Sketching rules for the multivariable root locus design technique

New results are summarized which extend the Evans (1950) root locus design technique to fully coupled, two-channel control law architectures. The new results are based upon various root migration plots, and the underlying framework concerning how the plots influence one another, for the closed-loop poles and zeros in each channel, as key system gains are varied. The new theory facilitates closure of all loops simultaneously, allowing efficient assessment of stability and performance in all channels. The closed-loop pole migration behavior is uniquely interesting in that poles "track moving zeros". A typical root migration features include direction reversal on real axis loci. Root locus sketching rules for this new framework are developed to assist the designer in implementing gain and compensation strategies by anticipating effects upon system stability and performance. The new theory is demonstrated with a lateral-directional flight control example.