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1 International Journal of Microelectronics and Computer Science

1 2014

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Fractional-order digital filter approximation method for embedded control applications

Tepljakov A., Petlenkov E., Belikov J.

International Journal of Microelectronics and Computer Science

2014

Vol. 5, nr 2

54--60

Fractional-order calculus presents a novel modeling approach for systems with extraordinary dynamical properties by introducing the notions of derivatives and integrals of noninteger order. In system theory this gives rise to extensions to linear, time invariant systems to enhance the description of complex phenomena involving memory or hereditary properties of systems. Standard industrial controllers, such as the PID controller and lead-lag compensator, have also been updated to beneﬁt from the effects of noninteger integration and differentiation, and have advantages over classical controllers in case of both conventional and fractional-order process control. However, given the deﬁnitions of fractional operators, accurate digital implementation of fractional-order systems and controllers is difﬁcult because it requires inﬁnite memory. In this work we study the speciﬁc implementation of a fractional-order PID controller and fractional-order lead-lag compensator based on an inﬁnite impulse response (IIR) ﬁlter structure obtained by applying the Oustaloup recursive ﬁlter synthesis technique. Software for generating digital fractional-order is developed and tested on an Atmel AVR microcontroller. The results are veriﬁed using a MATLAB/Simulink based real-time prototyping platform.