Nonminimum Phase Solutions of a Singular Integral Equation in Control

A synthesis procedure of a closed loop transfer function for a nonminimum phase plant, due to given boundary constraints in a Nichols Chart, is proposed. This involves the transformation of the problem into a Hilbert Boundary Value Problem. A corresponding singular integral equation with a Cauchy kernel is introduced. The nonminimum-phase solutions of such an equation are then derived with aid of generalized Bode integrals. These are compared to previously derived minimum-phase solutions of the same equation.