The analysis of cross-coupling effects on the stability of two-dimensional, orthogonal, feedback control systems

The analysis of two-dimensional cross-coupled feedback control systems is studied because many such systems are in existence, and methods for their analysis and criteria for measuring their performance have had only limited attention in the technical literature [1]-[6]. Previous literature has generally been in the area of matrix analysis of multidimensional or multiloop systems, and has not treated the handling of poles and zeros in the complex - plane or cross-coupling, as they are treated in this paper. An algebraic model is developed for a generalized system, using the assumption that all components of the system, including the cross-coupling transfer function, may be represented by expressions in the complex frequency domain which have real-time domain equivalents describable by linear differential equations. The stability of the two-dimensional, cross-coupled, feedback control system is studied by complex-plane methods, and a method is developed for determining whether a system is stable or not. A technique is also indicated to show how an unstable system may be made stable by the introduction of appropriate cross-coupling.