High-gain error-actuated controllers for a class of linear multivariable plants

The class of controllable and observable linear multivariable plants which are amenable to high-gain error-actuated control has been characterised [1] in terms of the relatively prime polynomial matrix factors of the transfer function matrices G(??) of such plants, and it has also been demonstrated [2] that the ´tight´ non-interacting closed-loop tracking behaviour of systems incorporating such controllers is achieved because of the distinctive asymptotic properties of the associated closed-loop eigenstructure. In the light of these results, the transfer function matrices K(??) of high-performance high-gain error-actuated controllers for a practically important class of controllable and observable linear multivariable plants are expressed directly in terms of properties of the transfer function matrices G(??) of such plants. The usefulness of the resulting simple closed-form formula for K(??) is illustrated by designing an error-actuated controller for an open-loop unstable chemical reactor which results in superior closed-loop behaviour to that obtained by using controllers for the same plant designed by alternative techniques [5] [6] [7].