Control quality enhancement by fractional order controllers

PID controllers belong to the dominating industrial controllers (Leššo, 1997) and therefore there is a continuous effort to improve their quality and robustness. One of the possibilities to improve PID controllers is to use fractional order controllers with non integer derivation and integration parts. The controlled objects are generally of fractional order, however for many of them, the fractionality is very low. Their integer order description can cause significant differences in the adequacy between the mathematical model and the real system (Dorčák, 1994; Sýkorová,1996). The main reasons for using integer order models were the absence of solution methods for fractional order equations. In the previous time important achievements were obtained (Oldham, 1974; Axtell and Bise, 1990; Podlubný, 1994; Dorčák, 1994) which enable to be taken into account the real order of dynamic systems. For fractional order systems (Outstaloup, 1995), fractional controller CRONE has been developed which is a modified PD controller. In this paper we present a synthesis of fractional PID controllers, analysis of their behaviour and simulation methods. We point out the non-adequate approximation of non-integer systems by integer order models and differences in their closed loop behaviour.