\fancyscript{H}_\infty Optimization-Based FOPID Design

In this chapter a fractional-orderFOPID controllers PID controller design based on the solution of a \(\fancyscript{H}_\infty \) model-matching problem for fractional first-order-plus-dead-time processes is proposed. Starting from the analytical solution of the problem, a fractional-order PID suboptimal controller is obtained. Guidelines for the tuning of the controller parameters are given in order to address the robust stability issue and to obtain the required performance.