Symposium on Computer-Aided Control System Design (Cat. No.00TH8537).

[26]  Shyam Krishna Nagar,et al.  Approximation and order reduction of fractional order SISO system , 2016, 2016 IEEE Annual India Conference (INDICON).

[27]  Crina Grosan,et al.  Feature Subset Selection Approach by Gray-Wolf Optimization , 2014, AECIA.

[28]  Shyam Krishna Nagar,et al.  Optimized fractional order PID controller for non-minimum phase system with time delay , 2016, 2016 International Conference on Emerging Trends in Electrical Electronics & Sustainable Energy Systems (ICETEESES).