Improved design of IIR-type digital fractional-order differentiators using continuous fraction expansion

Singh, Kunwar; Mehra, Rajesh; Pal, Gyan Prakash

doi:10.1109/raecs.2015.7453368

Cited by 2 publications

(1 citation statement)

References 11 publications

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“…Therefore, it is necessary to find a suitable method to fit the fractional calculus operator. The fitting methods usually used are as follows: power series expansion [7], continuous fraction expansion [8,9], Carlson method [10], Matsuda's method [11], Chareff's method [11], Oustaloup's approximation [12][13][14], etc. In this paper, the improved optimal rational approximation (ORA) is adopted.…”

Section: Numerical Realization Of Fractional Order Operatorsmentioning

confidence: 99%

Design and Application of Fractional Order PIλDµ Controller in Grid-Connected Inverter System

Pan

Wang

Hoang

et al. 2017

Volume 9: 13th ASME/IEEE International Conference on Mechatronic and Embedded Systems and Applications

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In comparison with the traditional controller PID, the fractional order controller PIλDμ is added with two parameters (μ and λ), that increases the flexibility of the controller. The larger adjustable space makes it more favorable to the control of the nonlinear system like the three-phase grid-connected inverter. However, since the fractional calculus operator is an irrational function on the complex plane, it can’t be implemented directly in simulation or in practical applications. In this paper, the advantages of the fractional order controller PIλDμ will be analyzed, then the fractional calculus operator is fitted by the frequency domain analysis method. Based on the vector method, the fractional order controller PIλDμ of the grid-connected inverter is designed. Simultaneously, the optimal controller parameters are searched with the ITAE and IAE as the performance index. And finally, the results are compared with those of the traditional controller PID. In consideration of the defects of fractional algorithm and single discretization method, a hybrid discretization method is proposed in order to ensure that the discretized controller can keep the same time-domain response and frequency characteristics as the designed controller. The experimental results show that the proposed method has the dynamic and static characteristics better than the traditional controller PID, which proves that the application of fractional order controller in three-phase grid-connected inverter is effective and feasible.

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