Status of noninteracting control

Abstract

The current status of decoupling theory for linear constant multivariable systems is described. The subject is treated in vector space terms and appropriate background concepts including invariant and controllability subspaces are discussed. Suggestions are given for translating vector space operations into matrix operations suitable for computation. The controllability subspace is used to formulate the restricted (static compensation) decoupling problem. Although the most general version of this problem is unsolved, there are known solutions for three special cases. A complete solution to the extended (dynamic compensation) decoupling problem is known. If a linear constant multivariable system can be decoupled at all, by any means whatever, then it can always be decoupled using linear dynamic compensation. The internal structure of a decoupled system is described in simple matrix terms. Using this representation, it is possible to characterize the system pole distributions which may be achieved while preserving a decoupled structure. A procedure is outlined for synthesizing a dynamic compensator of low order which will decouple a system. The procedure actually provides minimal order decoupling compensators for systems in which the number of open-loop inputs equal the number of outputs to be controlled.