A Characterisation of Interaction in Linear Multi-Variable Systems Using a Dyadic Expansion Method

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. However, under stated conditions, the representation given in this paper is exact. As the aim of the paper is to enable frequency response data to be interrupted physically, the method described does not generate a complete design technique. Examples indicate,however, that, if used with physical intuition, the procedure can provide guidelines to practical controller structures for highly interacting systems.