Dyadic expansion for the analysis of linear multivariable systems

In a practical situation, the control engineer may have experience with his system and have some insight into its dynamic behaviour. This paper suggests a theoretical method for making use of this background knowledge in the feedback-control design process by manipulating the frequency-response information available in the plant transfer-function matrix H(s) into a form suitable for physical interpretation. The approach used is that of dyadic expansion of H(s). The technique represents an extension of the dyadic-approximation method used in the analysis of nuclear-reactor spatial control systems to include a description of interactions in a general case in terms of the matrix H(s¿)H¿1(s). However, the representation given in this paper is exact. As the aim is to enable frequency-response data to be interpreted physically, the method described does not generate a complete design technique. An example indicates, however, that, if used with physical intuition, the procedure can provide guidelines to practical controller structures for highly interacting systems.