Mathematical modeling and control of pH processes are

Chapter 4, Problem 64

(choose chapter or problem)

Although the use of fractional calculus in control systems is not new, in the last decade there is increased interest in its use for several reasons. The most relevant are that fractional calculus differential equations may model certain systems with higher accuracy than integer differential equations, and that fractional calculus compensators might exhibit advantageous properties for control system design. An example of a transfer function obtained through fractional calculus is:

\(G(s)=\frac{1}{s^{2.5}+4 s^{1.7}+3 s^{0.5}+5}\)

This function can be approximated with an integer rational transfer function (integer powers of s) using Oustaloup’s method (Xue, 2005). We ask you now to do a little research and consult the aforementioned reference to find and run an M-file that will calculate the integer rational transfer function approximation to G(s) and plot its step response.