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"Fractionalization" A new approach for comparing different approximation methods of fractional order systems and disturbances rejection in PID control

Dib Riad, Bensafia Yassine, Khettab Khatir

Przegląd Elektrotechniczny

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2023

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R. 99, nr 7

227-231

EN

Recently, many research works have focused on fractional order systems and their approximation methods. It has been shown to be a useful tool for enhancing plant dynamics in terms of time and frequency performance. In this paper we propose a new approach for comparing between the different approximations methods of fractional order systems and disturbance rejection in PID control of DC motor by fractionalizing an integer order derivative operator in the original integer system. The implementation of the fractionalized terms is realized by mean of the well established approximation methods and in order to determine the best method, the responses of original integer system are compared to those of fractionalized systems. Illustrative simulations examples show that the fractionalization approach give the best decision (selected method) ,a good tool for comparison between different approximation methods and it give the good rejection of disturbances in PID control of DC motor . This approach can also be generalized to others numerical approximation methods and it can also be used in the area of systems control.

PL

Ostatnio wiele prac badawczych koncentrowało się na systemach rzędu ułamkowego i metodach ich aproksymacji. Wykazano, że jest to przydatne narzędzie do zwiększania dynamiki instalacji pod względem wydajności czasowej i częstotliwościowej. W tym artykule proponujemy nowe podejście do porównywania różnych metod aproksymacji systemów ułamkowego rzędu i odrzucania zakłóceń w sterowaniu PID silnika prądu stałego poprzez frakcjonowanie operatora pochodnej rzędu całkowitego w oryginalnym układzie całkowitym. Implementacja wyrazów ułamkowych jest realizowana za pomocą dobrze znanych metod aproksymacyjnych iw celu wyznaczenia najlepszej metody porównuje się odpowiedzi oryginalnego układu całkowitoliczbowego z odpowiedziami układów ułamkowych. Ilustracyjne przykłady symulacyjne pokazują, że podejście frakcyjne daje najlepszą decyzję (wybrana metoda), jest dobrym narzędziem do porównywania różnych metod aproksymacyjnych i zapewnia dobre odrzucanie zakłóceń w regulacji PID silnika prądu stałego. Podejście to można również uogólnić na inne metody aproksymacji numerycznej, a także można je stosować w obszarze sterowania systemami.

2

Repetitive neurocontroller with disturbance feedforward path active in the pass-to-pass direction for a VSI inverter with an output LC filter

Ufnalski B., Grzesiak L. M.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2016

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Vol. 64, nr 1

115--125

EN

An enhancement to the previously developed repetitive neurocontroller (RNC) is discussed and investigated in the paper. Originally, the time-base generator (TBG) has been used to produce the only input signal for the neural approximator. The resulting search space makes the dynamic optimization problem (DOP) of shaping the control signal solvable with the help of a function approximator such as the feed-forward neural network (FFNN). The plant under consideration, i.e. a constant-amplitude constant-frequency voltage-source inverter (CACF VSI) with an output LC filter, is assumed to be equipped with the disturbance load current sensor to enable implementation of the disturbance feed-forward (pDFF) path as a part of the non-repetitive subsystem acting in the along the pass p-direction. An investigation has been undertaken to explore potential benefits of using this signal also as an additional input for the RNC to augment the approximation space and potentially enhance the convergence rate of the real-time search process. It is numerically demonstrated in the paper that the disturbance feed-forward path active in the pass-to-pass k-direction (kDFF) improves the dynamics of the repetitive part as well indeed.

3

Plug-in direct particle swarm repetitive controller with a reduced dimensionality of a fitness landscape – a multi-swarm approach

Ufnalski B., Grzesiak L. M.

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2015

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Vol. 63, nr 4

857--866

EN

The paper describes a modification to the recently developed plug-in direct particle swarm repetitive controller (PDPSRC) for the sine-wave constant-amplitude constant-frequency (CACF) voltage-source inverter (VSI). The original PDPSRC algorithm assumes that the particle swarm optimizer (PSO) takes into account a performance index defined over the whole reference signal period. Each particle stores all the samples of the control signal, e.g. α = 200 samples for a controller working at 10 kHz and the reference frequency equal to 50 Hz. Therefore, the fitness landscape (i.e. the performance index) is -dimensional ( D), which makes optimization challenging. That solution can be categorized as the single-swarm one. It has been previously shown that the swarm controller does not suffer from long-term stability issues encountered in the classic iterative learning controllers (ILC). However, the convergence of the swarm has to be kept at a relatively low rate to enable successful exploitation in the D search space, which in turn results in slow responsiveness of the PDPSRC. Here a multi-swarm approach is proposed in which we divide a dynamic optimization problem (DOP) among less dimensional swarms. The reference signal period is segmented into shorter intervals and the control signal is optimized in each interval independently by separate swarms. The effectiveness of the proposed approach is illustrated with the help of numerical experiments on the CACF VSI with an output LC filter operating under nonlinear loads.