USING BOND GRAPHS TO SYNTHESIZE TREE-STRUCTURED TRANSFER-FUNCTIONS - IMPROVED FREQUENCY-DOMAIN ANALYSIS OF UNCERTAIN SYSTEMS

Various robust control applications require the value set of an uncert ain transfer function, G(s, q), which is the complex-plane legion {G(j omega, q): q is an element of Q}, where q is a vector of uncertain pa rameters. Although a value set can be synthesized by gridding the unce rtain parameters, this is only an option when a small number of the pa rameters are uncertain. When the transfer function can be decomposed i nto a tree structure with disjoint sets of uncertain parameters, the v alue set synthesis process is simplified. Bond graphs provide a means to synthesize tree-structured transfer functions, but the disjoint par ameter property has nor been guaranteed except for collocated input-ou tput variables. In this paper this property is extended to include a m uch broader class of systems, and the paper provides a means to determ ine by inspection if a given input-output variable pair will result in a transfer function with disjoint parameters. Furthermore, the tree s tructures generated here provide certain vertex-type results that simp lify value set synthesis. The ability to know a priori that a given in put-output variable pail will lead to a tree-structured transfer funct ion with disjoint parameters and the associated algorithms for synthes izing value sets expedite a normally problematic aspect of robust cont roller design. (C) 1998 Published by The Franklin Institute. Published by Elsevier Science Ltd.