Análise do controlador PID de ordem fracionária aplicado à simulação de sistemas reais

Abstract

Fractional order calculus presents a new modeling approach for systems with very interesting dynamic properties, introducing the notions of derivatives and integrals of noninteger order. In system theory, this gives rise to linear extensions, time-invariant systems, to enhance the description of complex phenomena involving memory or hereditary properties of systems. Standard industrial controllers, especially the PID controller can be upgraded to benefit from the effects of fractional integration and differentiation and have advantages over classic controllers in the case of conventional, full-order process control. In this paper, we study the concepts that guide this new type of controller, with studies on time and frequency domain stability, focusing mainly on the fractional order PID (FOPID) and making some specific implementations of FOPID in simulations to facilitate understanding and practical implementation. Results are verified using a MATLAB/Simulink based real-time prototyping platform.