A normalizing precompensator for the design of effective and reliable commutative controllers

Sensitivity to parameter perturbation represents the main caution regarding the use of the characteristic locus method on the design of multivariable control systems. The method is not effective when the condition number of the plant eigenvector matrix is high or, equivalently, when the plant transfer matrix differs a great deal from normality. With the view to coping with this problem, it is proposed in this paper a precompensator structure and, in the sequel, two optimization problems are formulated and solved: the first one, for 2 x 2 systems, aims at minimizing the eigenvector matrix condition number; the second one, for the general m x m case, is intended to make the precompensated system as normal as possible by minimizing a defined measure of normality. Once the precompensated system matrix has been made close to a normal one, the characteristic locus method can then be applied effectively, leading to reliable control systems, as far as stability in face of uncertainty is concerned.