Frequency band implementation of non-integer order functions

The role of non-integer calculus in the fields of signal processing, control and automation is gradually gaining high importance due to its additional degree of freedom. In this paper we focus on frequency band approximations of non-integer order differentiators and integrators in s-domain. The implementation of non-integer order proportional plus integral plus derivative (PID) controller to control a plant model is presented. This is done by first approximating the non-integer order terms to a finite value using different approximation techniques and then decomposing the finite model to obtain the circuit elements. The frequency response analysis of the approximated model is presented and it is shown that the number of circuit elements depends on the approximation technique. The time domain analysis of the closed loop system is presented by plotting the step response. The simulations have been performed using MATLAB and OrCAD Capture CIS simulator.