Introducing fractional operators in the adaptive control loop, and especially in Model Reference Adaptive Control (MRAC), has proven to be a good mean for improving the plant dynamics with respect to response time and disturbance rejection. The idea of introducing fractional operators in adaptation algorithms is very recent and needs to be more established, that is why many research teams are working on the subject. Previously, some authors have introduced a fractional model reference in the adaptation scheme, and then fractional integration has been used to deal directly with the control rule. Our original contribution in this paper is the use of a fractional derivative feedback of the plant output, showing that this scheme is equivalent to the fractional integration, one with a certain benefit action on the system dynamical behaviour and a good robustness effect. Numerical simulations are presented to show the effectiveness of the proposed fractional adaptive schemes.
In this study, we present an effective R-wave detection method in the QRS complex of the electrocardiogram (ECG) based on digital differentiation and integration of fractional order. The detection algorithm is performed in two steps. The pre-processing step is based on a fractional order digital band-pass filter whose fractional order is obtained by maximising the signal to noise ratio of the ECG signal, followed by a five points differentiator of fractional order 1.5 then the squaring transformation and the smoothing are used to generate peaks corresponding to the ECG parts with high slopes. The detection step is a new and simple strategy which is also based on fractional order operators for the localisation of the R waves. The MIT/ BIH arrhythmia database is used to test the effectiveness of the proposed method. The algorithm has provided very good performance and has achieved about 99.86% of the detection rate for the standard database. The results obtained are presented, discussed and compared to the most recent and efficient R-wave detection algorithms.
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