The Popov criterion and the inverse Nyquist method†

Abstract

Kosonbrock's inverse Nyquist array (I.N.A.) theory for linear multivariable control Bystema with constant feedback elements is extended, to include systems lip to m nonlinear feedback elements, where the system has m inputs and m outputs. This extension is achieved by considering the Popov criterion for the most general case and through two further theorems. It shows that, as in the ease of Rosenbrock's I.N.A. theory, when certain auxiliary conditions are met with the help of suitable controllers, the design of multivariable controllers containing many non-linear feedbacks, can be based on the m frequency response loci corresponding to the diagonal entries of the open-loop inverse transfer function matrix. This leads to a simple design technique identical to the I.N.A. design method, suitable for use with a computer-aided design facility which permits a designer to use his intuitive understanding of transfer functions based on classical theory. The I.N.A. theory has been extended by Rosenbrock to cover sy...