Design of PI and PID Controllers for Fractional Order Time Delay Systems

This paper deals with the computation of rational approximations of fractional derivatives and/or integrals. All rational approximations for fractional order of 0.1, 0.2,…, 0.9 are obtained using continued fraction expansion (CFE) method. Extension of the stability boundary locus approach to control systems with a fractional order transfer function is given for the computation of stabilizing PI and PID controllers using continuous approximations of fractional orders. Numerical examples are provided to illustrate the results and to show the effect of the order of approximation on the stability region.