Graphical tuning method for non-linear fractional-order PID-type controllers free of analytical model

Abstract

The main focus of this paper is on a graphical tuning method of non-linear fractional-order PID (FOPID)-type controllers, i.e. a class of FOPID-type controllers that non-linearly depend on the control parameters, e.g. FO[PI], FO[PD] etc. Firstly, a method is proposed to determine the stabilizing region of non-linear FOPID-type controllers, namely the complete sets of FOPID-type controllers providing stability of the control system. Secondly, two different approaches are proposed to determine the H∞ region of these FOPID-type controllers, namely the complete sets achieving H∞ robust performance specifications. The first approach maps the H∞ constraints into the parameter space by solving a series of non-linear equations. The second approach transforms the original H∞ region problem into simultaneous stabilization of a family of characteristic polynomials. It turns out that these two approaches are both very flexible, and the second approach is more efficient than the former. The main advantage of our proposed graphical tuning method is that the exact mathematical model of the controlled plant is not needed. The stabilizing and H∞ regions can be computed only from the frequency response data of the plant. Finally, numerical and experimental results are presented to demonstrate the proposed graphical tuning method.