Fractional-order digital filter approximation method for embedded control applications

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.